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Geometric Phases in Majorana Zero-Energy State

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Abstract

The usual Berry phase for a Majorana zero-energy state is zero. In this manuscript, we propose a generalized geometric phase for Majorana zero-energy state, which is non-zero for the electron or hole, respectively. We calculate these non-zero geometric phases in a Ferromagnet (FI)/Topological Insulator (TI)/Superconductor (SC) hybrid system, whose magnetization can be manipulated by changing adiabatically the spin degree of freedom. The non-zero geometric phases have potential application on the topological quantum computation treatment of Majorana zero-energy modes. We also discuss the non-adiabatic geometric phase associated with Majorana zero-energy state by the path integral method.

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Acknowledgments

This study is supported by the National Key R&D Program of China (Grant No. 2018FYA0305804), and the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB08-3).

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  1. Department of Physics & CAS Center for Excellence in Topological Quantum Computation, The University of Chinese Academy of Sciences, P. O. Box 4588, Beijing, 100049, China

    Zheng-Chuan Wang

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  1. Zheng-Chuan Wang
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Correspondence to Zheng-Chuan Wang.

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Wang, ZC. Geometric Phases in Majorana Zero-Energy State. Int J Theor Phys 58, 2703–2710 (2019). https://doi.org/10.1007/s10773-019-04160-1

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