**To know a bit more about the ARPES technique :**

The ARPES technique is a photon-in, electron-out technique performed on conducting samples with UV light. It is a surface technique because of the short mean free path of the photoelectrons in the sample. Thus, the experiment has to be performed in ultrahigh vacuum (UHV) to avoid contamination with cleaved samples or freshly prepared surfaces. The analysis of the kinetic energy and angles (polar, azimuthal and tilt) of emission of the electrons - usually plotted on a 2D map of intensity I(k,E) - is comparable to the single-particle spectral density function A(k,w) of the occupied states, a fundamental theoretical quantity.

In simple cases, the spectral function corresponds to the band diagram and, in particular, the Fermi surface of the material can be measured. For example, the Dirac cones in Graphene and at the surface of Topological Insulators are directly evidenced with ARPES data. A simple analysis 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.

For complex systems, it is then possible by comparing the experiment with the theoretical predictions to determine crucial many-body parameters of the model Hamiltonian. In particular, for Fermi Liquids, 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 emergence of new periodicities in the system 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 makes possible the (pseudo)-gaps determination of charge density wave systems, Mott insulators and superconductor. The wavevector dependence of the (pseudo)-gaps yields a direct access to the order parameter symmetry in unconventional superconductors. To summarize, the energy selectivity (meV to eV) of the ARPES 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. For all these reasons, Angle resolved photoemission spectroscopy was intensively used in the last few years for the study of quantum materials.