Density of States and Electron-Phonon Coupling in Two-Dimensional Electron Systems at High Magnetic Fields

Abstract

One of the central problems in the two-dimensional electron field1 is the determination of the Landau level density of states. This quantity plays an essential role in determining almost all physically measurable properties. For example, understanding the striking characteristics of the quantum Hall effect requires the existence of localized electronic states somewhere in the gap region between Landau levels2. How many such states are there and how are they distributed? Considerable effort, both theoretical and experimental, has been devoted to this problem over the last several years and much progress has been made. In these lectures I will discuss in detail two sets of experiments on 2D electron systems (2DES) in which the density of states (DOS) is directly observable. The first example will be our measurements of the static magnetization of the 2DES at high magnetic fields3. Being an equilibrium thermodynamic variable, the magnetization depends only on the DOS. The strength of the observed oscillations in the magnetic moment as a function of field (deHaas-van Alphen effect) gives a direct measure of the broadening of the Landau levels. Our observations have led to the conclusion, now widely corroborated, that a significant density of states exists in the gap region between Landau levels. The second example concerns our experiments on the thermal conductivity at high magnetic fields of multi-layer heterostructures that contain 2D electron systems4. Although these are really phonon transport measurements, the DOS of the 2DES enters through the coupling of the phonons to the electrons. Striking magneto-oscillations are observed in the temperature gradient generated by an applied heat flux.