# Dynamical transport measurement of the Luttinger parameter in helical edges states of 2D topological insulators

## TL;DR

This paper proposes a novel dynamical method using time-of-flight experiments to measure the Luttinger parameter in helical edge states of 2D topological insulators, leveraging their robustness against backscattering.

## Contribution

It introduces a new dynamical measurement technique for the Luttinger parameter K in helical Luttinger liquids of 2D topological insulators.

## Key findings

- The proposed method enables direct measurement of K.
- Helical edge states are ideal for testing due to their robustness.
- The approach offers a practical way to characterize electron interactions.

## Abstract

One-dimensional (1D) electron systems in the presence of Coulomb interaction are described by Luttinger liquid theory. The strength of Coulomb interaction in the Luttinger liquid, as parameterized by the Luttinger parameter K, is in general difficult to measure. This is because K is usually hidden in powerlaw dependencies of observables as a function of temperature or applied bias. We propose a dynamical way to measure K on the basis of an electronic time-of-flight experiment. We argue that the helical Luttinger liquid at the edge of a 2D topological insulator constitutes a preeminently suited realization of a 1D system to test our proposal. This is based on the robustness of helical liquids against elastic backscattering in the presence of time reversal symmetry.