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

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) by tuning Kondo couplings at a fixed Luttinger parameter $K<1$. The system can be mapped onto an anisotropic two-channel Kondo Hamiltonian, and the 2CK fixed point was argued to be stable for infinitesimally weak tunnelings between dot and the 2DTI. We re-examine this model beyond the bare scaling dimension analysis via a controlled perturbative renormalization group (RG) approach combined with bosonization and re-fermionization techniques near weak-coupling and strong-coupling (2CK) fixed points. For $K$ close to but less than $1$, we find 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. Our system serves as the first example of the 1CK-2CK QPT that is accessible by the controlled RG approach though this transition has been known to exist in Kondo dot coupled to two conventional Luttinger liquid leads with a critical value $K_c=1/2$. We extract quantum critical and crossover behaviors from various observables near criticality.