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Single-layer materials
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Single-layer materials
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In materials science, the term single-layer materials or 2D materials refers to crystalline solids consisting of a single layer of atoms. More broadly, these materials also include structures in which individual monolayers are held together by interlayer van der Waals interactions. These materials are promising for some applications but remain the focus of research. Single-layer materials derived from single elements generally carry the -ene suffix in their names, e.g. graphene. Single-layer materials that are compounds of two or more elements have -ane or -ide suffixes. 2D materials can generally be categorized as either 2D allotropes of various elements or as compounds (consisting of two or more covalently bonding elements).

It is predicted that there are hundreds of stable single-layer materials.[1][2] The atomic structure and calculated basic properties of these and many other potentially synthesisable single-layer materials, can be found in computational databases.[3] 2D materials can be produced using mainly two approaches: top-down exfoliation and bottom-up synthesis.[4] Exfoliation refers to the reduction of interlayer van der Waals interactions in bulk layered materials, leading to monolayer detach from the sample surface. The exfoliation methods include sonication, mechanical, hydrothermal, electrochemical, laser-assisted, and microwave-assisted exfoliation.[5]

Single element materials

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C: graphene and graphyne

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Graphene
Further information on Graphene: Potential applications of graphene
Graphene is an atomic-scale honeycomb lattice of carbon atoms.

Graphene is a crystalline allotrope of carbon in the form of a nearly transparent (to visible light) one atom thick sheet. It is hundreds of times stronger than most steels by weight.[6] It has the highest known thermal and electrical conductivity, displaying current densities 1,000,000 times that of copper.[7] It was first produced in 2004.[8]

Andre Geim and Konstantin Novoselov won the 2010 Nobel Prize in Physics "for groundbreaking experiments regarding the two-dimensional material graphene". They first produced it by lifting graphene flakes from bulk graphite with adhesive tape and then transferring them onto a silicon wafer.[9]

Graphyne

Graphyne is another 2-dimensional carbon allotrope whose structure is similar to graphene's. It can be seen as a lattice of benzene rings connected by acetylene bonds. Depending on the content of the acetylene groups, graphyne can be considered a mixed hybridization, spn, where 1 < n < 2,[10][11] compared to graphene (pure sp2) and diamond (pure sp3).

The existence of graphyne was conjectured before 1960.[12] In 2010, graphdiyne (graphyne with diacetylene groups) was synthesized on copper substrates.[13] In 2022 a team claimed to have successfully used alkyne metathesis to synthesise graphyne though this claim is disputed.[14][15] However, after an investigation the team's paper was retracted by the publication citing fabricated data.[16][17] Later during 2022 synthesis of multi-layered γ‑graphyne was successfully performed through the polymerization of 1,3,5-tribromo-2,4,6-triethynylbenzene under Sonogashira coupling conditions.[18][19] Recently, it has been claimed to be a competitor for graphene due to the potential of direction-dependent Dirac cones.[20][21]

B: borophene

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A B
36 cluster might be seen as smallest borophene; front and side view

Borophene is a crystalline atomic monolayer of boron and is also known as boron sheet. First predicted by theory in the mid-1990s in a freestanding state,[22] and then demonstrated as distinct monoatomic layers on substrates by Zhang et al.,[23] different borophene structures were experimentally confirmed in 2015.[24][25] First-principle calculations predict that a bilayer Kagome-phase borophene is an anisotropic superconductor with strong electron-phonon coupling and a critical temperature on the order of 17-35K.[26]

Ge: germanene

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Germanene is a two-dimensional allotrope of germanium with a buckled honeycomb structure.[27] Experimentally synthesized germanene exhibits a honeycomb structure.[28][29] This honeycomb structure consists of two hexagonal sub-lattices that are vertically displaced by 0.2 A from each other.[30] Experiments have demonstrated that germanene's quantum spin Hall edge states persist at room temperature and can be switched off by electrical field, indicating a robust and highly tunable topological phase.[31]

Si: silicene

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STM image of the first (4×4) and second layers (√3×√3-β) of silicene grown on a thin silver film. Image size 16×16 nm.

Silicene is a two-dimensional allotrope of silicon, with a hexagonal honeycomb structure similar to that of graphene.[32][33][34] Its growth is scaffolded by a pervasive Si/Ag(111) surface alloy beneath the two-dimensional layer.[35] By fabricating silicene between a 2D tin buffer layer, an encapsulated silicene sheet with stability under air is achieved.[36]

Sn: stanene

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Lattice image of stanene flake, with the middle inset showing a large-area electron micrograph of the sample. The right inset is an electron diffraction pattern confirming the hexagonal structure.

Stanene is a predicted topological insulator that may display dissipationless currents at its edges near room temperature. It is composed of tin atoms arranged in a single layer, in a manner similar to graphene.[37] Its buckled structure leads to high reactivity against common air pollutants such as NOx and COx and it is able to trap and dissociate them at low temperature.[38] A structure determination of stanene using low energy electron diffraction has shown ultra-flat stanene on a Cu(111) surface.[39]

Pb: plumbene

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Plumbene is a two-dimensional allotrope of lead, with a hexagonal honeycomb structure similar to that of graphene.[40] Because of its heavy atomic mass and strong spin-orbit coupling, plumbene is predicted to have a band gap ~0.2eV and to behave as a robust 2D topological insulator, potentially enabling the quantum spin Hall effect at room temperature.[41]

P: phosphorene

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Phosphorene structure: (a) tilted view, (b) side view, (c) top view. Red (blue) balls represent phosphorus atoms in the lower (upper) layer.

Phosphorene is a 2-dimensional, crystalline allotrope of phosphorus. Its mono-atomic hexagonal structure makes it conceptually similar to graphene. However, phosphorene has substantially different electronic properties; in particular it possesses a nonzero band gap while displaying high electron mobility.[42] This property potentially makes it a better semiconductor than graphene.[43] The synthesis of phosphorene mainly consists of micromechanical cleavage or liquid phase exfoliation methods. The former has a low yield while the latter produce free standing nanosheets in solvent and not on the solid support. The bottom-up approaches like chemical vapor deposition (CVD) are still blank because of its high reactivity. Therefore, in the current scenario, the most effective method for large area fabrication of thin films of phosphorene consists of wet assembly techniques like Langmuir-Blodgett involving the assembly followed by deposition of nanosheets on solid supports.[44]

Sb: antimonene

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Antimonene is a two-dimensional allotrope of antimony, with its atoms arranged in a buckled honeycomb lattice. Theoretical calculations[45] predicted that antimonene would be a stable semiconductor in ambient conditions with suitable performance for (opto)electronics. Antimonene was first isolated in 2016 by micromechanical exfoliation[46] and it was found to be very stable under ambient conditions. Its properties make it also a good candidate for biomedical and energy applications.[47]

Antimonene has shown great promise in both energy storage and electrochemical sensing applications. In supercapacitors, antimonene-based electrodes have achieved a high specific capacitance (~1578F g−1) along with an energy density of 20 Wh/kg and a power density of 4.8 kW/kg.[48] Furthermore, antimonene has been integrated into electroanalytical platforms to enhance detection of analytes.[49]

Bi: bismuthene

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Bismuthene is a two-dimensional topological insulator formed by a honeycomb lattice of bismuth atoms, first synthesized on silicon carbide in 2016.[50][51] Its large bandgap (~800mV), driven by strong spin-orbit coupling, supports room-temperature quantum spin Hall behavior, making it one of the most robust natural-state 2D topological insulators.[52][53] Top-down exfoliation of bismuthene has been reported in various instances[54][55] with recent works promoting the implementation of bismuthene in the field of electrochemical sensing.[56][57] Mechanical studies on bismuthene reveal this material combines high fracture strength, moderate stiffness and low thermal conductivity,[58] making it a strong candidate for thermoelectric and nanoelectronic devices.

