Two dimensional electron transport in disordered and ordered distributions of magnetic flux vortices

TL;DR

This paper investigates how a two-dimensional electron gas behaves under inhomogeneous magnetic fields, analyzing scattering phase shifts and Hall conductivity in disordered and periodic vortex arrangements, revealing topological effects.

Contribution

It provides analytical calculations of scattering phase shifts and numerical results for Hall conductivity, highlighting topological charge effects in vortex-induced magnetic fields.

Findings

Analytical phase shift calculations for electron-vortex scattering.

Numerical Hall conductivity showing characteristic spikes.

Interpretation of spikes as topological charge accumulation.

Abstract

We have considered the conductivity properties of a two dimensional electron gas (2DEG) in two different kinds of inhomogeneous magnetic fields, i.e.\ a disordered distribution of magnetic flux vortices, and a periodic array of magnetic flux vortices. The work falls in two parts. In the first part we show how the phase shifts for an electron scattering on an isolated vortex, can be calculated analytically, and related to the transport properties through the differential cross section. In the second part we present numerical results for the Hall conductivity of the 2DEG in a periodic array of flux vortices found by exact diagonalization. We find characteristic spikes in the Hall conductance, when it is plotted against the filling fraction. It is argued that the spikes can be interpreted in terms of ``topological charge'' piling up across local and global gaps in the energy spectrum.