Angle-resolved photoemission spectroscopy (ARPES) is an experimental technique used in condensed matter physics to probe the allowed energies and momenta of the electrons in a material, usually a crystalline solid. It is based on the photoelectric effect, in which an incoming photon of sufficient energy ejects an electron from the surface of a material. By directly measuring the kinetic energy and emission angle distributions of the emitted photoelectrons, the technique can map the electronic band structure and Fermi surfaces. ARPES is best suited for the study of one- or two-dimensional materials. It has been used by physicists to investigate high-temperature superconductors, graphene, topological materials, quantum well states, and materials exhibiting charge density waves.

ARPES systems consist of a monochromatic light source to deliver a narrow beam of photons, a sample holder connected to a manipulator used to position the sample of a material, and an electron spectrometer. The equipment is contained within an ultra-high vacuum (UHV) environment, which protects the sample and prevents scattering of the emitted electrons. After being dispersed along two perpendicular directions with respect to kinetic energy and emission angle, the electrons are directed to a detector and counted to provide ARPES spectra—slices of the band structure along one momentum direction. Some ARPES instruments can extract a portion of the electrons alongside the detector to measure the polarization of their spin.

Electrons in crystalline solids can only populate states of certain energies and momenta, others being forbidden by quantum mechanics. They form a continuum of states known as the band structure of the solid. The band structure determines if a material is an insulator, a semiconductor, or a metal, how it conducts electricity and in which directions it conducts best, or how it behaves in a magnetic field.

Angle-resolved photoemission spectroscopy determines the band structure and helps understand the scattering processes and interactions of electrons with other constituents of a material. It does so by observing the electrons ejected by photons from their initial energy and momentum state into the state whose energy is by the energy of the photon higher than the initial energy, and higher than the binding energy of the electron in the solid. In the process, the electron's momentum remains virtually intact, except for its component perpendicular to the material's surface. The band structure is thus translated from energies at which the electrons are bound within the material, to energies that free them from the crystal binding and enable their detection outside of the material.

By measuring the freed electron's kinetic energy, its velocity and absolute momentum can be calculated. By measuring the emission angle with respect to the surface normal, ARPES can also determine the two in-plane components of momentum that are in the photoemission process preserved. In many cases, if needed, the third component can be reconstructed as well.

A typical instrument for angle-resolved photoemission consists of a light source, a sample holder attached to a manipulator, and an electron spectrometer. These are all part of an ultra-high vacuum system that provides the necessary protection from adsorbates for the sample surface and eliminates scattering of the electrons on their way to the analyzer.

The light source delivers to the sample a monochromatic, usually polarized, focused, high-intensity beam of ~10¹² photons/s with a few meV energy spread. Light sources range from compact noble-gas discharge UV lamps and radio-frequency plasma sources (10–⁠40 eV), ultraviolet lasers (5–⁠11 eV) to synchrotron insertion devices that are optimized for different parts of the electromagnetic spectrum (from 10 eV in the ultraviolet to 1000 eV X-rays).

The sample holder accommodates samples of crystalline materials, the electronic properties of which are to be investigated. It facilitates their insertion into the vacuum, cleavage to expose clean surfaces, and precise positioning. The holder works as the extension of a manipulator that makes translations along three axes, and rotations to adjust the sample's polar, azimuth and tilt angles possible. The holder has sensors or thermocouples for precise temperature measurement and control. Cooling to temperatures as low as 1 kelvin is provided by cryogenic liquefied gases, cryocoolers, and dilution refrigerators. Resistive heaters attached to the holder provide heating up to a few hundred °C, whereas miniature backside electron-beam bombardment devices can yield sample temperatures as high as 2000 °C. Some holders can also have attachments for light beam focusing and calibration.