Au: goldene

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On 16 April 2024, scientists from Linköping University in Sweden reported that they had produced goldene, a single layer of gold atoms 100 nm wide. Lars Hultman, a materials scientist on the team behind the new research, is quoted as saying "we submit that goldene is the first free-standing 2D metal, to the best of our knowledge", meaning that it is not attached to any other material, unlike plumbene and stanene. Researchers from New York University Abu Dhabi (NYUAD) previously reported to have synthesised Goldene in 2022, however various other scientists have contended that the NYUAD team failed to prove they made a single-layer sheet of gold, as opposed to a multi-layer sheet. Goldene is expected to be used primarily for its optical properties, with applications such as sensing or as a catalyst.[59]

Metals

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3D AFM topography image of multilayered palladium nanosheet.[60]

Single and double atom layers of platinum in a two-dimensional film geometry has been demonstrated.[61][62] These atomically thin platinum films are epitaxially grown on graphene,[61] which imposes a compressive strain that modifies the surface chemistry of the platinum, while also allowing charge transfer through the graphene.[62] Single atom layers of palladium with the thickness down to 2.6 Å,[60] and rhodium with the thickness of less than 4 Å[63] have been synthesized and characterized with atomic force microscopy and transmission electron microscopy.

A 2D titanium formed by additive manufacturing (laser powder bed fusion) achieved greater strength than any known material (50% greater than magnesium alloy WE54). The material was arranged in a tubular lattice with a thin band running inside, merging two complementary lattice structures. This reduced by half the stress at the weakest points in the structure.[64]

2D supracrystals

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The supracrystals of 2D materials have been proposed and theoretically simulated.[65][66] These monolayer crystals are built of supra atomic periodic structures where atoms in the nodes of the lattice are replaced by symmetric complexes. For example, in the hexagonal structure of graphene patterns of 4 or 6 carbon atoms would be arranged hexagonally instead of single atoms, as the repeating node in the unit cell.

2D alloys

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Two-dimensional alloys (or surface alloys) are a single atomic layer of alloy that is incommensurate with the underlying substrate. One example is the 2D ordered alloys of Pb with Sn and with Bi.[67][68] Surface alloys have been found to scaffold two-dimensional layers, as in the case of silicene.[35]

Compounds

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Crystal structure of bilayer hexagonal boron nitride. Each layer is bonded with van der Waals interaction.

Transition metal dichalcogenide monolayers

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Further information: Transition-metal dichalcogenide and Transition metal dichalcogenide monolayers

Monolayer MoS2, a prototypical transition metal dichalcogenide(TMD), consists of a single layer of molybdenum atoms sit between two layers of sulfur atoms in a hexagonal lattice. It is 0.65nm thick, yet with remarkable electronic properties. Unlike bulk MoS2, which has an indirect band gap of 1.2eV, the monolayer is a direct band gap semiconductor with a gap roughly 1.8eV.[72] The direct band gap leads to great enhancement on photoluminescence, which means it emits light more efficiently than the bulk material.[73]

Structures of the 1T and 2H phases of molybdenum disulfide (MoS2), as seen down the b axis. Two layers are shown for each phase to illustrate covalent bonding, which is only present within sheets.

Monolayer MoS2 also lacks inversion symmetry, which couples the electron's spin with the distinct valley states.[74] These unique structural and electronic features make it a board use for a wide range of applications.

MoS2 monolayer has been used to create field-effect transistors with high on/off current ratio.[75] The direct band gap of the monolayer leads to an efficient photodetectors with high sensitivity in the visible light range.[76][77] Furthermore, the atomic thickness and mechanically flexible make it a good material for flexible circuits or wearable sensors.

MoS2 plays an important role in catalysis. The edges of MoS2 monolayers act as active sites for chemical reaction.[78] For this reason, device engineering and fabrication may involve considerations for maximizing catalytic surface area, for example by using small nanoparticles rather than large sheets[78] or depositing the sheets vertically rather than horizontally.[79]

Graphane

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Further information: Graphane
Graphane

While graphene has a hexagonal honeycomb lattice structure with alternating double-bonds emerging from its sp2-bonded carbons, graphane, still maintaining the hexagonal structure, is the fully hydrogenated version of graphene with every sp3-hybrized carbon bonded to a hydrogen (chemical formula of (CH)n). Furthermore, while graphene is planar due to its double-bonded nature, graphane is rugged, with the hexagons adopting different out-of-plane structural conformers like the chair or boat, to allow for the ideal 109.5° angles which reduce ring strain, in a direct analogy to the conformers of cyclohexane.[80]

Graphane was first theorized in 2003,[81] was shown to be stable using first principles energy calculations in 2007,[82] and was first experimentally synthesized in 2009.[83] There are various experimental routes available for making graphane, including the top-down approaches of reduction of graphite in solution or hydrogenation of graphite using plasma/hydrogen gas as well as the bottom-up approach of chemical vapor deposition.[80] Graphane is an insulator, with a predicted band gap of 3.5 eV;[84] however, partially hydrogenated graphene is a semi-conductor, with the band gap being controlled by the degree of hydrogenation.[80]

Germanane

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Germanane is a single-layer crystal composed of germanium with one hydrogen bonded in the z-direction for each atom.[85][86] Germanane's structure is similar to graphane, Bulk germanium does not adopt this structure. Germanane is produced in a two-step route starting with calcium germanide. From this material, the calcium (Ca) is removed by de-intercalation with HCl to give a layered solid with the empirical formula GeH.[87] The Ca sites in Zintl-phase CaGe2 interchange with the hydrogen atoms in the HCl solution, producing GeH and CaCl2.

SLSiN

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SLSiN (acronym for Single-Layer Silicon Nitride), a novel 2D material introduced as the first post-graphene member of Si3N4, was first discovered computationally in 2020 via density-functional theory based simulations.[88] This new material is inherently 2D, insulator with a band-gap of about 4 eV, and stable both thermodynamically and in terms of lattice dynamics.

Hexagonal Boron Nitride

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Crystal structure of cubic boron nitride. The transformation occurs under extremely high pressure ~3000-8000MPa and temperature ~800-1900oC.[89]

Hexagonal boron nitride monolayer(h-BN) is two-dimensional material analogous to graphene, consisting of a planar honeycomb lattice of alternating boron and nitrogen atoms with nearly the same lattice constant with graphene.[90] Hexagonal boron nitride has strong sp2 covalent bonding within the layers and weak van der Waals coupling between layers leading to pronounced anisotropy. The monolayer hBN is an electrical insulator with wide band gap ~5.9-6.4eV.[91] Furthermore, a single layer hBN exhibits a direct band gap while the few layer and bulk one have an indirect gap and shows strong photoluminescence in UV regime due to tightly bound excitons.[92] It also exhibits excellent in-plane thermal conductivity and outsanding mechanical robustness, with a Young's modulus ~0.8TPa and fracture strength ~70GPa.[93]

Combined surface alloying

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Often single-layer materials, specifically elemental allotrops, are connected to the supporting substrate via surface alloys.[35][37] By now, this phenomenon has been proven via a combination of different measurement techniques for silicene,[35] for which the alloy is difficult to prove by a single technique, and hence has not been expected for a long time. Hence, such scaffolding surface alloys beneath two-dimensional materials can be also expected below other two-dimensional materials, significantly influencing the properties of the two-dimensional layer. During growth, the alloy acts as both, foundation and scaffold for the two-dimensional layer, for which it paves the way.[35]

