Quantum interference effects in topological nanowires in a longitudinal magnetic field

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 EF 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 G0 and 1 G0. This contrasts strongly with the average behavior of many wires, which shows Aharonov-Bohm oscillations in the ballistic regime and AltshulerAronov-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 EF and studying the sign of the AB signal, which depends periodically on EF in ballistic wires and randomly on EF 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. Strong topological insulators (TIs) possess a band gap that can be used to eliminate electrical conduction through their interior, but unlike standard insulators they robustly host conducting surface states which completely wrap all of the TI sample's surfaces.1,2 This unique circumstance allows realization of the celebrated Aharonov-Bohm effect, where electrons are sensitive to the total magnetic flux through a specific loop.3,4 If a TI wire has strictly constant cross-section along the wire's length, and the surface state has strictly zero penetration into the interior, then the wire's conductance G will be a strictly periodic function of the magnetic flux Φ through the wire's cross-section, i.e. G(Φ) = G(Φ + Φ 0 ), where Φ 0 = h/e is the magnetic flux quantum. This periodic dependence on the total magnetic flux threading the electron's path, and not on any local details of the path, is the hallmark of the Aharonov-Bohm (AB) effect.A long string of experiments has realized the AB effect in TI wires, and has observed a zoo of periodic conductance features. One may distinguish between AharonovBohm oscillations with period Φ 0 and Altshuler-AronovSpivak (AAS) oscillations with period Φ 0 /2.5-23 In addition Universal Conductance Fluctuations (UCFs) are observed -a noise-like component of G(Φ) which depends sensitively on the Fermi level and on disorder. 5,9,24-30TIs also host a Perfectly Conducting Channel (PCC) -a conductance quantum which is remarkable for its persistence in very long TI wires, its topological...

Adjustable Quantum Interference Oscillations in Sb-Doped Bi2Se3 Topological Insulator Nanoribbons

“…In addition, the temperature dependence of ABOs follows the diffusive 16,19 or quasi-ballistic 14,17,20 transport behavior for the same kind of NRs with similar geometric dimensions. Finally, the crossover between AB and AAS oscillations in TI NRs is expected based on theory 11,24 ; however, its experimental verification has not been performed yet.…”

Quantum Transport in Nanostructures of 3D Topological Insulators

“…The interplay between the disorder and the perfectly transmitted mode was further investigated in ref. [16].…”

“…[ 1 ] Such new properties have direct consequences on the quantum transport of Dirac fermions, showing a very rich physics that can be revealed in simple geometries of mesoscopic conductors such as nanowires (NWs) or nanoribbons. [ 4–20 ]…”

Electronic Conduction in Disordered Materials: Wave-like or Particle-like?

“…We performed numerical simulations of conduction in single TI wires where the scattering length was comparable to or longer than the wire perimeter, but was much smaller than the wire length, putting each wire in the diffusive regime. 22 We showed that in a single wire [or nanotube, etc.] ALL winding numbers will be seen, including AB oscillations, AAS oscillations, and all higher winding numbers.…”