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 $ϕ$ 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 $σ_{xx}(ω)$. Using a scaling analysis, we have found $\Reσ_{xx}(ω)$ behaves as $1/ω^γ$ \,$(γ=0.55)$ when $ϕ=τ,(τ=\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.