Organic

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Ni3(HITP)2 is an organic, crystalline, structurally tunable electrical conductor with a high surface area. HITP is an organic chemical (2,3,6,7,10,11-hexaaminotriphenylene). It shares graphene's hexagonal honeycomb structure. Multiple layers naturally form perfectly aligned stacks, with identical 2-nm openings at the centers of the hexagons. Room temperature electrical conductivity is ~40 S cm−1, comparable to that of bulk graphite and among the highest for any conducting metal-organic frameworks (MOFs). The temperature dependence of its conductivity is linear at temperatures between 100 K and 500 K, suggesting an unusual charge transport mechanism that has not been previously observed in organic semiconductors.[94]

The material was claimed to be the first of a group formed by switching metals and/or organic compounds. The material can be isolated as a powder or a film with conductivity values of 2 and 40 S cm−1, respectively.[95]

Polymer

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Using melamine (carbon and nitrogen ring structure) as a monomer, researchers created 2DPA-1, a 2-dimensional polymer sheet held together by hydrogen bonds. The sheet forms spontaneously in solution, allowing thin films to be spin-coated. The polymer has a yield strength twice that of steel, and it resists six times more deformation force than bulletproof glass. It is impermeable to gases and liquids.[96][97]

Combinations

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Single layers of 2D materials can be combined into layered assemblies. For example, bilayer graphene is a material consisting of two layers of graphene. One of the first reports of bilayer graphene was in the seminal 2004 Science paper by Geim and colleagues, in which they described devices "which contained just one, two, or three atomic layers". Layered combinations of different 2D materials are generally called van der Waals heterostructures. Twistronics is the study of how the angle (the twist) between layers of two-dimensional materials can change their electrical properties.

Characterization

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Microscopy techniques such as transmission electron microscopy,[98][99][100] 3D electron diffraction,[101] scanning probe microscopy,[102] scanning tunneling microscope,[98] and atomic-force microscopy[98][100][102] are used to characterize the thickness and size of the 2D materials. Electrical properties and structural properties such as composition and defects are characterized by Raman spectroscopy,[98][100][102] X-ray diffraction,[98][100] and X-ray photoelectron spectroscopy.[103]

Mechanical characterization

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The mechanical characterization of 2D materials is difficult due to ambient reactivity and substrate constraints present in many 2D materials. To this end, many mechanical properties are calculated using molecular dynamics simulations or molecular mechanics simulations. Experimental mechanical characterization is possible in 2D materials which can survive the conditions of the experimental setup as well as can be deposited on suitable substrates or exist in a free-standing form. Many 2D materials also possess out-of-plane deformation which further convolute measurements.[104]

Nanoindentation testing is commonly used to experimentally measure elastic modulus, hardness, and fracture strength of 2D materials. From these directly measured values, models exist which allow the estimation of fracture toughness, work hardening exponent, residual stress, and yield strength. These experiments are run using dedicated nanoindentation equipment or an Atomic Force Microscope (AFM). Nanoindentation experiments are generally run with the 2D material as a linear strip clamped on both ends experiencing indentation by a wedge, or with the 2D material as a circular membrane clamped around the circumference experiencing indentation by a curbed tip in the center. The strip geometry is difficult to prepare but allows for easier analysis due to linear resulting stress fields. The circular drum-like geometry is more commonly used and can be easily prepared by exfoliating samples onto a patterned substrate. The stress applied to the film in the clamping process is referred to as the residual stress. In the case of very thin layers of 2D materials bending stress is generally ignored in indentation measurements, with bending stress becoming relevant in multilayer samples. Elastic modulus and residual stress values can be extracted by determining the linear and cubic portions of the experimental force-displacement curve. The fracture stress of the 2D sheet is extracted from the applied stress at failure of the sample. AFM tip size was found to have little effect on elastic property measurement, but the breaking force was found to have a strong tip size dependence due stress concentration at the apex of the tip.[105] Using these techniques the elastic modulus and yield strength of graphene were found to be 342 N/m and 55 N/m respectively.[105]

Poisson's ratio measurements in 2D materials is generally straightforward. To get a value, a 2D sheet is placed under stress and displacement responses are measured, or an MD calculation is run. The unique structures found in 2D materials have been found to result in auxetic behavior in phosphorene[106] and graphene[107] and a Poisson's ratio of zero in triangular lattice borophene.[108]  

Shear modulus measurements of graphene has been extracted by measuring a resonance frequency shift in a double paddle oscillator experiment as well as with MD simulations.[109][110]

Fracture toughness of 2D materials in Mode I (KIC) has been measured directly by stretching pre-cracked layers and monitoring crack propagation in real-time.[111] MD simulations as well as molecular mechanics simulations have also been used to calculate fracture toughness in Mode I. In anisotropic materials, such as phosphorene, crack propagation was found to happen preferentially along certain directions.[112] Most 2D materials were found to undergo brittle fracture.

Applications

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Main article: Potential applications of graphene

The major expectation held amongst researchers is that given their exceptional properties, 2D materials will replace conventional semiconductors to deliver a new generation of electronics.

Biological applications

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Research on 2D nanomaterials is still in its infancy, with the majority of research focusing on elucidating the unique material characteristics and few reports focusing on biomedical applications of 2D nanomaterials.[113] Nevertheless, recent rapid advances in 2D nanomaterials have raised important yet exciting questions about their interactions with biological moieties. 2D nanoparticles such as carbon-based 2D materials, silicate clays, transition metal dichalcogenides (TMDs), and transition metal oxides (TMOs) provide enhanced physical, chemical, and biological functionality owing to their uniform shapes, high surface-to-volume ratios, and surface charge.

Two-dimensional (2D) nanomaterials are ultrathin nanomaterials with a high degree of anisotropy and chemical functionality.[114] 2D nanomaterials are highly diverse in terms of their mechanical, chemical, and optical properties, as well as in size, shape, biocompatibility, and degradability.[115][116] These diverse properties make 2D nanomaterials suitable for a wide range of applications, including drug delivery, imaging, tissue engineering, biosensors, and gas sensors among others.[117][118] However, their low-dimension nanostructure gives them some common characteristics. For example, 2D nanomaterials are the thinnest materials known, which means that they also possess the highest specific surface areas of all known materials. This characteristic makes these materials invaluable for applications requiring high levels of surface interactions on a small scale. As a result, 2D nanomaterials are being explored for use in drug delivery systems, where they can adsorb large numbers of drug molecules and enable superior control over release kinetics.[119] Additionally, their exceptional surface area to volume ratios and typically high modulus values make them useful for improving the mechanical properties of biomedical nanocomposites and nanocomposite hydrogels, even at low concentrations. Their extreme thinness has been instrumental for breakthroughs in biosensing and gene sequencing. Moreover, the thinness of these molecules allows them to respond rapidly to external signals such as light, which has led to utility in optical therapies of all kinds, including imaging applications, photothermal therapy (PTT), and photodynamic therapy (PDT).

Despite the rapid pace of development in the field of 2D nanomaterials, these materials must be carefully evaluated for biocompatibility in order to be relevant for biomedical applications.[120] The newness of this class of materials means that even the relatively well-established 2D materials like graphene are poorly understood in terms of their physiological interactions with living tissues. Additionally, the complexities of variable particle size and shape, impurities from manufacturing, and protein and immune interactions have resulted in a patchwork of knowledge on the biocompatibility of these materials.

