Manipulation of the Majorana Ising spin via Rashba-Dresselhaus spin-orbit coupling

doi:10.1088/1674-1056/ae43cd

中国物理B ›› 2026, Vol. 35 ›› Issue (6): 67404-067404.doi: 10.1088/1674-1056/ae43cd

Manipulation of the Majorana Ising spin via Rashba-Dresselhaus spin-orbit coupling

Lili Liu(刘利利)^1,2,†,‡, Qi-Sheng Xu(徐其胜)^2,†, Cai Chen(陈才)³, Chui-Zhen Chen(陈垂针)^4,§, and Dong-Hui Xu(许东辉)^2,5,¶

1 College of Teacher Education, Chongqing Three Gorges University, Chongqing 404100, China;
2 Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 400044, China;
3 School of Civil Engineering, Chongqing Three Gorges University, Chongqing 404100, China;
4 Institute for Advanced Study and School of Physical Science and Technology, Soochow University, Suzhou 215006, China;
5 Center of Quantum Materials and Devices, Chongqing University, Chongqing 400044, China

收稿日期:2025-12-14 修回日期:2026-01-28 接受日期:2026-02-10 出版日期:2026-05-28 发布日期:2026-05-28
通讯作者: Lili Liu, Chui-Zhen Chen, Dong-Hui Xu E-mail:liulili0612@163.com;czchen@suda.edu.cn;donghuixu@cqu.edu.cn

Manipulation of the Majorana Ising spin via Rashba-Dresselhaus spin-orbit coupling

Lili Liu(刘利利)^1,2,†,‡, Qi-Sheng Xu(徐其胜)^2,†, Cai Chen(陈才)³, Chui-Zhen Chen(陈垂针)^4,§, and Dong-Hui Xu(许东辉)^2,5,¶

1 College of Teacher Education, Chongqing Three Gorges University, Chongqing 404100, China;
2 Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 400044, China;
3 School of Civil Engineering, Chongqing Three Gorges University, Chongqing 404100, China;
4 Institute for Advanced Study and School of Physical Science and Technology, Soochow University, Suzhou 215006, China;
5 Center of Quantum Materials and Devices, Chongqing University, Chongqing 400044, China

Received:2025-12-14 Revised:2026-01-28 Accepted:2026-02-10 Online:2026-05-28 Published:2026-05-28
Contact: Lili Liu, Chui-Zhen Chen, Dong-Hui Xu E-mail:liulili0612@163.com;czchen@suda.edu.cn;donghuixu@cqu.edu.cn

摘要/Abstract

摘要： Majorana surface states in time-reversal invariant (TRI) topological superconductors (TSCs) typically exhibit a highly anisotropic magnetic response, a phenomenon termed “Majorana Ising spins.” This Ising character is governed by the crystalline symmetries protecting the topological phase. In this work, we investigate the orientation and tunability of Majorana Ising spins within TRI TSCs engineered in two-dimensional spin-orbit coupled systems proximitized to an extended s-wave superconductor. We demonstrate that the interplay between Rashba and Dresselhaus spin-orbit couplings (SOC) plays a decisive role in determining the Ising spin orientation. In the limit of pure Rashba SOC, the Ising spin aligns along the $x$-axis, protected by mirror symmetry $M_x$, whereas for pure Dresselhaus SOC, it orients along the $y$-axis, protected by the rotational symmetry $C_{2y}$. Crucially, we reveal that when both Rashba and Dresselhaus interactions coexist, the Ising spin direction becomes continuously tunable within the basal plane. By adjusting the relative strengths of the SOC parameters-experimentally accessible via gating in semiconductor heterostructures-any orientation between the $x$-and $y$ axes can be achieved. We validate these findings by calculating the topological winding number $W$ and elucidating the symmetry-protection mechanism for the tunable phases. Our results propose a pathway for manipulating Majorana fermions in quantum devices through purely electrical means, bridging the gap between symmetry-protected topology and functional spintronic applications.

