Helical Quantum Edge Gears in 2D Topological Insulators

TL;DR

This paper proposes a method to measure the Luttinger liquid parameter in helical edge states of 2D topological insulators using Coulomb drag, revealing temperature-dependent conductance behaviors.

Contribution

It introduces a two-terminal transport technique in Coulomb drag geometry to determine the LL parameter in helical edge states of 2D TIs with Rashba coupling, including temperature effects.

Findings

Conductance in perfect drag regime is $(e^2/h)(2 K + 1)/(K + 1)$ at low T.

Conductivity scales as $T^{-4K+3}$ at higher T.

Single edge conductivity is also calculated.

Abstract

We show that two-terminal transport can measure the Luttinger liquid (LL) parameter $K$, in helical LLs at the edges of two dimensional topological insulators (TIs) with Rashba spin-orbit coupling. We consider a Coulomb drag geometry with two coplanar TIs and short-ranged spin-flip inter-edge scattering. Current injected into one edge loop induces circulation in the second, which floats without leads. In the low-temperature ($T \rightarrow 0$) perfect drag regime, the conductance is $(e^2/h)(2 K + 1)/(K + 1)$. At higher $T$ we predict a conductivity $\sim T^{-4K+3}$. The conductivity for a single edge is also computed.