Conductivity of 2D lattice electrons in an incommensurate magnetic field

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 σxx(ω). Using a scaling analysis, we have found Rσxx(ω) behaves as 1/ω γ (γ = 0.55) when φ = τ, (τ = √ 5−1 2 ) and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum. Typeset using REVTEX ∗present address: Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan. 1