Conductivity of 2D lattice electrons in an incommensurate magnetic field

TL;DR

This paper investigates the electrical conductivity of two-dimensional lattice electrons under incommensurate magnetic flux, revealing a power-law frequency dependence linked to spectral scaling.

Contribution

It introduces a method to analyze conductivity in incommensurate magnetic fields by approximating irrational fluxes with converging commensurate systems, and identifies a specific frequency scaling behavior.

Findings

Re(σ_xx(ω)) scales as 1/ω^γ with γ=0.55 near zero Fermi energy.

The conductivity behavior is closely related to the spectral scaling properties.

The study provides insights into electron transport in incommensurate magnetic systems.

Abstract

We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette $\phi$ 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 $\phi =\tau,(\tau =\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.