Transport Properties of the Quantum Hall State

In this thesis, I analyze the transport properties of the two-dimensional electron gas(2DEG) in the quantum Hall regime. This analysis is based on the model in which the 2DEG breaks into compressible and incompressible regions. ^1 I first describe the progress in the study of the quantum Hall effect from its experimental discovery to the point where the role of the compressible liquid became crucial. The key concept here is the existence of the incompressible state. In Chapter 2 I show through a self-consistent electrostatic calculation that wide compressible strips are present parallel to the edges of a sample. ^2 This leads to an explanation of certain data from equilibration experiments. In Chapter 3 I analyze the effect of compressible strips on the conductance of a narrow wire.^3 The presence of the compressible state leads to narrow plateaus in conductance vs. magnetic field plots. These predictions are yet to be tested. The model of compressible and incompressible regions is used in Chapter 4 to study transport properties of the 2DEG in the bulk.^4 I show that depending on the level of disorder in a sample one can have either narrow or wide compressible regions. In the first case the conventional network model analysis applies, while in the second case I use the composite fermion approach to obtain transport properties. This provides a way of understanding the nature of the compressible state. The main predictions of this part are on the longitudinal resistivity peak values in the quantum Hall effect in the limit of zero temperature. These predictions are compatible with existing experimental data. ftn^1A. L. Efros, Solid State Commun. 67, 1019 (1988), S. Luryi in High Magnetic fields in Semiconductor Physics, edited by Landwehr (Springer, New York, 1987). ^2D. B. Chklovskii, B. I. Shklovskii, and L. I. Glazman, Phys. Rev. 46, 4026 (1992); 46, 15606(E) (1992). ^3D. B. Chklovskii, K. A. Matveev, and B. I. Shklovskii Phys. Rev. B 47, 12605 (1993). ^4D. B. Chklovskii and P. A. Lee, Phys. Rev. B 48, 18060 (1993). (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).