Density of states between Landau levels in a two-dimensional electron gas.

Two-dimensional electron systems (2D ES}in a perpendicular magnetic field B display fascinating quantum oscillations. ' Examples of 2D ES's are electrons confined to interfaces in GaAs-Ga& „Al„As layered heterostructures and electrons at surfaces in Si metal-oxidesemiconductor field-effect transistors (MOSFET's). Earliest interest was in electron transport properties, the integer quantum hall effect' (QHE) and the fractional quantum Hall effect' (FQHE), and in distinguishing localized from delocalized states. However, transport measurements do not readily observe the total density of states (DOS) available to the electrons. Recently, several experiments " measuring single-electron behavior determine the DOS directly. These find that the Landau levels (LL's) are significantly broadened, due to disorder in the samples, and that there is a substantial DOS lying between LL's not obtained in existing calculations. ' An important outstanding problem ' is to identify the origin of the large DOS between LL's in a direct and consistent manner. We present here a straightforward evaluation of the DOS in the presence of disorder which provides broad LL's which overlap to give a DOS between LL's in a single unified theory. The new feature is to keep the correlation length of the disorder finite within a theory which is valid for the case of overlapping Landau levels. The importance of a finite correlation length has been stressed" ' in the past, but usually within a model which does not permit an overlap of LL's. In zero magnetic field the DOS of a 2D electron gas (2D EG), per unit area A and for both spins, is a constant, no —Mlitt . In a field B applied perpendicular to the 2D plane, the electron energies are confined to the LL's, E„=ftco,(n+ —, '), where ,c=oeB/ cM. The DOS is n(E)=noftco, +„5(E E„). In rea—l samples "the electrons interact and there is disorder due to charged impurities, defects, and sample inhomogeneities. Here, we ignore e-e interactions and represent the disorder by a potential V(r), seen by an electron at r, which fluctuates from point to point. The disorder broadens the LL's. Indeed recent experiments of specific heat, capacitance, and magnetization' " of 2D ES's show that DENSITY OF STATES AT 5 T