Studying conduction-electron/interface interactions using transverse electron focusing

Understanding the microscopic processes by which the electrons within conductors are scattered at surfaces and interfaces is important for both fundamental physics and technology. The authors review what has been learned so far about scattering of electrons at a variety of surfaces and interfaces using a technique, transverse electron focusing (TEF), that involves two point contacts in a uniform magnetic field. Transverse electron focusing is a sort of β-ray spectrometer in a metal, except that, whereas the β-ray spectrometer requires a narrow beam because the energy and momentum of a free electron can be arbitrary, in TEF the electrons of interest all have the Fermi energy and momentum, so focusing occurs even for electrons injected isotropically in angle. Transverse electron focusing is unique in its ability to probe localized and selectable portions of the interface from inside the conductor, using conduction electrons on only small parts of the Fermi surface. The authors first briefly review the essential features of TEF and of ideal and rough surfaces and describe the three techniques now used for injecting and detecting electrons: needle contacts, lithographically fabricated contacts, and light-induced injection. They then turn to measurements in metals and semimetals of the probability of specular reflection q from a given interface for electrons at the Fermi energy impinging at perpendicular incidence. They examine how q varies over different crystal faces for different electron orbits on the Fermi surfaces of a variety of conductors and how it is affected by changes in the de Broglie wavelength ${\lambda }_{\mathrm{dB}},$ by chemical etching, ion etching, or physical damage, by a molecular overlayer condensed from the surrounding atmosphere, and, for semimetals, by surface band bending (surface charge). The authors also explain how to measure the dependence of q upon the angle of incidence $q\left(\theta \right),$ which gives information about surface structure. Transverse electron focusing studies of a variety of quasiparticle effects arising because the electrons are in a solid are described. These include (a) scattering of excitations moving on “holelike” orbits—q can depend upon the sign of the particle charge; (b) scattering involving a surface reciprocal-lattice vector ${\mathbf{G}}_{\tau },$ including surface resonances induced by an artificial grating etched onto a Bi surface; and (c) scattering between different parts of the Fermi surface—intervalley scattering (IVS)—including scattering in which the sign of the quasiparticle charge changes. The authors review studies of scattering of electrons from a normal-metal (or semimetal)/superconductor interface, which involves an unusual phenomenon called Andreev reflection, in which the signs of both the charge and mass change. Also described are TEF studies of scattering of light-excited electrons from an intercrystalline boundary and recent TEF measurements of q for scattering from the boundary of the two-dimensional electron gas. The authors conclude with a list of future TEF studies of conduction-electron/interface interactions that they believe to be interesting and important.