See also

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References

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Additional reading

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Single-layer materials

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Single-layer materials, also referred to as two-dimensional (2D) materials, are crystalline solids consisting of a single atomic layer or few layers of atoms, typically with thicknesses ranging from 1 to 10 angstroms, where electrons are confined in the plane but free to move within it, leading to quantum mechanical effects and distinctive physical properties. Many of these materials are derived from layered bulk counterparts through processes like mechanical or chemical exfoliation, while others are synthesized via bottom-up approaches such as epitaxial growth, enabling the isolation or creation of atomically thin sheets that retain strong in-plane covalent or while exhibiting weak van der Waals interactions between layers in their bulk form. The field gained prominence with the isolation of in 2004 by and using to exfoliate , a breakthrough that earned them the 2010 for groundbreaking experiments on this two-dimensional material. Subsequent discoveries expanded the family to include transition metal dichalcogenides (TMDs) such as (MoS₂), hexagonal boron nitride (hBN), phosphorene (a single layer of black phosphorus), and group-IV Xenes like and germanene, each offering tailored electronic, optical, and mechanical characteristics. These materials are synthesized via methods including (CVD), (MBE), and liquid-phase exfoliation, allowing scalable production for research and applications. Single-layer materials exhibit exceptional properties, such as graphene's ultrahigh exceeding 200,000 cm²/V·s at and tensile strength of about 130 GPa, alongside TMDs' tunable direct bandgaps (e.g., 1.8 eV for monolayer MoS₂) that enable semiconducting behavior absent in their bulk forms. Their large surface-to-volume ratio and flexibility make them promising for applications in (e.g., high-speed transistors and flexible displays), energy storage (e.g., batteries and supercapacitors), (e.g., photodetectors and LEDs), and (e.g., ). Ongoing research focuses on heterostructures—stacked layers of different 2D materials—to engineer novel functionalities, such as in for , highlighting their potential to revolutionize .

Introduction

Definition and characteristics

Single-layer materials, also referred to as two-dimensional (2D) materials, are crystalline solids composed of a single atomic layer, typically ranging from 0.3 to 1 nm in thickness, with atoms connected by strong covalent or ionic bonds within the plane and weakly interacting via van der Waals forces perpendicular to the plane. This atomic-scale structure distinguishes them from their bulk counterparts, where multiple layers are stacked, leading to emergent properties unique to the form. The prototypical example is , isolated in , which exemplifies the foundational structure of these materials. A defining characteristic of single-layer materials is their exceptionally high surface-to-volume ratio, which amplifies surface-related phenomena such as adsorption and compared to three-dimensional solids. Quantum confinement effects arise due to the restricted thickness, resulting in tunable electronic bandgaps that can transition from indirect in bulk forms to direct in monolayers, enabling applications in . These materials also display anisotropic properties, with mechanical stiffness often being orders of magnitude higher in-plane than out-of-plane, reflecting the directional nature of their bonding. Single-layer materials are broadly classified into elemental types, such as and black phosphorus, frequently named with the suffix "-ene" to denote their single-layer composition, and compound types, including dichalcogenides like MoS₂, often termed with suffixes such as "-ide" or "-ane." Stability in these structures is intrinsically linked to lattice symmetry, which minimizes energy in hexagonal arrangements, while non-hexagonal lattices achieve dynamic stability through buckling that optimizes orbital interactions. This buckling, observed in materials like , prevents collapse into three-dimensional forms under ambient conditions.

Historical development

The study of single-layer materials, also known as two-dimensional (2D) materials, began with early theoretical explorations of their electronic properties. In 1947, Philip R. Wallace developed the first band theory model for using the tight-binding approximation, which laid the groundwork for understanding the electronic structure of what would later be recognized as , predicting its semimetallic behavior with Dirac cones at the . Although the isolation of a single atomic layer remained elusive for decades, this work highlighted the potential of atomically thin carbon sheets as distinct from bulk . The field advanced dramatically in 2004 when and at the successfully isolated single-layer through mechanical exfoliation using , demonstrating its exceptional electronic properties such as high carrier mobility. This breakthrough, which sparked widespread interest in 2D materials beyond , earned them the in 2010 for their pioneering experiments on the two-dimensional material. Graphene's isolation ignited a surge in research, prompting explorations of analogous single-layer structures in other elements and compounds. Theoretical predictions soon expanded the scope to non-carbon materials. , a analog of , was first proposed in 1994 as a buckled lattice with potential for tunable band gaps, though stability analyses in the mid-2000s further refined its electronic properties using . Experimental progress followed with the isolation of phosphorene from black phosphorus via mechanical exfoliation in 2014, revealing its direct bandgap and high anisotropy. , a boron-based 2D sheet, was synthesized on silver substrates in 2015 through , showcasing polymorphic structures with metallic conductivity. More recently, goldene—a freestanding single-atom-thick layer—was created in 2024 by etching a MAX phase precursor, achieving lattice contraction and enhanced reactivity compared to bulk . In 2022, multilayer γ-graphyne, a carbon allotrope with acetylenic linkages, was synthesized via cross-coupling , confirming its predicted semiconducting nature. By , the field had evolved to include complex compositions, with advances in high-entropy 2D alloys such as amorphous-crystalline denary systems fabricated as ultrathin films, enabling tunable electrocatalytic performance through multi-element mixing. Concurrently, progress in amorphous single-layer materials pushed toward the limit, with solution-based syntheses yielding stable 2D networks for . Theoretical efforts, exemplified by the Computational 2D Materials Database (C2DB), have screened over 10,000 candidate structures using high-throughput , identifying thousands of stable 2D materials across diverse chemistries and predicting their thermodynamic viability. These milestones underscore the rapid maturation of single-layer materials research from isolated predictions to a vast, computationally guided landscape.

