Band gap in Bi2Se3 topological insulator nanowires: magnetic and geometrical effects

TL;DR

This paper investigates how magnetic fields and geometrical shapes influence the electronic band gap in Bi2Se3 topological insulator nanowires, revealing unexpected gap closures due to interference effects.

Contribution

It provides a comprehensive theoretical analysis of quantum interference effects on the low energy spectrum of variously shaped Bi2Se3 nanowires, including new insights into geometrical influences.

Findings

Magnetic fields larger than expected are needed to close the band gap.

Geometrical quantum interference can close the gap without magnetic fields.

Different cross-sectional shapes significantly affect the electronic properties.

Abstract

Stimulated by the recent realization of three dimensional topological insulator nanowire interfer- ometers, a theoretical analysis of quantum interference effects on the low energy spectrum of Bi2Se3 nanowires is presented. The electronic properties are analyzed in nanowires with circular, square and rectangular cross-sections starting from a continuum three dimensional model with particular emphasis on magnetic and geometrical effects. The theoretical study is based on numerically exact diagonalizations of the discretized model for all the geometries. In the case of the cylindrical wire, an approximate analytical solution of the continuum model is also discussed. Although a magnetic field corresponding to half quantum flux is expected to close the band gap induced by Berry phase, in all the studied geometries with finite area cross-sections, the gap closes for magnetic fields typically larger than those expected. Furthermore, unexpectedly, due to geometrical quantum interference effects, for a rectangular wire with a sufficiently large aspect ratio and smaller side ranging from 50{\deg}A and 100{\deg}A, the gap closes for a specific finite area cross-section without the application of a magnetic field.