ARPES

ARPES, or angle-resolved photoemission spectroscopy, is a spectroscopy technique used to study the electronic structure of solids. It measures the energy and momentum of electrons ejected from a material when illuminated by photons, providing direct information about the occupied band structure and Fermi surface.

In ARPES, the kinetic energy E_k and the emission angle θ of the photoelectrons are measured. By energy conservation, E_k = hν − φ − E_b, where hν is the photon energy, φ is the work function, and E_b is the binding energy relative to the Fermi level. The in-plane momentum is determined from k_parallel = (√(2mE_k)/ħ) sin θ. The perpendicular momentum k_z can be accessed by varying the photon energy, though it is strongly influenced by the surface potential and is less well defined in typical measurements.

Experiments are conducted under ultra-high vacuum on clean crystalline samples, using photon sources such as synchrotron radiation or ultraviolet lasers, and an electron energy analyzer to measure kinetic energy and emission angle. Some setups include spin resolution or time-resolved capabilities. Modern ARPES can achieve meV energy resolution and sub-degree angular resolution, enabling detailed mapping of electronic dispersions.

Applications include mapping electronic band structures and Fermi surfaces, studying superconductivity, density-wave states, and topological materials, and exploring many-body interactions through self-energy features. Spin-resolved ARPES adds spin information, while time-resolved ARPES probes ultrafast dynamics after excitation.

Limitations arise from surface sensitivity, requiring clean, well-ordered surfaces, and interpretation can be affected by matrix elements. Conventional ARPES observes occupied states, though pump-probe variants can access transient unoccupied states. It is a central tool in condensed matter physics for electronic structure studies.