Quantum criticality in Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators

TL;DR

This paper theoretically investigates the quantum phase transition between one-channel and two-channel Kondo fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators, revealing conditions for stability and critical behavior.

Contribution

It re-examines the Kondo transition in helical edge states using a 1-loop RG approach, identifying the instability of the 2CK fixed point near K=1 and characterizing the quantum critical point.

Findings

The 2CK fixed point becomes unstable as K approaches 1.

A quantum phase transition occurs between 1CK and 2CK fixed points.

Quantum critical and crossover behaviors are characterized near the transition.

Abstract

We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (1CK) and two-channel Kondo (2CK) fixed points in a quantum dot coupled to helical edge states of interacting 2D topological insulators (2DTI) with Luttinger parameter $0<K<1$. The model has been studied in Ref. 21, and was mapped onto an anisotropic two-channel Kondo model via bosonization. For K<1, the strong coupling 2CK fixed point was argued to be stable for infinitesimally weak tunnelings between dot and the 2DTI based on a simple scaling dimensional analysis[21]. We re-examine this model beyond the bare scaling dimension analysis via a 1-loop renormalization group (RG) approach combined with bosonization and re-fermionization techniques near weak-coupling and strong-coupling (2CK) fixed points. We find for K -->1 that the 2CK fixed point can be unstable towards the 1CK fixed point and the system may undergo a quantum phase transition between 1CK and 2CK fixed points. The QPT in our model comes as a result of the combined Kondo and the helical Luttinger physics in 2DTI, and it serves as the first example of the 1CK-2CK QPT that is accessible by the controlled RG approach. We extract quantum critical and crossover behaviors from various thermodynamical quantities near the transition. Our results are robust against particle-hole asymmetry for 1/2<K<1.