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

Abstract

We investigate theoretically the quantum phase transition (QPT) between the one-channel Kondo (ICK) 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 was studied by Law et al (2010 Phys. Rev. B 81 041305(R)), 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 the dot and the 2DTI based on a simple scaling dimensional analysis (Law et al 2010 Phys. Rev. B 81 041305(R). We re-examine this model beyond the bare scaling dimension analysis via a one-loop renormalization group (RG) approach combined with bosonization and re-fermionization techniques near weak-coupling and strong-coupling (2CK) fixed points. We find for a fixed value of K < 1 that the 2CK fixed point can be unstable towards the 1CK fixed point and the system is expected to undergo a quantum phase transition between 1CK and 2CK fixed points with changing Kondo couplings. Our RG approach is controlled near K = 1. In general, this QPT can also occur upon tuning the Luttinger parameter K to a critical value K-c smaller than unity (0 < K-c < 1) for fixed Konodo couplings. 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.