Non-Superconducting Non-Abelian Statistics in One-Dimensional Topological Insulators

TL;DR

This paper predicts that certain one-dimensional topological insulators can exhibit non-Abelian statistics and support topologically-protected quantum gates without the need for superconductivity, based on theoretical and numerical evidence.

Contribution

It introduces a new class of topological phases in 1D insulators with large bandgaps that show non-Abelian statistics without superconductivity or magnetic fields.

Findings

Presence of gapless boundary states linked to nontrivial Zak phases

Quantized electric polarization in these materials

Transverse fields induce a longitudinal polarization

Abstract

Topological materials are of great interest for applications in quantum computing, providing intrinsic robustness against environmental noises. A popular direction is to look for Majorana modes in integrated systems interfaced with superconducting materials. However, is superconductivity necessary for materials to exhibits non-abelian statistics? Here we predict with strong theoretical and numerical evidences that there exist topologically phases in a class of one-dimensional single crystals, which contain large bandgaps and are within experimental reach. Specifically, the nontrivial Zak phases are associated with gapless boundary states, which provides the non-Abelian statistics required for constructing topologically-protected quantum gates, even without superconductivity and magnetic field. Another anomalous feature of these materials is that the electric polarization is quantized and a transverse field induces a longitudinal polarization. This novel material property provides an experimentally-accessible mechanism for braiding the non-Abelian anyons.