Synthesis methods

Top-down approaches

Top-down approaches to synthesizing single-layer materials involve deriving atomically thin sheets from bulk through physical or chemical exfoliation processes, which dismantle layered structures to isolate individual layers. These methods leverage the weak van der Waals interactions between layers in bulk materials like or dichalcogenides (TMDCs), offering a route to high-quality monolayers without the need for epitaxial growth. However, they often face challenges in achieving uniform layer control and large-scale production due to the reliance on mechanical shear or selective dissolution. Mechanical exfoliation, pioneered by the "Scotch-tape" method, remains a cornerstone for producing pristine single-layer flakes from bulk crystals. In this technique, adhesive tape is repeatedly applied to (HOPG) to cleave and transfer progressively thinner layers until monolayers are obtained, as first demonstrated for in 2004. The method yields exceptionally high-quality, defect-free sheets with electron mobilities exceeding 15,000 cm²/V·s, making it ideal for fundamental . It has been extended to TMDCs like MoS₂, where similar tape-based peeling from bulk crystals produces monolayers suitable for optoelectronic devices, though the process is labor-intensive and limited to small flake sizes typically below 100 µm. Yields are inherently low, often less than 1% of the starting material, restricting scalability. Liquid-phase exfoliation addresses some scalability issues by dispersing bulk materials in solvents and applying ultrasonic energy to shear layers apart. of layered precursors like black phosphorus or MoS₂ in suitable solvents, such as N-methyl-2-pyrrolidone (NMP), generates stable suspensions of single- and few-layer nanosheets through solvophobic interactions that match the material's surface energy. For phosphorene, derived from black phosphorus, this method produces flakes with thicknesses around 1 nm after centrifugation-based size selection, enabling yields up to 10 mg/mL in optimized conditions. In MoS₂ exfoliation, like sodium cholate enhance dispersion stability and increase fractions to over 50% by preventing restacking, as shown in systematic solvent screening studies. While this approach scales to gram quantities per batch, it introduces minor defects from sonication-induced , slightly reducing electronic performance compared to mechanical methods. Electrochemical exfoliation provides a controlled alternative for graphite-to-graphene conversion by applying voltage to drive ionic intercalation and . In a typical setup, electrodes are immersed in an like , where an anodic potential of 5–10 V promotes anion insertion between layers, followed by gas evolution that expands and exfoliates the structure into sheets. This process achieves yields up to 50 wt% few-layer with lateral sizes of 1–5 µm, benefiting from the tunability of voltage to minimize oxidation. Intercalation mechanisms, involving ions, ensure selective layer separation without harsh chemicals, though electrolyte choice affects sheet purity. For , selective etching transforms MAX phase precursors into single-layer carbides or nitrides by targeted removal of atomic layers. The seminal HF-based etching of Ti₃AlC₂ selectively dissolves the aluminum layers, yielding accordion-like multilayered Ti₃C₂Tₓ (where Tₓ denotes surface terminations like -OH, -F), which can be further delaminated into single sheets via intercalation or . This top-down route preserves the metallic conductivity of MXenes, with Ti₃C₂Tₓ sheets exhibiting up to 10,000 S/cm, suitable for applications. conditions, such as 50% HF for 24 hours at , control the degree of , though safer alternatives like HCl/HF mixtures have been developed to reduce toxicity. Overall, top-down approaches excel in delivering high-purity single-layer materials with minimal structural defects, outperforming bottom-up methods in quality for proof-of-concept devices. However, their poor —often limited to milligrams—poses challenges for industrial applications, compounded by variability in flake size and yield. Recent advancements, such as wet-jet milling, have improved this by using high-pressure fluid jets to exfoliate into dispersions at a rate of 3.2 g/hr with 15 wt% loading in , yielding few-layer sheets with mean thickness of 4.2 nm while maintaining reasonable quality.

Bottom-up approaches

Bottom-up approaches to synthesizing single-layer materials involve constructing atomic layers from precursor molecules or atoms, enabling precise control over , composition, and defects for scalable production. These methods contrast with top-down techniques by focusing on directed assembly rather than isolation from bulk precursors, often achieving uniform over large areas through epitaxial or processes. (CVD) is a cornerstone bottom-up technique, particularly for , where hydrocarbon precursors decompose on substrates at temperatures around 1000°C to form continuous single-layer films. The process relies on copper's low carbon solubility to promote surface-mediated growth, yielding centimeter-scale domains with minimal multilayer formation when precursor ratios (e.g., CH₄:H₂ ≈ 1:1000) are optimized. For dichalcogenides (TMDCs) like MoS₂, metal-organic CVD (MOCVD) variants use organometallic precursors such as Mo(CO)₆ and H₂S at 500–700°C, enabling wafer-scale monolayer growth on or SiO₂ with controlled sulfurization to minimize defects. Molecular beam epitaxy (MBE) facilitates epitaxial growth of elemental single-layers like germanene, where germanium atoms are deposited onto Ag(111) substrates under at 150–200°C, achieving lattice matching via a (√3×√3)R30° reconstruction. This method ensures atomic precision, with growth rates of 0.1–1 per minute, producing buckled structures stable up to 200°C due to substrate interactions. Wet-chemical synthesis offers solution-based routes for compound layers, such as hexagonal boron nitride (h-BN), where and precursors react in molten salts at 800–900°C to form few-layer sheets via and exfoliation . For MXene analogues, bottom-up liquid-phase methods assemble Nb₂CSe₂ layers from Nb, , Se, and precursors at 800°C under inert conditions, yielding terminated structures with high conductivity (up to 10⁴ S/cm) without steps. Precursor ratios (e.g., Nb:C:Se = 2:1:2) and temperature control are critical to prevent phase segregation and ensure single-layer thickness. Recent advances include automated CVD systems for wafer-scale TMDCs, such as multitube atmospheric-pressure setups that achieve uniform MoS₂ monolayers over 4-inch wafers at 650°C with real-time monitoring of gas flows, reducing variability by 50% compared to manual processes. Liquid-phase synthesis has also enabled high-entropy 2D alloys, like (MoVNbTaW)S₂, through one-pot reactions of metal precursors, forming 0.92 nm-thick crystals with entropy-stabilized homogeneity.

Elemental single-layer materials

Carbon-based materials

Carbon-based single-layer materials represent a class of two-dimensional (2D) allotropes derived from carbon atoms arranged in planar lattices, often featuring motifs that enable unique electronic behaviors. These structures arise from variations in carbon hybridization—primarily sp² and sp—leading to diverse properties such as high mechanical strength and tunable conductivity. Unlike bulk carbon forms like or , single-layer variants isolate atomic-thin sheets, isolating their intrinsic characteristics for applications in and . Graphene, the archetypal single-layer carbon material, consists of a formed by sp²-hybridized carbon atoms, each bonded to three neighbors in a planar arrangement. This structure results in a zero-bandgap semimetallic nature, where charge carriers behave as massless Dirac fermions, exhibiting linear dispersion near the Dirac points and ultrahigh mobilities exceeding 200,000 cm²/V·s at . Graphene was first isolated in via mechanical exfoliation of using , enabling the study of its pristine properties. For scalable production, (CVD) on substrates has become a standard method, yielding large-area films with controlled layer thickness. Graphyne extends the motif by incorporating acetylenic linkages (–C≡C–) between sp²-hybridized carbon rings, forming extended networks with increased and reduced compared to graphene. These linkages introduce tunable Dirac cones in the , allowing band gaps to be modulated from near-zero to several volts through structural variations like α-, β-, or γ-graphyne isomers. Although predicted since 1987, practical synthesis remained elusive until 2022, when triangular γ-graphyne fragments were realized via dynamic covalent metathesis of hexaalkynylbenzene monomers, confirming their thermal stability up to 400°C. Graphane, a fully hydrogenated of , features an sp³-hybridized carbon lattice where each carbon atom is covalently bonded to a , distorting the planar sheet into a puckered configuration while maintaining overall two-dimensionality. This modification opens a wide indirect bandgap of approximately 3.5 eV, transforming 's metallic behavior into insulating properties suitable for applications. Predicted theoretically in 2007, partial providing evidence for graphane-like properties was demonstrated in 2009 through hydrogen adsorption on supported by (111), with coverage up to 8% demonstrating bandgap opening proportional to density. Fully hydrogenated remains experimentally challenging and has not been realized as a stable freestanding . Among predicted single-layer carbon variants, planar structures like and exhibit greater stability than linear forms such as carbyne, which consists of infinite sp-hybridized carbon chains but suffers from high reactivity and without encapsulation. Finite carbyne chains have been synthesized within carbon nanotubes for stabilization, yet extended planar allotropes remain the focus due to their thermodynamic favorability and ease of integration into devices. Ongoing efforts explore hybrid variants, emphasizing those with robust lattice energies exceeding 7 eV per atom for practical viability.

