Münster 1999 – wissenschaftliches Programm

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HL: Halbleiterphysik

HL 16: Quanten Hall Effekt

HL 16.9: Vortrag

Dienstag, 23. März 1999, 12:30–12:45, H3

Semiclassical theory of transport in a random magnetic field — •A. Mirlin, F. Evers, D. Polyakov, and P. W"olfle — Institut f"ur Theorie der Kondensierten Materie, Uni Karlsruhe, 76128 Karlsruhe

We present a detailed description of the semiclassical kinetics of two-dimensional fermions in a smoothly varying inhomogeneous magnetic field B(r). We show that the nature of the transport depends crucially on the strength of the random component of B(r). At zero mean B, the governing parameter is α=d/R₀, where d is the correlation length of disorder and R₀ is the Larmor radius in the field B₀, the characteristic amplitude of the fluctuations of B(r). While at α≪ 1 the conventional Drude theory applies, at α≫ 1 most particles follow adiabatic dynamics and are localized on almost periodic orbits. The conductivity is determined by the percolation of a special class of trajectories, the “snake states". The field B also suppresses the stochastic diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to the (exponentially weak) violation of the adiabaticity of the rapid cyclotron rotation. We argue that at α≫ 1 the external field yields a sharp transition between the snake-state percolation and the percolation of the drift orbits. The peculiar nature of the transport in the random magnetic field shows up in the ac conductivity, leading to a strong dispersion at low frequencies. We demonstrate that σ_xx(ω) of the composite fermions at ν=1/2 has a sharp kink at zero ω (σ_xx∝ |ω|) and falls off exponentially at large ω. We discuss the nature of the quantum magnetooscillations. We also perform detailed numerical study of the transport in the field B(r).