Dimensional crossover of transport characteristics in topological insulator nanofilms

TL;DR

This paper investigates how stacking 2D topological insulator layers leads to different 3D topological phases, revealing two distinct conduction regimes and the effects of stacking on topological properties and conductance.

Contribution

It introduces a new conjecture on the dimensional crossover of topological insulators and analyzes conductance and topological indices during stacking-induced phase transitions.

Findings

Identification of two complementary conduction regimes: surface and edge conduction.

Demonstration that stacking layers can invert the energy gap, offering an alternative to spin-orbit coupling control.

Observation that the quantum spin Hall phase can occur with both odd and even layer numbers.

Abstract

We show how the two-dimensional (2D) topological insulator evolves, by stacking, into a strong or weak topological insulator with different topological indices, proposing a new conjecture that goes beyond an intuitive picture of the crossover from quantum spin Hall to the weak topological insulator. Studying the conductance under different boundary conditions, we demonstrate the existence of two conduction regimes in which conduction happens through either surface- or edge-conduction channels. We show that the two conduction regimes are complementary and exclusive. Conductance maps in the presence and absence of disorder are introduced, together with 2D $\mathbb{Z}_2$-index maps, describing the dimensional crossover of the conductance from the 2D to the 3D limit. Stacking layers is an effective way to invert the gap, an alternative to controlling the strength of spin-orbit coupling. The emerging quantum spin Hall insulator phase is not restricted to the case of odd numbers of layers.