09-27-2021-2025 - Angle-resolved photoemission spectroscopy (ARPES)

 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.

ARPES spectrum of a two-dimensional electronic state localized at the (111) surface of copper. The energy has free-electron-like momentum dependence, p²/2m, where m=0.46m_e. Color scale represents electron counts per kinetic energy and emission angle channel. When 21.22 eV photons are used, the Fermi level is imaged at 16.64 eV.

Typical laboratory setup of an ARPES experiment: Helium discharge lamp as an ultraviolet light source, sample holder that attaches to a vacuum manipulator, and hemispherical electron energy analyzer.

Electron trajectories in an ARPES spectrometer electrostatic lens shown in the plane of angular dispersion. The instrument shows a certain degree of focusing on the same detection channel of the electrons leaving the crystal at the same angle but originating from two separate spots on the sample. Here, the simulated separation is 0.5 mm.

Angle- and energy-resolving electron spectrometer for ARPES (schematic)

Left: Analyzer angle - Energy map I₀(α,E_k) around vertical emission. Right: Analyzer angle - Energy maps I_θ(α,E_k) at several polar angles away from vertical emission.

ARPES spectrum of the renormalized π band of electron-doped graphene; p-polarized 40eV light, T=80K. Dotted line is the bare band. The kink at -0.2 eV is due to graphene's phonons.^[13]

https://en.wikipedia.org/wiki/Angle-resolved_photoemission_spectroscopy