Group 13-15 elemental materials

Single-layer materials from group 13 and 15 elements represent a class of two-dimensional (2D) structures distinct from carbon-based analogs, featuring puckered or buckled geometries that arise from the elements' valence electron configurations and bonding preferences. These materials, including borophene from group 13 and phosphorene, antimonene, and bismuthene from group 15, exhibit unique electronic properties such as metallic behavior or tunable bandgaps, enabling potential applications in electronics and sensing similar to those of transition metal dichalcogenides. Unlike graphene's planar honeycomb lattice, these structures accommodate electron deficiencies through polymorphic arrangements, leading to anisotropic and often metastable phases. Borophene, the single-layer form of , was first synthesized in 2015 via on an Ag(111) substrate, where boron atoms self-assemble into striped domains due to the with the silver surface. This synthesis revealed polymorphic phases, including the β12 phase characterized by a rectangular lattice with embedded hexagonal voids and the χ3 phase featuring a triangular lattice with periodic vacancies, both stabilized by the substrate's influence. These phases demonstrate metallic conductivity, with the β12 structure hosting anisotropic Dirac-like fermions and high exceeding 10^3 cm²/V·s at , attributed to boron's light and delocalized states. Theoretical and experimental studies confirm borophene's polymorphism stems from boron's ability to form diverse bonding motifs, ranging from three-center two-electron bonds to sp²-hybridized networks, distinguishing it from more rigid 2D materials. Phosphorene, derived from the group 15 element , adopts a puckered orthorhombic resembling the armchair and zigzag motifs of bulk black phosphorus, with phosphorus atoms forming covalent bonds in a layered configuration that imparts high in-plane . This geometry results in a direct bandgap of approximately 1.5-2 eV, tunable by strain or layer thickness, making it suitable for optoelectronic devices where zero-bandgap falls short. However, phosphorene exhibits significant air instability, rapidly degrading through oxidation upon exposure to oxygen and moisture, which limits its practical handling to inert environments or protective encapsulations. Exfoliation from bulk black phosphorus yields few-layer flakes, but achieving isolated monolayers requires advanced techniques to mitigate degradation. Antimonene and , single-layer forms of and respectively, typically crystallize in buckled honeycomb lattices, where the larger atomic sizes compared to lead to increased buckling heights of about 1-2 , enhancing spin-orbit coupling effects. Antimonene's β-phase, synthesized via van der Waals on substrates like PdTe₂ or on Ag(111), displays a buckled hexagonal arrangement with indirect bandgap characteristics around 1-2 eV, though it can transition to semimetallic behavior under strain. , grown epitaxially on SiC(0001), exhibits pronounced properties, including a quantum spin Hall state with a large bulk bandgap of ~0.5 eV, driven by strong relativistic effects from bismuth's heavy nucleus, positioning it as a for room-temperature spintronic applications. These buckled structures maintain stability through substrate interactions, contrasting with phosphorene's reactivity. Synthesis of these group 13-15 single-layer materials predominantly relies on epitaxial growth methods, such as , to achieve stability on metallic or semiconducting substrates, as freestanding forms are prone to reconstruction or clustering due to high surface energies. For borophene, recent variants include amorphous-like sheets observed in boron-rich environments, such as within MgB₂ interlayers, which display dynamical disorder but retain metallic traits, with advancements in 2024-2025 focusing on scalable production via analogs. Phosphorene, antimonene, and bismuthene face challenges from environmental degradation and phase instability, necessitating low-temperature growth and passivation strategies to preserve their puckered or buckled morphologies. These approaches have enabled larger domain sizes and improved transferability, though scalability remains a key hurdle for device integration.

Group 14 and metallic materials

Single-layer materials from group 14 elements, such as , tin, and lead, form buckled honeycomb lattices analogous to but with distinct structural distortions due to their larger atomic sizes and weaker pi-bonding. These materials, known as silicene, germanene, stanene, and plumbene, exhibit predicted topological properties arising from strong spin-orbit coupling (SOC), enabling potential applications in quantum spin Hall (QSH) insulators. Silicene consists of silicon atoms in a low-buckled with a buckling height of approximately 0.44 , which introduces a sublattice that opens a tunable bandgap under external fields. This buckling preserves much of graphene's electronic features near the Dirac points while enhancing SOC effects, leading to a predicted in hydrogenated forms. Experimental realization of has been achieved via epitaxial growth on silver substrates, where it maintains a lattice despite interface interactions. Germanene, the germanium analog, features a more pronounced buckling of about 0.67 due to the larger , resulting in a substantial SOC-induced bandgap of around 24 meV that supports the QSH effect at elevated temperatures. calculations predict a topological in germanene under perpendicular electric fields, shifting from a QSH insulator to a trivial insulator. Epitaxial germanene has been synthesized on and surfaces, confirming its buckled structure via scanning tunneling . Stanene, composed of tin atoms, displays an even greater buckling height of roughly 0.85 Å, with an exceptionally large SOC gap exceeding 100 meV, enabling nearly 100% spin polarization and room-temperature QSH states. This strong SOC stems from tin's heavy atomic mass, making stanene a promising candidate for topological without cryogenic cooling. Stanene has been epitaxially grown on bismuth telluride substrates, where strain further enhances its topological phase. Plumbene, the lead-based counterpart, adopts a highly buckled lattice with a height difference up to 2.5 , exhibiting robust topological insulation due to lead's dominant SOC. Theoretical studies highlight plumbene's potential for large-bandgap QSH phases, with stability improved through or substrate interactions. Recent experimental efforts have realized plumbene overlayers on magnesium surfaces, revealing transitions between buckled and planar configurations under adsorption. Metallic single-layers, distinct from the semiconducting group 14 analogs, include freestanding or substrate-supported monolayers of noble metals like , , and . Goldene, synthesized in 2024 via selective etching of a titanium-gold precursor, forms a triangular lattice with a 9% contraction relative to bulk , exhibiting metallic conductivity and enhanced reactivity. Platinum and single-atom layers demonstrate superior catalytic activity for evolution and oxidation reactions compared to bulk counterparts, attributed to their high surface-to-volume ratio and exposed active sites. monolayers on supports show exceptional performance in CO oxidation, with activity enhanced by lattice strain effects. These group 14 and metallic single-layers face significant stability challenges, as they are highly reactive toward ambient oxygen and , leading to rapid oxidation without protection. To mitigate this, synthesis typically involves inert substrates like Ag(111) for epitaxial growth or Al₂O₃ encapsulation to preserve the atomic structure in air. Additionally, 2D supracrystals of multimetal spinels, incorporating up to nine metals in mesoporous lattices, have been developed for extreme-condition , offering tunable electronic properties through compositional variation.

Compound single-layer materials

Transition metal dichalcogenides

dichalcogenides (TMDCs) are a prominent class of compound single-layer materials with the general MX₂, where M represents a such as molybdenum (Mo) or tungsten (W), and X denotes a atom like (S), (Se), or (Te). These adopt a structure, consisting of a central layer of metal atoms sandwiched between two layers of chalcogen atoms, forming a trigonal prismatic coordination in the stable phase. In their single-layer form, TMDCs exhibit a direct bandgap typically ranging from 1 to 2 eV, enabling strong light-matter interactions, in contrast to the indirect bandgap observed in their bulk counterparts, such as ~1.2 eV for bulk MoS₂ versus ~1.8 eV direct in the . This transition arises from quantum confinement effects that lift the degeneracy of conduction band minima, making TMDCs particularly suitable for optoelectronic applications. TMDCs display polymorphism, with distinct phases exhibiting varied electronic properties. The thermodynamically stable 2H phase features a semiconducting character due to its trigonal prismatic arrangement, while the metastable 1T phase adopts an octahedral coordination, resulting in metallic behavior. Phase transitions between 2H and 1T can be induced by chemical intercalation or strain, influencing and catalytic activity. In MoS₂ monolayers, the broken inversion symmetry in the 2H phase enables , where the two inequivalent valleys at the K and K' points of the can be selectively addressed using circularly polarized light, leveraging valley-dependent selection rules for excitonic transitions. A key unique feature of TMDCs is the strong spin-valley coupling, where spin and valley degrees of freedom are locked due to spin-orbit interaction and time-reversal symmetry, particularly in group-VI materials like MoS₂ and WS₂. This coupling allows for valley-specific spin manipulation, with opposite spins preferred in opposite valleys, facilitating potential spin-valleytronic devices. Additionally, monolayer TMDCs such as MoS₂ exhibit piezoelectricity arising from their non-centrosymmetric structure, with a measurable piezoelectric coefficient in odd-numbered layers due to the absence of inversion symmetry, while even-layered stacks show negligible response. For instance, free-standing odd-layered MoS₂ generates oscillating voltage under cyclic strain, with the effect diminishing in even layers. Synthesis of TMDC monolayers often employs (CVD) to achieve large-area, high-quality films, typically on substrates like or SiO₂/Si, using metal-organic precursors for metals and chalcogen sources. This bottom-up approach enables epitaxial growth of wafer-scale monolayers with controlled polymorphism and minimal defects, as demonstrated for MoS₂ and WS₂ over areas exceeding 10 cm². Recent advances include high-entropy TMDCs, synthesized in 2025 by alloying multiple transition metals (e.g., Mo, , Nb, Ta) in the MX₂ framework, which stabilizes metastable phases through configurational entropy and enhances basal plane activity for . These multi-element compositions, such as (MoWNbTa)Se₂, exhibit tunable bandgaps and improved stability compared to binary TMDCs.

