Past exam of the condensed matter physics major option course of the University of Oxford / 2018 / 2 / d

Angle-resolved photoemission spectroscopy illuminates a surface with photons of known energy and measures the kinetic energy and emission direction of the escaping electrons. Referencing the initial binding energy to the Fermi level givesHere $\Phi$ is the sample/analyser work-function reference appropriate to the calibrated energy scale, and $\theta$ is the emission angle from the surface normal. Parallel crystal momentum is conserved modulo a surface reciprocal lattice vector; measuring two angular coordinates maps the two in-plane momentum components.

Sweeping angle and energy traces the occupied spectral weight and its dispersion. In a quasi-two-dimensional sheet, no detailed free-electron model of the perpendicular final-state momentum is required to map the in-plane bands. Peaks reflect the occupied single-particle spectral function, multiplied by Fermi occupation and photoemission matrix elements and broadened by finite lifetimes and resolution. Ordinary photoemission does not directly measure empty conduction bands; a gap may need complementary information. A clean surface, vacuum and charge control are especially important for an insulating specimen.