The angle resolved photoemission spectroscopy (ARPES) technique consists in illuminating a sample with a monochromatic source of UV photons and analyzing the out-coming electrons emitted through the photoelectric effect. The analysis of the kinetic energy and angles (polar, azimuthal and tilt) of emission of the electrons yields to the band diagram of the material. In simple case, where the materials can be described by a nearly free electron or a tight binding model, i.e. a one-electron effective Hamiltonian, one can consider an electronic dispersion consisting of well-defined relations between wavevectors and energy (Dirac function δ(E, k) ). For example, the Dirac cones in Topological Insulators (insert) are perfectly well evidenced with ARPES.

In that case, simple conservation rules enable plotting the band diagram:

Ekin = hυ + E - Φ

Where Ekin is the kinetic energy of the photoemitted electron, hυ is the energy of the incoming photon, Φ is the work function and E the binding energy prior to the photoemission process.

Where k// is the parallel wave vector prior to the photoemission process, m is the mass of the free electron and θ is the angle of photoemission.

Since the translational symmetry is broken at the surface the kz component is not conserved during the photoemission process.

For more complex systems where interactions are relevant, there is a broadening of the electronic dispersion in wavevector (k) and energy (E). The concept of quasi-particle is introduced for considering the electronic states with their dressing by surrounding excitations. In particular, for Fermi Liquids, a class of materials including most of the metallic samples, the width and spectral weight of the quasi-particle band are renormalized by the interactions, and the line shape exhibits a characteristic asymmetry. Incoherent features of the quasi-particle at characteristic excitations energies (phonon, magnon, Coulomb, Plasmon, etc…), represent the dressing by the relevant interactions. The data - usually plotted on a 2D map of intensity I(k,E) - are comparable to the single-particle spectral density function A(k,ω) of the occupied states, a fundamental theoretical quantity of Fermi Liquids.

When many-body interactions cannot be considered in the frame of Fermi Liquids, for example in the case of superconductors, Mott-insulators, Luttinger Liquids and peculiar materials, a different spectral density function can also be established by theoreticians. It is then possible to determine crucial many-body parameters of the model Hamiltonian by comparing the experiment with the theoretical predictions.

The angle resolved photoemission spectroscopy is the best technique for measuring predicted band diagrams, spectral functions and wavevector dependence of low energy excitations. A simple analysis of the data gives the bandwidth and the hybridization potentials of the orbitals of any conducting materials. The cross section of the photoemission process with respect to the light polarization yields the symmetry of the orbitals. So, for example, the orbital nature of the bands impacted by the superconductivity can be established in high temperature superconductors. The emergence of new periodicities in the system appear clearly in data because they yields new Fermi surface shapes, reduced Brillouin Zones or the formation of shadow bands. So, the wavevectors related to excitations (charge/spin density waves) can be extracted from the intensity maps. A precise analysis of the spectral weight at the Fermi level enables the determination of the power law dependence of the density of states of Luttinger Liquids and of the (pseudo)-gaps related to charge density wave systems, Mott insulators and superconductor. The analysis of wavevector dependence of (pseudo)-gaps yields a direct access to the order parameter symmetry in unconventional superconductors.

To summarize, the energy selectivity (meV to eV) of the angle resolved photoemission spectroscopy technique allows the experimentalist to study simultaneously the hybridization potentials, the Coulomb repulsion, but also the charge or spin fluctuations or the electron-phonon interactions in the reciprocal space.

By comparing ARPES data to scanning tunneling spectroscopy, one can expect a deep insight in the most important physical mechanism of complex materials.