Aharonov-Bohm interference for a hole in a two-dimensional Ising antiferromagnet in a transverse magnetic field

TL;DR

This paper demonstrates that considering Trugman loops results in a low effective mass for a hole in a 2D Ising antiferromagnet and explores how Aharonov-Bohm interference affects its magnetic properties.

Contribution

It introduces a detailed analysis of hole dynamics including Trugman loops and reveals the impact of Aharonov-Bohm interference on magnetic field dependence.

Findings

Low effective mass due to Trugman loops.

Unusual magnetic field dependence of hopping integrals.

Altered cyclotron frequency and Hofstadter butterfly patterns.

Abstract

We show that a proper consideration of the contribution of Trugman loops leads to a fairly low effective mass for a hole moving in a square lattice Ising antiferromagnet, if the bare hopping and the exchange energy scales are comparable. This contradicts the general view that because of the absence of spin fluctuations, this effective mass must be extremely large. Moreover, in the presence of a transverse magnetic field, we show that the effective hopping integrals acquire an unusual dependence on the magnetic field, through Aharonov-Bohm interference, in addition to significant retardation effects. The effect of the Aharonov-Bohm interference on the cyclotron frequency (for small magnetic fields) and the Hofstadter butterfly (for large magnetic fields) is analyzed.