Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice

TL;DR

This paper demonstrates that quantum spin Hall effects can exist in quasicrystal lattices, expanding the scope of topological insulators beyond crystalline materials by introducing a spin Bott index to characterize their topological states.

Contribution

It introduces the concept of realizing QSH effects in quasicrystals and develops a spin Bott index to identify topological phases in aperiodic systems.

Findings

QSH effect can occur in quasicrystal lattices.

A nonzero spin Bott index indicates a topological QSH state.

Topological phase diagram shows QSH state between insulator and metal phases.

Abstract

Despite the rapid progresses in the field of quantum spin Hall (QSH) effect, most of the QSH systems studied up to now are based on crystalline materials. Here we propose that the QSH effect can be realized in quasicrystal lattices (QLs). We show that the electronic topology of aperiodic and amorphous insulators can be characterized by a spin Bott index $B_s$. The nontrivial QSH state in a QL is identified by a nonzero spin Bott index $B_s=1$, associated with robust edge states and quantized conductance. We also map out a topological phase diagram in which the QSH state lies in between a normal insulator and a weak metal phase due to the unique wavefunctions of QLs. Our findings not only provide a better understanding of electronic properties of quasicrystals but also extend the search of QSH phase to aperiodic and amorphous materials that are experimentally feasible.