Electrically tunable two-channel Kondo fixed points in helical liquids

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.

6 pages, 1 figure

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Conductance of a helical edge liquid coupled to a magnetic impurity
• Properties of anisotropic magnetic impurities on surfaces
• Electrical manipulation and measurement of spin properties of quantum spin Hall edge states
• Electrical control of the Kondo effect in a helical edge liquid

Cited by in corpus (4)

• Transport via double constrictions in integer and fractional topological insulators
• Edge Physics of the Quantum Spin Hall Insulator from a Quantum Dot Excited by Optical Absorption
• Two-channel Kondo problem in coupled interacting helical liquids
• Natural orbitals renormalization group approach to a spin-1/2 impurity interacting with two helical liquids