Conductivity of 2D lattice electrons in an incommensurate magnetic field

Abstract

We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette $\varphi$ is irrational (incommensurate flux). To realize the system with the incommensurate flux, we consider a series of systems with commensurate fluxes which converge to the irrational value. We have calculated a real part of the longitudinal conductivity ${\sigma }_{xx}(\omega )$. Using a scaling analysis, we have found $\Re {\sigma }_{xx}(\omega )$ behaves as $1/{\omega }^{\gamma }$ \,$(\gamma =0.55)$ when $\varphi =\tau ,(\tau =\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.

arXiv comment16 pages, postscript files are available on request

References in corpus (1)

• Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field

Cited by in corpus (2)

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• The effect of in-plane magnetic field on the spin Hall effect in Rashba-Dresselhaus system