Critical conductance of two-dimensional chiral systems with random magnetic flux

TL;DR

This study numerically investigates the zero-temperature conductance of 2D chiral systems with random magnetic flux, confirming a critical state at the band center and analyzing conductance distributions and localization properties.

Contribution

It provides the first detailed numerical analysis of critical conductance and localization in 2D chiral systems with random magnetic flux, including critical exponents and conductance distribution universality.

Findings

Existence of a critical chiral state at the band center.

Critical exponent for localization length divergence: nu=0.35 +/- 0.03.

Universal conductance distribution outside the band center.

Abstract

The zero temperature transport properties of two-dimensional lattice systems with static random magnetic flux per plaquette and zero mean are investigated numerically. We study the two-terminal conductance and its dependence on energy, sample size, and magnetic flux strength. The influence of boundary conditions and of the oddness of the number of sites in the transverse direction is also studied. We confirm the existence of a critical chiral state in the middle of the energy band and calculate the critical exponent nu=0.35 +/- 0.03 for the divergence of the localization length. The sample averaged scale independent critical conductance <g>_c turns out to be a function of the amplitude of the flux fluctuations whereas the variance of the respective conductance distributions appears to be universal. All electronic states outside of the band center are found to be localized.