Geometry-induced Monopole Magnetic Field and Quantum Spin Hall Effect

• URL: http://arxiv.org/abs/2109.09122v2
• Date: Sun, 26 Sep 2021 10:15:30 GMT
• Title: Geometry-induced Monopole Magnetic Field and Quantum Spin Hall Effect
• Authors: Yong-Long Wang, Hao Zhao, Hua Jiang, Hui Liu, Yan-Feng Chen
• Abstract summary: A relativistic particle confined to a nontrivial M"obius surface is studied. We find a geometric gauge potential that results from the rotation transformation of the local frame moving on M"obius strip. As potential applications, effective monopole magnetic fields and spin Hall phenomena can be generated and manipulated by designing geometries and topologies of two-dimensional nanodevices.
• Score: 7.6280835896399966
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The geometric effects of two-dimensional curved systems have been an interesting topic for a long time. A M\"{o}bius surface is specifically considered. For a relativistic particle confined to the nontrivial surface, we give the effective Dirac equation in the thin-layer quantization formalism, and we find a geometric gauge potential that results from the rotation transformation of the local frame moving on M\"obius strip, and an effective mass that is from the rescaling transformation. Intriguingly, the geometric gauge potential can play a role of monopole magnetic field for the particles with spin, and which can produce quantum spin Hall effects. As potential applications, effective monopole magnetic fields and spin Hall phenomena can be generated and manipulated by designing the geometries and topologies of two-dimensional nanodevices.

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