The Oscillations of 2D-Electron Density of States in a Transverse Magnetic Field

Abstract

The problem of dealing with the electron density of states (DOS) in the presence of disorder associated with a random potential due to defects1 is the focus of discussion of the energy spectrum of 2D-systems in a transverse magnetic field. The importance of this problem is caused by the necessity of a microscopic description of the magnetotransport properties of the 2D-space charge layers for a wide range of variations of the filling of the quantum states, including the regimes of integral and fractional quantum Hall effect (QHE). In order to construct a microscopic theory one. has to have detailed information on disorder in the system, viz., on the random potential of scatter ers. Here comes the question of screening of random potential fluctuations as a function of the filling factor of quantum states. These problems can be solved experimentally in terms of a spectroscopic method employed to study the energy distribution of the density of one-particle electronic states — D(E). The previously employed methods for investigations of 2D-D0S at the Fermi level — dns/dEF were based on the measurements of magnetization,2 electron heat capacity,3 magnet ocapacitance,4 contact potential difference5 and thermaly activated conductivity.6 With account taken of the electron-electron interaction and the related effects of random potential screening, the thermodynamic DOS — dns/dEF and D(EF) are different. An advantage of the spectroscopic method is that it enables one to detect how the energy distribution of the DOS varies with the filling factor v of the quantum states (v = nsh/eB, ns being the electron density) and, also, with the amplitude and linear scale of long-range random potential fluctuations, the magnetic field and the electron mobility. Finally, the spectroscopic method may be used to determine the gap values in one-electron energy spectrum of 2D-electrons in a transverse magnetic field and, what is especially important, the Coulomb gap values of incompressible Fermi-liquids in the fractional QHE regimes.