Coulomb drag between helical Luttinger liquids

TL;DR

This paper investigates Coulomb drag between helical edges in quantum spin Hall insulators, revealing a nonmonotonic temperature dependence and unique plasmon-mediated effects due to the helical nature and Dirac spectrum.

Contribution

It introduces a theoretical analysis of Coulomb drag in helical Luttinger liquids, highlighting novel temperature behavior and plasmon effects absent in conventional systems.

Findings

Drag resistivity vanishes as temperature decreases at low T.

Drag is mediated by plasmons at higher T, unlike in standard Luttinger liquids.

Unique Umklapp scattering linked to Dirac points influences drag behavior.

Abstract

We theoretically study Coulomb drag between two helical edges with broken spin-rotational symmetry, such as would occur in two capacitively coupled quantum spin Hall insulators. For the helical edges, Coulomb drag is particularly interesting because it specifically probes the inelastic interactions that break the conductance quantization for a single edge. Using the kinetic equation formalism, supplemented by bosonization, we find that the drag resistivity $\rho_D$ exhibits a nonmonotonic dependence on the temperature $T$. In the limit of low $T$, $\rho_D$ vanishes with decreasing $T$ as a power law if intraedge interactions are not too strong. This is in stark contrast to Coulomb drag in conventional quantum wires, where $\rho_D$ diverges at $T\to 0$ irrespective of the strength of repulsive interactions. Another unusual property of Coulomb drag between the helical edges concerns higher $T$ for which, unlike in the Luttinger liquid model, drag is mediated by plasmons. The special type of plasmon-mediated drag can be viewed as a distinguishing feature of the helical liquid---because it requires peculiar Umklapp scattering only available in the presence of a Dirac point in the electron spectrum.