关键词: topological superconductors, Majorana zero modes, Majorana Ising spin

Abstract: Majorana surface states in time-reversal invariant (TRI) topological superconductors (TSCs) typically exhibit a highly anisotropic magnetic response, a phenomenon termed “Majorana Ising spins.” This Ising character is governed by the crystalline symmetries protecting the topological phase. In this work, we investigate the orientation and tunability of Majorana Ising spins within TRI TSCs engineered in two-dimensional spin-orbit coupled systems proximitized to an extended s-wave superconductor. We demonstrate that the interplay between Rashba and Dresselhaus spin-orbit couplings (SOC) plays a decisive role in determining the Ising spin orientation. In the limit of pure Rashba SOC, the Ising spin aligns along the $x$-axis, protected by mirror symmetry $M_x$, whereas for pure Dresselhaus SOC, it orients along the $y$-axis, protected by the rotational symmetry $C_{2y}$. Crucially, we reveal that when both Rashba and Dresselhaus interactions coexist, the Ising spin direction becomes continuously tunable within the basal plane. By adjusting the relative strengths of the SOC parameters-experimentally accessible via gating in semiconductor heterostructures-any orientation between the $x$-and $y$ axes can be achieved. We validate these findings by calculating the topological winding number $W$ and elucidating the symmetry-protection mechanism for the tunable phases. Our results propose a pathway for manipulating Majorana fermions in quantum devices through purely electrical means, bridging the gap between symmetry-protected topology and functional spintronic applications.

Key words: topological superconductors, Majorana zero modes, Majorana Ising spin

中图分类号: (Properties of superconductors)

74.25.-q

74.78.Na (Mesoscopic and nanoscale systems)

Lili Liu(刘利利), Qi-Sheng Xu(徐其胜), Cai Chen(陈才), Chui-Zhen Chen(陈垂针), and Dong-Hui Xu(许东辉). Manipulation of the Majorana Ising spin via Rashba-Dresselhaus spin-orbit coupling[J]. 中国物理B, 2026, 35(6): 67404-067404.

参考文献

[1] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[2] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[3] Sato M and Ando Y 2017 Reports on Progress in Physics 80 076501
[4] Nayak C, Simon S H, Stern A, Freedman M and Das Sarma S 2008 Rev. Mod. Phys. 80 1083
[5] Altland A and Zirnbauer M R 1997 Phys. Rev. B 55 1142
[6] Read N and Green D 2000 Phys. Rev. B 61 10267
[7] Schnyder A P, Ryu S, Furusaki A and Ludwig A W W 2008 Phys. Rev. B 78 195125
[8] Alicea J 2012 Reports on Progress in Physics 75 076501
[9] Nagato Y, Higashitani S and Nagai K 2009 J. Phys. Soc. Jpn. 78 123603
[10] Chung S B and Zhang S C 2009 Phys. Rev. Lett. 103 235301
[11] Mizushima T, Sato M and Machida K 2012 Phys. Rev. Lett. 109 165301
[12] Sato M and Fujimoto S 2009 Phys. Rev. B 79 094504
[13] Mizushima T and Machida K 2011 J. Low Temp. Phys. 162 204
[14] Shindou R Furusaki A and Nagaosa N 2010 Phys. Rev. B 82 180505
[15] Shiozaki K and Sato M 2014 Phys. Rev. B 90 165114
[16] Silaev M A 2011 Phys. Rev. B 84 144508
[17] Yada K, Sato M, Tanaka Y and Yokoyama T 2011 Phys. Rev. B 83 064505
[18] Fu L and Berg E 2010 Phys. Rev. Lett. 105 097001
[19] Liu C X and Trauzettel B 2011 Phys. Rev. B 83 220510
[20] Nakosai S, Tanaka Y and Nagaosa N 2012 Phys. Rev. Lett. 108 147003
[21] Zhang F, Kane C L and Mele E J 2013 Phys. Rev. Lett. 111 056402
[22] Xu Q S, Wang Z M, Chen C Z, Hu L H, Wang R and Xu D H 2026 Phys. Rev. B 113 L161404
[23] Alicea J 2010 Phys. Rev. B 81 125318
[24] Simon E, Szilva A, Ujfalussy B and Lazarovits B, Zarand G and Szunyogh L 2010 Phys. Rev. B 81 235438
[25] Xiong Y, Yamakage A, Kobayashi S, Sato M and Tanaka Y 2017 Crystals 7 58
[26] Mazin I I, Singh D J, Johannes M D and Du M H 2008 Phys. Rev. Lett. 101 057003
[27] Kuroki K, Onari S, Arita R, Usui H, Tanaka Y, Kontani F H and Aoki H 2008 Phys. Rev. Lett. 101 087004
[28] Hanaguri T, Niitaka S, Kuroki K and Takagi H 2010 Science 328 474
[29] Koralek J D, Weber C P, Orenstein J, Bernevig B A, Zhang S C, Mack S and Awschalom D D 2009 Nature 458 610
[30] Walser M P, Reichl C, Wegscheider W and Salis G 2012 Nat. Phys. 8 757
[31] Kohda M, et al. 2012 Phys. Rev. B 86 081306
[32] Sasaki A, et al. 2014 Nat. Nanotech. 9 703
[33] Chang W, et al. 2014 Nat. Nanotech. 10 232

