Electrical control and interaction effects of the RKKY interaction in helical liquids

Yu Wen Lee, Yu-Li Lee

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We study the RKKY interaction mediated by the helical edge states of a quantum spin Hall insulator in the presence of the Rashba spin-orbital coupling induced by an external electric field and the electron-electron interaction. We show that in the presence of the Rashba coupling, the RKKY interaction induced by the helical edge states contains not only the Heisenberg-like and the Dzyaloshinskii-Moria terms, but also the nematic-type term that is not present in the absence of the Rashba coupling. Moreover, the range functions depend on the strength of the Rashba coupling. We also show that the electron-electron interaction changes the strength of the RKKY interaction by modifying the power of the 1/|x| dependence of the range functions. In particular, by varying the strength of the interaction or the Rashba coupling, there is an (impurity) quantum phase transition involving the sign change of the RKKY interaction at the value of the Luttinger liquid parameter K=1/2. Since both the strength of the Rashba coupling and the chemical potential of the helical edge states are electrically controllable by external gate voltages, our results not only shed light on the nature of magnetic impurity correlations in the edge of a two-dimensional topological insulator, but also pave a way to manipulate the qubits in quantum computing.

Original languageEnglish
Article number214431
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume91
Issue number21
DOIs
Publication statusPublished - 2015 Jun 26

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Electron-electron interactions
Impurities
Chemical potential
Liquids
liquids
Phase transitions
Electric fields
interactions
electron scattering
Electric potential
insulators
impurities
quantum computation
electrons
orbitals
electric fields
electric potential

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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title = "Electrical control and interaction effects of the RKKY interaction in helical liquids",
abstract = "We study the RKKY interaction mediated by the helical edge states of a quantum spin Hall insulator in the presence of the Rashba spin-orbital coupling induced by an external electric field and the electron-electron interaction. We show that in the presence of the Rashba coupling, the RKKY interaction induced by the helical edge states contains not only the Heisenberg-like and the Dzyaloshinskii-Moria terms, but also the nematic-type term that is not present in the absence of the Rashba coupling. Moreover, the range functions depend on the strength of the Rashba coupling. We also show that the electron-electron interaction changes the strength of the RKKY interaction by modifying the power of the 1/|x| dependence of the range functions. In particular, by varying the strength of the interaction or the Rashba coupling, there is an (impurity) quantum phase transition involving the sign change of the RKKY interaction at the value of the Luttinger liquid parameter K=1/2. Since both the strength of the Rashba coupling and the chemical potential of the helical edge states are electrically controllable by external gate voltages, our results not only shed light on the nature of magnetic impurity correlations in the edge of a two-dimensional topological insulator, but also pave a way to manipulate the qubits in quantum computing.",
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Electrical control and interaction effects of the RKKY interaction in helical liquids. / Lee, Yu Wen; Lee, Yu-Li.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 91, No. 21, 214431, 26.06.2015.

Research output: Contribution to journalArticle

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