Aharonov-Bohm effect in clean strong topological insulator wires

TL;DR

This paper investigates the Aharonov-Bohm effect in clean strong topological insulator wires, revealing flux-dependent electronic transitions, oscillations, and conductance behaviors linked to the Berry phase and wire geometry.

Contribution

It provides a detailed analysis of flux-induced semimetal-semiconductor transitions and conductance oscillations in topological insulator wires, highlighting novel quantum effects.

Findings

Long wires show semimetal-semiconductor transitions at half-odd integer flux.

Conductance peaks at half-odd integer flux approach $e^{2}/h$ for long wires.

Short wires exhibit a universal conductivity of $e^{2}/\pi h$.

Abstract

Surface electrons of strong topological insulator wires acquire a Berry phase difference of $\pi$ on orbiting the wire. This can be detected in response of clean wires (whose Fermi level is tuned to the Dirac point) to the presence of the Aharonov-Bohm flux. Specifically, at half-odd integer applied flux (in units of $hc/e$), long wires undergo semimetal-semiconductor transitions characterized by logarithmically divergent susceptibility. Associated with these are oscillations of magnetization (persistent current) that vanish both at integer and half-odd integer flux. Additionally wires of arbitrary aspect ratio exhibit conductance maxima at half-odd integer applied flux and minima at integer flux. For long wires the maxima are sharp with their height approaching $e^{2}/h$. Short wires are characterized by a universal conductivity $e^{2}/\pi h$ attained in the disc limit.