Measuring the Electronic Energy Spectrum On and Off the Fermi Surface

Abstract

Abstract This chapter discusses various methods that have been used to measure the energy spectrum of electrons in both metals and insulators. For metals a property of paramount importance is the detailed shape of the Fermi surface and the accompanying Fermi velocity, since together they affect transport and other phenomena. Methods to measure these quantities include various magneto-acoustic effects (e.g., the geometric resonance phenomenon), the Gantmakher and Sondheimer size effects, the Azbel–Kaner cyclotron resonance, the anomalous skin effect, the high-field magneto-resistance (as it relates to open versus closed orbits), and various quantum oscillations, the most important of which is the de Hass–van Alphen effect. For determining the energy spectrum at energies below the Fermi surface, the most powerful technique is angle resolved photo-emission spectroscopy (ARPES) which, with the emergence of synchrotron sources, has become increasingly important. Also of growing importance is inverse photo-emission spectroscopy (IPS), a special case of which is termed bremsstrahlung isochromat spectroscopy (BIS). Here the roles of the incoming photon and the final state electron are reversed: electrons of known energy (and angle) impinge on the surface and (in the BIS variant) the energy spectrum of the emitted photons is measured. This technique probes the spectrum for energies above the Fermi energy.