Electrically tunable two-channel Kondo fixed points in helical liquids

TL;DR

This paper explores how a quantum dot coupled to helical edge states exhibits electrically tunable two-channel Kondo fixed points, revealing a new phase and critical behavior influenced by electron interactions and external electric fields.

Contribution

It identifies a new two-channel Kondo fixed point in helical liquids and demonstrates how external electric fields can tune between different quantum phases.

Findings

Existence of two distinct two-channel Kondo fixed points depending on interaction strength.

Discovery of a continuous phase transition between fixed points controlled by electric field.

Characterization of the critical point as a free Dirac fermion backscattered by a local potential.

Abstract

We study a quantum dot coupled to two edge states of a quantum spin Hall insulator through electron tunnelings in the presence of a Rashba spin-orbital interaction induced by an external electric field. We show that if the electron interactions on the edge states are repulsive, there are two possible phases, depending on the Luttinger liquid parameter $K$. For $1/2<K<1$, the low-temperature physics is controlled by a previously identified two-channel Kondo fixed point. For the edge states with even stronger repulsive interactions, i.e. $1/4<K<1/2$, the system reaches another phase at low temperatures, described by a new two-channel Kondo fixed point. This phase is separated from the original one by a continuous phase transition upon varying the value of $K$ through the external electric field. The corresponding critical point is described by a free Dirac fermion backscattered by a local potential. We investigate the low-temperature properties associated with this new fixed point and also discuss the scaling behaviors of the system at the critical point.