Manipulation of the Majorana Ising spin via Rashba-Dresselhaus spin-orbit coupling

Manipulation of the Majorana Ising spin via Rashba-Dresselhaus spin-orbit coupling

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 10

Metrics

本文评价

推荐阅读 0

[1]	Zhi-Jian Li(李志坚) and Qiang Han(韩强). Emergent topological superconductivity in skyrmion magnet/d-wave superconductor heterostructures[J]. 中国物理B, 2026, 35(6): 67403-067403.
[2]	Shi Huang(黄石) and Xi Luo(罗熙). Topological superconductors with spin-triplet pairings and Majorana Fermi arcs[J]. 中国物理B, 2024, 33(8): 87301-087301.
[3]	Conghao Lin(林丛豪), Chuanshuai Huang(黄传帅), and Xiancong Lu(卢仙聪). Customizing topological phases in the twisted bilayer superconductors with even-parity pairings[J]. 中国物理B, 2023, 32(8): 87401-087401.
[4]	Erhu Zhang(张二虎) and Yu Zhang(张钰). Enhanced topological superconductivity in an asymmetrical planar Josephson junction[J]. 中国物理B, 2023, 32(4): 40307-040307.
[5]	Lupei Qin(秦陆培), Wei Feng(冯伟), and Xin-Qi Li(李新奇). Cross correlation mediated by distant Majorana zero modes with no overlap[J]. 中国物理B, 2022, 31(1): 17402-017402.
[6]	Xiang-Ping Jiang(蒋相平), Yi Qiao(乔艺), and Junpeng Cao(曹俊鹏). Non-Hermitian Kitaev chain with complex periodic and quasiperiodic potentials[J]. 中国物理B, 2021, 30(7): 77101-077101.
[7]	王一鸣, 李志聃, 韩强. Explicit forms of zero modes in symmetric interacting Kitaev chain without and with dimerization[J]. 中国物理B, 2018, 27(6): 67101-067101.
[8]	王一鸣, 李志聃, 韩强. Topological phase diagrams and Majorana zero modes of the Kitaev ladder and tube[J]. 中国物理B, 2018, 27(4): 47401-047401.
[9]	刘大平. Topological phase boundary in a generalized Kitaev model[J]. 中国物理B, 2016, 25(5): 57101-057101.
[10]	周博臻, 周斌. Topological phase transition in a ladder of the dimerized Kitaev superconductor chains[J]. 中国物理B, 2016, 25(10): 107401-107401.