Angle-resolved photoemission spectroscopy

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.

The equipment is contained within an ultra-high vacuum (UHV) environment, which protects the sample and prevents scattering of the emitted electrons.

Angle-resolved photoemission spectroscopy determines the band structure and helps understand the scattering processes and interactions of electrons with other constituents of a material.

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.

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.

[2][3] 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.

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.

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.

The electron spectrometer disperses the electrons along two spatial directions in accordance with their kinetic energy and their emission angle when exiting the sample; in other words, it provides mapping of different energies and emission angles to different positions on the detector.

Electron detection events are recorded using an outside camera and are counted in hundreds of thousands of separate angle vs. kinetic energy channels.

Because of incomplete determination of the three-dimensional wave vector, and the pronounced surface sensitivity of the elastic photoemission process, ARPES is best suited to the complete characterization of the band structure in ordered low-dimensional systems such as two-dimensional materials, ultrathin films, and nanowires.

[13] Electron analyzers that use a slit to prevent the mixing of momentum and energy channels are only capable of taking angular maps along one direction.

To map the band structure over a two-dimensional momentum space, the sample is rotated while keeping the light spot on the surface fixed.

The most common choice is to change the polar angle θ around the axis that is parallel to the slit and adjust the tilt τ or azimuth φ so emission from a particular region of the Brillouin zone can be reached.

, and the components of the electron's crystal momentum determined by ARPES in this mapping geometry are If high symmetry axes of the sample are known and need to be aligned, a correction by azimuth φ can be applied by rotating around z, when

is then expressed as the products of summed over all allowed initial and final states leading to the energy and momentum being observed.

in Bloch's decomposition of the wave functions, it follows the only allowed transitions when no other particles are involved are between the states whose crystal momenta differ by the reciprocal lattice vectors

Those can lead to the suppression of the photoemission signal in certain parts of the reciprocal space or can tell about the specific atomic-orbital origin of the initial and final states.

In the case of increased electron correlations, the spectral function broadens and starts developing richer features that reflect the interactions in the underlying many-body system.

, reads This function is known from ARPES as a scan along a chosen direction in momentum space and is a two-dimensional map of the form

(1), and feed to the algorithm its fit to a suitable curve as a new ansatz bare band; convergence is usually achieved in a few quick iterations.

[16] From the self-energy obtained in this way one can judge on the strength and shape of electron-electron correlations, electron-phonon (more generally, electron-boson) interaction, active phonon energies, and quasiparticle lifetimes.

[21] For strongly correlated systems like cuprate superconductors, self-energy knowledge is unfortunately insufficient for a comprehensive understanding of the physical processes that lead to certain features in the spectrum.

A typical example is the pseudogap in the cuprates, i.e., the momentum-selective suppression of spectral weight at the Fermi level, which has been related to spin, charge or (d-wave) pairing fluctuations by different authors.

[24] ARPES has been used to map the occupied band structure of many metals and semiconductors, states appearing in the projected band gaps at their surfaces,[10] quantum well states that arise in systems with reduced dimensionality,[25] one-atom-thick materials like graphene,[26] transition metal dichalcogenides, and many flavors of topological materials.

[2][29][30][9] When the electron dynamics in the bound states just above the Fermi level need to be studied, two-photon excitation in pump-probe setups (2PPE) is used.

ARPES spectrum of a two-dimensional electronic state localized at the (111) surface of copper. The energy has free-electron -like momentum dependence, p 2 /2 m , where m = 0.46 ‍ m 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 (not to scale): Helium discharge lamp as an ultraviolet light source, sample holder that attaches to a vacuum manipulator , and hemispherical electron energy analyzer .
A view through the window of an ultrahigh vacuum chamber for angle-resolved photoemission spectroscopy. The crystal holder with integrated e-beam heating is attached to a xyz+theta manipulator on top, and by a silver braid to a cryocooler on the bottom. The lens of the electron analyzer and UV source capillary are visible on the right.
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)
ARPES spectrum of the renormalized π band of electron-doped graphene ; p-polarized 40 eV light, T = 80 K . Dotted line is the bare band. The kink at −0.2 eV is due to graphene's phonons . [ 16 ]
Constant energy cuts of the spectral function are approximately Lorentzians whose width at half maximum is determined by the imaginary part of the self-energy , while their deviation from the bare band is given by its real part.