Helical Liquids in Semiconductors

TL;DR

This review discusses the theory, realization, and experimental challenges of helical liquids in semiconductors, highlighting their topological properties, stability, and potential for quantum computing applications.

Contribution

It provides a comprehensive overview of the theoretical understanding and experimental status of helical liquids in semiconductors, including their topological protection and superconducting prospects.

Findings

Quantized conductance predicted but challenging to observe experimentally

Various backscattering mechanisms affect conductance quantization

Proximity-induced superconductivity enables Majorana bound states

Abstract

One-dimensional helical liquids can appear at boundaries of certain condensed matter systems. Two prime examples are the edge of a quantum spin Hall insulator and the hinge of a three-dimensional second-order topological insulator. For these materials, the presence of a helical state at the boundary serves as a signature of their nontrivial electronic bulk topology. Additionally, these boundary states are of interest themselves, as a novel class of strongly correlated low-dimensional systems with interesting potential applications. Here, we review existing results on such helical liquids in semiconductors. Our focus is on the theory, though we confront it with existing experiments. We discuss various aspects of the helical liquids, such as their realization, topological protection and stability, or possible experimental characterization. We lay emphasis on the hallmark of these states, being the prediction of a quantized electrical conductance. Since so far reaching a well-quantized conductance has remained challenging experimentally, a large part of the review is a discussion of various backscattering mechanisms which have been invoked to explain this discrepancy. Finally, we include topics related to proximity-induced topological superconductivity in helical states, as an exciting application towards topological quantum computation with the resulting Majorana bound states.