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 tothe 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{√{5}-1}{2}) and the Fermi energy is near zero.This behavior is closely related to the known scaling behavior of the spectrum.