The effect of a small magnetic flux on the metal-insulator transition

TL;DR

This study demonstrates that even tiny magnetic fluxes can significantly influence the metal-insulator transition in disordered systems, revealing a power-law relationship and boundary condition effects.

Contribution

The paper provides numerical evidence that small magnetic fluxes cause a strong shift in the transition point, confirming theoretical predictions and exploring boundary condition impacts.

Findings

Small magnetic fluxes significantly shift the transition point.

The power law for the shift holds only at very small fields.

Critical level-spacing distribution is identical under certain boundary conditions.

Abstract

We numerically show that very small magnetic flux can significantly shift the metal-insulator transition point in a disordered electronic system. The shift we observe for the 3d Anderson model obeys a power law as predicted by Larkin and Khmel'nitskii (1981). We compute the exponent and find good agreement with the prediction. However, the power law holds only for much smaller magnetic fields than has been previously assumed, and is accompanied by a large prefactor, leading to a surprising strong dependence of the transition point on the applied magnetic field. Furthermore, we show that the critical level-spacing distribution is identical in the presence and absence of a magnetic field if hard-wall boundary conditions are applied. This result is surprising since both cases belong to different universality classes and different distributions have been reported for periodic boundary conditions.