The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

Details The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations

2004-01-28

arxiv.org/abs/cond-mat/0401564v1

Phys. Rev. B 70, 165318 (2004).

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

13 pages, 11 figures

Scientific paper

10.1103/PhysRevB.70.165318

We use the Kubo-Landauer formalism to compute the longitudinal (two-terminal) conductance of a two dimensional electron system placed in a strong perpendicular magnetic field, and subjected to periodic modulations and/or disorder potentials. The scattering problem is recast as a set of inhomogeneous, coupled linear equations, allowing us to find the transmission probabilities from a finite-size system computation; the results are exact for non-interacting electrons. Our method fully accounts for the effects of the disorder and the periodic modulation, irrespective of their relative strength, as long as Landau level mixing is negligible. In particular, we focus on the interplay between the effects of the periodic modulation and those of the disorder. This appears to be the relevant regime to understand recent experiments [S. Melinte {\em et al}, Phys. Rev. Lett. {\bf 92}, 036802 (2004)], and our numerical results are in qualitative agreement with these experimental results. The numerical techniques we develop can be generalized straightforwardly to many-terminal geometries, as well as other multi-channel scattering problems.

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