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 language | English |
|---|---|
| Article number | 214431 |
| Journal | Physical Review B - Condensed Matter and Materials Physics |
| Volume | 91 |
| Issue number | 21 |
| DOIs | |
| Publication status | Published - 2015 Jun 26 |
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All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
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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 journal › Article
TY - JOUR
T1 - Electrical control and interaction effects of the RKKY interaction in helical liquids
AU - Lee, Yu Wen
AU - Lee, Yu-Li
PY - 2015/6/26
Y1 - 2015/6/26
N2 - 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.
AB - 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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U2 - 10.1103/PhysRevB.91.214431
DO - 10.1103/PhysRevB.91.214431
M3 - Article
AN - SCOPUS:84934324060
VL - 91
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
SN - 1098-0121
IS - 21
M1 - 214431
ER -