Two-dimensional electron transport in the presence of magnetic flux vortices

TL;DR

This paper investigates how inhomogeneous magnetic flux vortices affect the electrical conductivity and Hall effect in a two-dimensional electron gas, revealing characteristic peaks linked to topological properties.

Contribution

It analytically calculates phase shifts for electron scattering on isolated vortices and numerically explores Hall conductivity in vortex arrays, connecting results to topological charge effects.

Findings

Analytical phase shift calculations for vortex scattering.

Numerical Hall conductivity results showing peaks at specific filling fractions.

Interpretation of peaks 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 a force balance equation. In the second part we present numerical results for the Hall conductivity of the 2DEG in a periodic array of flux vortices. We find characteristic peaks in the Hall conductance, when plotted against the filling fraction. It is argued that the peaks can be interpreted in terms of ``topological charge'' piling up across local and global gaps in the energy spectrum.