# Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator

## TL;DR

This paper demonstrates the presence of Tomonaga-Luttinger liquid behavior in the edge channels of a 2D topological insulator, bismuthene on SiC, revealing significant electronic correlations at the edges.

## Contribution

It provides the first spectroscopic evidence of 1D electronic correlation effects in topological edge states of a 2D topological insulator, identifying a Tomonaga-Luttinger liquid regime.

## Key findings

- Observation of metallic edge channels with 1D correlation effects
- Identification of Tomonaga-Luttinger liquid behavior through universal scaling
- Derivation of a TLL parameter indicating intermediate electronic interactions

## Abstract

Topological quantum matter is characterized by non-trivial global invariants of the bulk which induce gapless electronic states at its boundaries. A case in point are two-dimensional topological insulators (2D-TI) which host one-dimensional (1D) conducting helical edge states protected by time-reversal symmetry (TRS) against single-particle backscattering (SPB). However, as two-particle scattering is not forbidden by TRS [1], the existence of electronic interactions at the edge and their notoriously strong impact on 1D states may lead to an intriguing interplay between topology and electronic correlations. In particular, it is directly relevant to the question in which parameter regime the quantum spin Hall effect (QSHE) expected for 2D-TIs becomes obscured by these correlation effects that prevail at low temperatures [2]. Here we study the problem on bismuthene on SiC(0001) which has recently been synthesized and proposed to be a candidate material for a room-temperature QSHE [3]. By utilizing the accessibility of this monolayer-substrate system on atomic length scales by scanning tunneling microscopy/spectroscopy (STM/STS) we observe metallic edge channels which display 1D electronic correlation effects. Specifically, we prove the correspondence with a Tomonaga-Luttinger liquid (TLL), and, based on the observed universal scaling of the differential tunneling conductivity (dI/dV), we derive a TLL parameter K reflecting intermediate electronic interaction strength in the edge states of bismuthene. This establishes the first spectroscopic identification of 1D electronic correlation effects in the topological edge states of a 2D-TI.