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arXiv:1303.1896 · Physical Review B

Electrically tunable two-channel Kondo fixed points in helical liquids

Yu-Li Lee, Yu-Wen Lee

Published Jul 9, 2013• 5 citations
arXivHTMLPDF

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.

DOI
10.1103/physrevb.88.035112

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We investigate the effects of the electron-electron interactions on the quantum transport through a charge Kondo circuit. The setup consists of a quantum dot sandwiched between two leads by two nearly transparent single mode quantum point contacts. The size of the interacting area LLL in the Luttinger liquid formed in the vicinities of the narrow constrictions is assumed to be much smaller compared to the size of the quantum dot aaa. We predict that the interplay between the electron-electron interactions in the Luttinger liquid and the fingerprints of the non-Fermi liquid behavior in the vicinity of the two channel Kondo intermediate coupling fixed point allows one to determine the interaction strength through the power-law temperature scaling of the electric conductance.
We report on exact results for the low-temperature thermodynamics of a spin- 12\frac{1}{2}21​ magnetic impurity coupled to a one-dimensional interacting electron system. By using boundary conformal field theory, we show that there are only two types of critical behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a theory with an anomalous response identical to that recently proposed by Furusaki and Nagaosa. Suppression of backscattering off the impurity leads to the same critical properties as for the two-channel Kondo effect.