Quantum Interference Effects in Topological Nanowires In a Longitudinal Magnetic Field

TL;DR

This paper investigates quantum interference effects in topological nanowires under a longitudinal magnetic field, revealing how Fermi energy tuning affects conduction regimes and interference oscillations, with implications for experimental observations.

Contribution

It predicts the behavior of quantum interference effects in topological nanowires in the quantum limit, including the coexistence of Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations and the visibility of perfectly conducting channels.

Findings

Both AB and AAS oscillations are observed with similar strengths in single wires.

Conductance fluctuations can dominate the average conductance signal.

The sign of the AB signal varies periodically or randomly with Fermi energy depending on conduction regime.

Abstract

We study the magnetoconductance of topological insulator nanowires in a longitudinal magnetic field, including Aharonov-Bohm, Altshuler-Aronov-Spivak, perfectly conducting channel, and universal conductance fluctuation effects. Our focus is on predicting experimental behavior in single wires in the quantum limit where temperature is reduced to zero. We show that changing the Fermi energy $E_F$ can tune a wire from from ballistic to diffusive conduction and to localization. In both ballistic and diffusive single wires we find both Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations with similar strengths, accompanied by quite strong universal conductance fluctuations (UCFs), all with amplitudes between $0.3 \, G_0$ and $1\,G_0$. This contrasts strongly with the average behavior of many wires, which shows Aharonov-Bohm oscillations in the ballistic regime and Altshuler-Aronov-Spivak oscillations in the diffusive regime, with both oscillations substantially larger than the conductance fluctuations. In single wires the ballistic and diffusive regimes can be distinguished by varying $E_F$ and studying the sign of the AB signal, which depends periodically on $E_F$ in ballistic wires and randomly on $E_F$ in diffusive wires. We also show that in long wires the perfectly conducting channel is visible at a wide range of energies within the bulk gap. We present typical conductance profiles at several wire lengths, showing that conductance fluctuations can dominate the average signal. Similar behavior will be found in carbon nanotubes.