Hydrogenated and silicene-like derivatives

Graphane, the fully hydrogenated form of graphene, features sp³-hybridized carbon atoms in a chair-like configuration, transforming the semimetallic graphene into an insulating material with a direct bandgap of approximately 5.4 eV. This structure was theoretically predicted in 2007 using first-principles calculations, demonstrating stability comparable to common hydrocarbons like benzene. Experimental evidence for graphane emerged in 2009 through reversible hydrogenation of graphene via exposure to hydrogen plasma, confirming the sp³ bonding and bandgap opening. Hydrogenated analogs of group 14 silicene-like materials, such as germanane and stanane, exhibit similar bandgap engineering but with lower energy gaps due to heavier atomic masses. Germanane (GeH), derived from hydrogenating germanene, possesses a direct bandgap tunable from 1.4 to 1.7 eV depending on synthesis conditions and functionalization, enabling applications in . It was first synthesized in 2014 via topotactic deintercalation of CaGe₂ in HCl, yielding stable, millimeter-scale sheets with high . Stanane (SnH₂), the hydrogenated stanene, is predicted to have a tunable bandgap of approximately 0.3 to 1.7 eV, influenced by strain or partial , though experimental synthesis remains elusive, with stability confirmed through calculations. A silicon-based compound, SLSiN (a single-layer Si₃N₄ allotrope), represents a silicene-like derivative incorporating for enhanced stability. Predicted in 2020 using first-principles methods, SLSiN exhibits dynamic and mechanical stability in its and conformations, with a wide bandgap of about 4 eV, positioning it as a potential insulator for 2D . Functionalization beyond , such as or oxidation, further tunes properties in these materials by altering hybridization and introducing dipoles. For instance, fluorination of yields fluorographene (CF), an insulator with a bandgap exceeding 3 eV, synthesized via direct exposure to ; a scalable 2025 method using picolylamine substitution on fluorographene intermediates has advanced its use in high-performance supercapacitors. Oxidation similarly opens bandgaps in silicene-like sheets, with partial coverage enabling semiconducting behavior for tunable devices.

Other inorganic compounds

Hexagonal boron nitride (h-BN) serves as an insulating counterpart to , featuring a planar composed of alternating and atoms bonded covalently within each layer, with weak van der Waals interactions between layers. h-BN exhibits a wide indirect bandgap of approximately 5.8 eV, rendering it electrically insulating and optically transparent in the visible range. Due to its atomically flat surface, chemical inertness, and thermal stability up to 900°C, h-BN monolayers are frequently employed as substrates in van der Waals heterostructures to isolate and protect other two-dimensional materials from . MXenes represent a family of two-dimensional carbides, nitrides, or carbonitrides, typically derived from MAX phase precursors through selective . The archetypal MXene, (where Tₓ denotes surface terminations such as -O, -OH, or -F), consists of alternating and carbon atomic planes, with the surface terminations arising from the process in , conferring hydrophilicity and enabling aqueous dispersion. These terminations stabilize the structure while influencing electronic properties; for instance, Ti₃C₂Tₓ displays metallic conductivity exceeding 10,000 S/cm in thin films, attributed to high from the d-orbitals of transition metals. The hydrophilic surfaces, primarily from -OH and -O groups, facilitate easy exfoliation into single or few-layer flakes, broadening applications in and sensing. Among emerging non-TMDC inorganic single-layers, (CdPS₃) nanosheets have garnered attention for their proton conduction capabilities. These van der Waals materials feature layered structures with Cd atoms coordinated to S and P in a distorted octahedral arrangement, enabling exfoliation into ultrathin nanosheets where Cd vacancies enhance proton mobility through the interlayer space. Membranes assembled from CdPS₃ nanosheets achieve proton conductivities up to 0.95 S/cm at 90°C and 98% relative humidity, surpassing many conventional proton-exchange materials due to the facilitated by labile protons. Transition metal carbo-chalcogenides, such as Nb₂S₂C, exemplify hybrid structures blending features of TMDCs and , with a buckled of alternating Nb-S and C planes held by van der Waals forces. Synthesized via or flux methods, Nb₂S₂C exhibits metallic behavior with high carrier mobility, stemming from the embedded carbon layer that modulates the electronic . Surface terminations like -OH or -F can be introduced during synthesis, tuning wettability and reactivity while preserving the alternating atomic plane architecture common to these compounds.

Advanced and hybrid structures

2D alloys and high-entropy variants

Two-dimensional (2D) alloys represent a class of single-layer materials where multiple elements are incorporated within the plane to achieve enhanced tunability of properties, such as electronic bandgaps and catalytic activity, through compositional control. Unlike pure elemental 2D materials, these alloys enable gradual variation in characteristics by adjusting atomic ratios, often synthesized via (CVD) or methods to maintain atomic-scale uniformity. This in-plane mixing distinguishes them from vertically stacked heterostructures and allows for disorder-tolerant phases stabilized by . A prominent example of 2D alloys involves mixtures of group 14 elements, such as silicene-germanene hybrids, where and atoms form alloyed sheets with tunable bandgaps ranging from indirect to direct depending on the Si:Ge ratio. These hydrogen-terminated germanane/silicane alloys exhibit bandgaps that can be engineered from approximately 1.8 eV to 2.5 eV, enabling applications in by leveraging the differing atomic sizes and electronegativities of Si and Ge. Similarly, gersiloxene variants, incorporating oxygen bridges in Si-Ge frameworks, demonstrate bandgap tunability from 1.8 eV to 2.57 eV through composition, as confirmed by calculations and experimental synthesis via topochemical deintercalation. High-entropy variants extend this concept to multi-principal-element compositions, particularly in dichalcogenides (TMDCs), where five or more metals are randomly distributed to maximize configurational and stabilize the 2D phase. For instance, (MoWVNbTa)S₂, a quintuple-element TMDC , has been synthesized in 2025 using NaCl-assisted CVD, yielding large-area flakes with thicknesses around 1-2 nm and a bandgap of approximately 1.87 eV. In late 2024, single-crystal 2D high-entropy TMDCs were synthesized, further advancing scalable production of entropy-stabilized alloys with tunable properties. This high-entropy approach enhances electrocatalytic performance for the (HER). Earlier work on similar high-entropy TMDCs demonstrated performance for CO₂ reduction to CO, achieving turnover frequencies over 100 s⁻¹ at low overpotentials, due to synergistic electronic effects from the diverse metal centers. Such materials exhibit superior thermal stability up to 650°C compared to binary TMDCs, attributed to lattice distortion resistance from high . Boridenes, another category of 2D boron-metal alloys, feature boron networks interspersed with transition metals like , forming sheets with ordered metal vacancies for structural stability. Synthesized by selective of bulk MoAlB phases, these Mo₄/₃B₂₋ₓ materials exhibit superhard properties, with predicted ideal exceeding 40 GPa, stemming from the strong covalent B-B bonds and metallic reinforcement. Their mechanical resilience, combined with metallic conductivity, positions boridenes as candidates for durable coatings and electrodes. Substrate-induced surface alloying provides a method to create 2D alloys without direct synthesis of freestanding sheets, as seen in Pt-Ru alloys formed on supported by Ru(0001). By depositing Pt atoms onto the Ru surface, a surface alloy layer forms that interacts weakly with overlying , tuning adhesion energy from 0.1 to 0.3 J/m² and enabling controlled growth or transfer. This approach leverages epitaxial strain to stabilize the alloy composition, offering a pathway to integrate metallic 2D alloys with carbon-based platforms for .

