Magnetic response of non-interacting and interacting electrons in a M\"{o}bius strip

TL;DR

This paper explores the magnetic response of electrons in a M"{o}bius strip, revealing how topology, interactions, and temperature influence persistent currents, with implications for topological material transport.

Contribution

It provides a combined analytical and Hartree-Fock approach to study electron behavior in a M"{o}bius strip, highlighting anomalous persistent current features due to topology and interactions.

Findings

Persistent current shows anomalous flux dependence.

Current decreases exponentially with temperature for certain sizes.

Interplay of topology and interactions causes unique electronic features.

Abstract

We investigate characteristic features of both non-interacting and interacting electrons in a M\"{o}bius strip, the simplest possible one-sided topological system, in presence of an Aharonov-Bohm flux $\phi$. Using Hartree-Fock mean field theory we determine energy eigenvalues for the interacting model, while for the non-interacting system an analytical prescription is given. The interplay between longitudinal and vertical motions of electrons along with on-site Hubbard interaction yield several anomalous features of persistent current associated with energy-flux characteristics. The variation of current with system size and its temperature dependences are also critically examined. Current is highly sensitive to both these two factors, and we find that for a particular system size it decreases exponentially with temperature. Our analysis can be helpful in investigating electronic transport through any non-trivial topological material.