Quasiparticle interference (QPI) imaging is a technique used in condensed matter physics that allows a scanning tunneling microscope to image the electronic structure of a material and infer information about the momentum space electronic structure from imaging the density of states in real space. In a scanning tunneling microscope, a very sharp metal tip is brought within a few angstrom of a sample. When a voltage is applied between the two and the tip is sufficiently close, a tunneling current ${\displaystyle I(\mathbf {r} ,V)}$ between the two can be measured and used, for example, to record atomically resolved images of the surface. Keeping the position of the tip constant and changing the bias voltage ${\displaystyle V}$ allows acquisition of tunneling spectra.

While scanning tunneling microscopy and spectroscopy of a perfect crystal would show the same tunneling spectrum at each point on the surface of the crystal due to translational invariance, if there is a defect, the density of states acquires a spatial dependence with modulated patterns that reflect the characteristic wavelength of the electrons in the material. These spatial modulations are effectively Friedel oscillations, except that Friedel oscillations describe the modulation in the charge density rather than the density of states.

Quasiparticle interference imaging has been applied to the study of a range of quantum materials and low-energy electronic structures. While angle-resolved photoemission spectroscopy (ARPES) is a more direct technique to study the electronic structure of a material, QPI differs from ARPES that its energy resolution is only limited by the temperature of the experiment. QPI measures both occupied and unoccupied states in the same measurement, and it can be measured in a magnetic field.

Quasiparticle interference was first reported in two papers in 1993 by Mike Crommie and Yukio Hasegawa, showing standing wave patterns due to quantum interference in the surface states of Cu(111) and Au(111), respectively. The noble metal (111) surfaces exhibit surface states that are quasi-free two-dimensional electronic states living in a directional bulk band gap. Subsequently, these studies were extended to resonator structures constructed by atomic manipulation. The interference patterns were described by scattering theory. Subsequently, QPI was used by J. C. Séamus Davis and J.E. Hoffman to map out the structure of the superconducting gap in high-tc superconducting cuprates. Since then, QPI has been applied to many complex materials (often called "quantum materials"), from heavy fermion materials via high temperature superconductors and iron-based superconductors to graphene and topological insulators.

Quasiparticle interference is measured by spatially mapping the local density of states. From the Bardeen theory of electron tunneling, it can be shown that the differential conductance as a function of bias voltage ${\displaystyle V}$ and position ${\displaystyle \mathbf {r} }$ recorded by scanning tunneling spectroscopy (for a derivation see there) is proportional to the density of states ${\displaystyle \rho (\mathbf {r} ,eV)}$, i.e.

${\displaystyle g(\mathbf {r} ,V)={\frac {\mathrm {d} I}{\mathrm {d} V}}(\mathbf {r} ,V)\sim \rho (\mathbf {r} ,eV),}$

where ${\displaystyle I(\mathbf {r} ,V)}$ is the tunneling current between tip and sample. This equation is valid if one assumes that the tip density of states is featureless and in the low temperature and low energy limit. It is important to note that the tunneling junction is symmetric, so the differential conductance ${\displaystyle g(V,\mathbf {r} )}$ is a convolution of the tip and sample density of states.

The differential conductance ${\displaystyle g(\mathbf {r} ,V)}$ is typically measured using a lock-in technique, modulating the bias voltage ${\displaystyle V}$ by a small additional component ${\displaystyle V_{\mathrm {ac} }=V_{0}\sin(\omega t)}$ and detecting the response in the current at the same frequency ${\displaystyle \omega }$, or by numerical differentiation of the current as a function of voltage, ${\displaystyle I(\mathbf {r} ,V)}$. To obtain a spatial map of the local density of states, either the differential conductance can be mapped in closed feedback loop conditions (using a lock-in amplifier operating at a frequency larger than the cut off frequency of the feedback loop), i.e. while a topographic image is recorded, or a set of tunneling spectra are acquired on an equally spaced grid, turning of the feedback loop at each point before the spectrum is recorded (sometimes also referred to as "current-imaging-tunneling spectroscopy" (CITS) map, see Scanning tunneling spectroscopy). Acquisition of these spectroscopic maps is typically slow, taking from a few hours to a few days. The QPI map is typically analysed from the Fourier transformation of ${\displaystyle g(\mathbf {r} ,V)}$, i.e. ${\displaystyle {\tilde {g}}(\mathbf {q} ,V)={\cal {F}}(g(\mathbf {r} ,V))}$.