On the Cutting Edge: Helical Liquids in Time-Reversal-Invariant Topological Materials

Abstract

In this perspective, we discuss the unique electronic properties of helical liquids appearing at the boundaries of time-reversal-invariant topological materials and highlight the key challenges impeding progress in this field. We advocate for a deeper theoretical understanding of the many-body aspects of these systems to gain insights into helical liquids and the potential stabilization of topological zero modes. Such advancements are crucial for extensively exploring quantum phenomena and for the advancement of quantum science and engineering.

Figures (2)

• Figure 1: Fundamental properties and observable features of helical liquids, spanning their band structure, spectroscopic signatures, and transport behavior. (a) Energy spectrum of helical edge states crossing the bulk gap, illustrating spin-momentum locking. (b) When the Fermi level, tuned by the gate voltage, lies within the bulk gap, the edge conductance becomes quantized at the universal value $e^{2}/h$ (with $e$ the elementary charge and $h$ the Planck constant) in the absence of elastic backscattering, as illustrated in panel (d). (c) Schematic illustration of a QSHI protected by time-reversal symmetry. The gapless modes reside in the edge channels, with counter-propagating spin states indicated in red and blue. (d) In helical liquids, elastic backscattering processes are forbidden in the absence of spin-flip mechanisms, while forward scattering due to electron-electron interactions remains allowed and can lead to correlated effects. (e) The rescaled local density of states $\rho(\epsilon)$ follows the curve described by Eq. (\ref{['Eq:DOS']}), where the exponent $\alpha$ depends on the forward-scattering strength of electron–electron interactions, as schematically depicted in panel (d).
• Figure 2: Illustrations of device concepts for probing helical liquids or exploiting them in realistic architectures. (a) A Josephson junction composed of a QSHI ring and a C-shaped superconducting layer, where the supercurrent is mediated by helical edge states and its flux dependence reveals the topological nature of the junction. (b) Heterostructure integrating a QSHI layer with a van der Waals (vdW) material, allowing proximity-induced spin-orbit coupling or superconductivity. (c) Quantum point contact formed in a QSHI, serving as a controllable constriction for probing backscattering and correlation effects when multiple helical edges are brought into proximity. (d) Two QSHI layers coupled to a superconductor, where nonlocal pairing can stabilize Majorana Kramers pairs, and in the fractional regime, parafermion zero modes may emerge.