Studies of Anisotropy in Two-Dimensional Electron Systems and Quenching of Quantum Hall Behavior.

The effect of anisotropy on electron behavior in low-dimensional systems in magnetic fields is studied. The systems studied include the superconducting wire network system and the 2D Bloch electron system. For the superconducting wire network system we consider a square network with two different wire sizes in the x and y directions. The asymmetry parameter lambda in this case is the cross-sectional-area ratio of wires in the two directions. A symmetry of lambda to 1/lambda is related to the Aubry-Andre duality and an obvious geometric property of the system. We predict a power-law fading behavior of the magnetic phase boundary on lambda, verified experimentally recently by Itzler el al. (1991). By numerically solving the magnetic band structure of a 2D Bloch electron system of tuneable anisotropy, we find that asymmetry in the hopping strength parameters can lead to closing of the Landau gaps. The asymmetry parameter lambda is the ratio of the hopping strength in the x and y directions for this system. We find that gap closing begins at the center of the band and leads to a curve in Fermi-energy and asymmetry-parameter space which we interpret as a phase boundary. We predict that large anisotropy can lead to quenching of the quantum Hall behavior. The quenching due to large anisotropy in low-dimentional electron systems is speculated to be a general phenomenon. In both the wire-network and Bloch electron systems, electrons are forced to move in a quasi-1D fashion when the asymmetry parameter is large. The 2D phenomena are, thereby, quenched due to the effective reduction of the spatial dimensions.