Organic and polymeric single-layers

Organic and polymeric single-layers represent a class of two-dimensional (2D) materials constructed from molecular building blocks linked by covalent bonds, enabling precise control over structure and function through rational design. These materials, including covalent organic frameworks (COFs) and 2D polymers, form extended networks in a single atomic layer, where in-plane covalent linkages provide mechanical integrity while maintaining nanoscale thickness. Molecular design in these systems leverages dynamic covalent chemistry, such as or boronate formation, to assemble monomers into ordered lattices with tailored pore sizes and functionalities. A prominent example of 2D organic frameworks is porphyrin-based sheets, which incorporate units as nodes connected via linkages like imines to form porous single-layer structures. These frameworks exhibit high with uniform nanopores, making them suitable for applications such as gas separation, where selective of molecules like CO₂ over N₂ is achieved through size-exclusion and interaction tuning. For instance, imine-linked porphyrin COFs synthesized on surfaces demonstrate ordered square lattices with pore apertures around 1-2 nm, facilitating efficient molecular sieving. The modular nature of porphyrin building blocks allows for metalation or functionalization, enhancing selectivity in separation processes. Single-layer polymers, such as polyimine networks, feature fully covalent in-plane bonding that extends across large domains, distinguishing them from stacked multilayers. A notable advancement is the synthesis of crystalline 2D polyimine thin films via on-liquid surface methods, where water-insoluble monomers preorganize at a surfactant-stabilized interface before with dialdehydes, yielding free-standing films up to 28 cm² with hexagonal of 4.8-5.3 nm. These polymers exhibit tunable by varying linker lengths and flexibility, evidenced by a of 2.3 GPa, enabling applications in flexible membranes. Synthesis often employs interfacial , such as liquid-air or solid-liquid interfaces, to confine reactions and promote growth. Despite these advances, challenges persist in scaling production beyond small domains, as controlling reaction kinetics and achieving defect-free uniformity over large areas remains difficult due to limitations in interfacial stability and solubility. Current methods produce high-quality films but struggle with and expansion to wafer-scale without compromising crystallinity. Ongoing efforts focus on optimizing and conditions to address these issues.

Heterostructures and combinations

Heterostructures formed by vertically stacking distinct single-layer materials via weak van der Waals interactions represent a cornerstone of advanced 2D material engineering, allowing precise control over interfacial properties without covalent bonding. Graphene stacked on hexagonal (h-BN) exemplifies this approach, where h-BN acts as an atomically flat, substrate that minimizes charge impurity in , achieving carrier mobilities exceeding 100,000 cm²/V·s at low temperatures compared to substrates like SiO₂. This enhancement stems from the similar lattice constants of and h-BN (mismatch ~1.8%), enabling high-quality epitaxial alignment during transfer or growth processes. Seminal demonstrations involved mechanical transfer techniques to encapsulate graphene within h-BN layers, preserving intrinsic electronic quality for device applications. Moiré patterns emerge in these graphene/h-BN stacks due to the slight lattice mismatch and rotational misalignment, creating a superlattice potential that modifies the electronic band structure. This results in observable effects like the Hofstadter butterfly spectrum in magnetic fields and the emergence of massive Dirac fermions with tunable band gaps up to ~0.3 eV, as confirmed through low-temperature scanning tunneling microscopy. In twisted bilayer graphene (TBG), a related heterostructure variant, precise twist angles near the "magic angle" of ~1.1° produce moiré patterns with flat electronic bands, fostering strong electron correlations that lead to unconventional superconductivity with critical temperatures up to 1.7 K under doping. This phenomenon, first reported experimentally in 2018, arises from enhanced electron-electron interactions within the moiré unit cell, spanning areas ~100 times larger than the atomic lattice. Twistronics, the field exploring angle-dependent properties in stacked 2D layers, builds on these moiré effects, with TBG as the prototypical system where small twist angles (<5°) dramatically alter band topology, enabling insulating states at half-filling and tunable superconductivity. Theoretical foundations trace to models predicting flat bands at magic angles due to interlayer coupling, validated by angle-resolved photoemission spectroscopy showing bandwidths reduced to ~10 meV. Colloidal assembly techniques further extend heterostructure formation to 2D supracrystals, where transition metal dichalcogenide (TMDC) flakes like WS₂ are dispersed in solution and self-organize into ordered, large-area arrays via depletion attraction or electrostatic forces, yielding polycrystalline films with aligned domains up to micrometers in size for scalable integration. Recent advances as of 2024 have focused on robotic assembly for cleaner interfaces in 2D heterostructures, utilizing specialized robotic systems to stack large pieces of atomically clean materials, minimizing contamination and enabling scalable production for devices including quantum simulators. Such automation facilitates the creation of stacked devices exhibiting topological superconductivity, advancing toward scalable quantum information processing.

Properties

Mechanical properties

Single-layer materials exhibit exceptional mechanical properties due to their atomic-scale thickness and strong in-plane covalent bonding, which confer high stiffness and strength while allowing flexibility in the out-of-plane direction. The Young's modulus, a measure of in-plane elasticity, reaches approximately 1 TPa for , reflecting its robust honeycomb lattice structure. In contrast, transition metal dichalcogenides like monolayer MoS₂ display a lower but still remarkable in-plane Young's modulus of about 270 GPa, attributed to weaker metal-sulfur bonds compared to carbon-carbon bonds in . These materials show pronounced anisotropy: in-plane responses are dominated by stretching modes with high modulus, whereas out-of-plane deformations involve bending with much lower rigidity, on the order of eV for flexural phonons in . Under tensile loading, single-layer materials demonstrate high strength and ductility before failure. Graphene's intrinsic tensile strength is around 130 GPa, with a strain-to-failure of approximately 25%, enabling significant elastic deformation without permanent damage. Freestanding layers often exhibit rippling—out-of-plane undulations stabilized by thermal fluctuations—that modulates local strain but preserves overall mechanical integrity, as these ripples suppress long-wavelength instabilities in the 2D structure. Fracture in these materials follows adapted brittle fracture models, such as the Griffith criterion modified for two-dimensional systems, where the critical stress σ\sigma for crack propagation from a defect of length aa is given by σ=2Eγπa,\sigma = \sqrt{\frac{2E\gamma}{\pi a}},
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