拓扑超导表面态涡核内部束缚态研究
Study on Bound States inside Vortices of Topological Superconductors Surface
摘要: 近年来，拓扑超导体的研究引起了人们极大的兴趣。特别是对于马约拉纳零能模(MZM)的研究，由于其在拓扑量子计算机中有着重要应用。在本文中，我们研究了一个8 × 8 Bogoliubov-de Gennes哈密顿量的系统，该系统具有粒子空穴对称性。我们介绍了该系统的拓扑相图，分析了系统表面束缚态的最低能量与角动量之间的关系。此外，我们还分析了该系统在拓扑平庸和非平庸的情况下是否存在MZM，并求解了相应的波函数。
Abstract: In recent years, the research of topological superconductor has attracted tremendous interest, especially in Majorana zero mode (MZM) due to its significance application in topological quantum computer. In this work, we study of a system with 8 × 8 Bogoliubov-de Gennes Hamiltonian, the system has particle-hole symmetry, and we introduce the phase diagrams of this system. We have analyzed the relationship between the lowest energy and angular momentum of surface bound states. In addition, we have analyzed whether the system exists MZM in the case of topo-logical trivial and non-trivial, and have solved the corresponding wave function.
文章引用：邓名文. 拓扑超导表面态涡核内部束缚态研究[J]. 应用物理, 2023, 13(4): 156-163. https://doi.org/10.12677/APP.2023.134018

参考文献

[1] Majorana, E. (1937) Teoria simmetrica dell’elettrone e del positrone. Il Nuovo Cimento (1924-1942), 14, 171-184. [Google Scholar] [CrossRef] 
[2] Elliott, S.R. and Franz, M. (2015) Colloquium: Majorana Fermions in Nuclear, Particle, and Solid-State Physics. Reviews of Modern Physics, 87, 137. [Google Scholar] [CrossRef] 
[3] Nayak, C., Simon, S.H., Stern, A., Freedman, M. and Das Sarma, S. (2015) Non-Abelian Anyons and Topological Quantum Computation. Reviews of Modern Physics, 80, 1083. [Google Scholar] [CrossRef] 
[4] Kitaev, A.Y. (1997) Quantum Computations: Algo-rithms and Error Correction. Russian Mathematical Surveys, 52, 1191. [Google Scholar] [CrossRef] 
[5] Kitaev, A.Y. (2003) Fault-Tolerant Quantum Computation by Anyons. Annals of Physics, 303, 2-30. [Google Scholar] [CrossRef] 
[6] Kitaev, A.Y. (2006) Anyons in an Exactly Solved Model and Beyond. Annals of Physics, 321, 2-111. [Google Scholar] [CrossRef] 
[7] Aasen, D., Hell, M., Mishmash, R.V., Higginbotham, A., et al. (2016) Milestones toward Majorana-Based Quantum Computing. Physical Review X, 6, Article ID: 031016. [Google Scholar] [CrossRef] 
[8] Read, N. and Green, D. (2000) Paired States of Fermions in Two Dimensions with Breaking of Parity and Time-Reversal Symmetries and the Fractional Quantum Hall Effect. Physical Review B, 61, Article ID: 10267. [Google Scholar] [CrossRef] 
[9] Ivanov, D.A. (2001) Non-Abelian Statistics of Half-Quantum Vortices in p-Wave Superconductors. Physical Review Letters, 86, 268. [Google Scholar] [CrossRef] 
[10] Volovik, G.E. (1999) Fermion Zero Modes on Vortices in Chiral Superconductors. JETP Letters, 70, 609-614. [Google Scholar] [CrossRef] 
[11] Senthil, T. and Fisher, M.P.A. (2000) Quasiparticle Localization in Superconductors with Spin-Orbit Scattering. Physical Review B, 61, 9690. [Google Scholar] [CrossRef] 
[12] Stone, M. and Roy, R. (2004) Edge Modes, Edge Currents, and Gauge Invariance in px + ipy Superfluids and Superconductors. Physical Review B, 69, Article ID: 184511. [Google Scholar] [CrossRef] 
[13] Mackenzie, A.P., Scaffidi, T., Hicks, C.W. and Maeno, Y. (2017) Even Odder after Twenty-Three Years: The Superconducting Order Parameter Puzzle of Sr2RuO4. NPJ Quantum Information, 2, 40. [Google Scholar] [CrossRef] 
[14] Fu, L. and Kane, C.L. (2008) Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator. Physical Review Letters, 100, Article ID: 096407. [Google Scholar] [CrossRef] 
[15] Beenakker, C.W.J. (2013) Search for Ma-jorana Fermions in Superconductors. Annual Review of Condensed Matter Physics, 4, 113-136. [Google Scholar] [CrossRef] 
[16] Mourik, V., Zuo, K., Frolov, S.M., et al. (2012) Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices. Science, 336, 1003-1007. [Google Scholar] [CrossRef] [PubMed]
[17] Deng, M.T., Yu, C.L., Huang, G.Y., et al. (2012) Anomalous Zero-Bias Conductance Peak in a Nb-InSb Nanowire-Nb Hybrid Device. Nano Letters, 12, 6414-6419. [Google Scholar] [CrossRef] [PubMed]
[18] Finck, A.D.K., Van Harlingen, D.J., Mohseni, P.K., Jung, K. and Li, X. (2013) Anomalous Modulation of a Zero-Bias Peakin a Hybrid Nanowire-Superconductor Device. Physical Review Letters, 110, Article ID: 126406. [Google Scholar] [CrossRef] 
[19] Lee, E.J.H., Jiang, X., Houzet, M., et al. (2014) Spin-Resolved Andreev Levels and Parity Crossings in Hybrid Superconductor-Semiconductor Nanostructures. Nature Nanotechnology, 9, 79-84. [Google Scholar] [CrossRef] [PubMed]
[20] Nadj-Perge, S., Drozdov, I.K., Li, J., et al. (2014) Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor. Sci-ence, 346, 602-607. [Google Scholar] [CrossRef] [PubMed]
[21] Kong, L.Y., Zhu, S.Y., Papaj, M., Chen, H., Cao, L., Isobe, H., Xing, Y.Q., Liu, W.Y., Wang, D.F., Fan, P., Sun, Y.J., Du, S.X., Schneeloch, J., Zhong, R., Gu, G., Fu, L., Gao, H.J. and Ding, H. (2019) Half-Integer Level Shift of Vortex Bound States in an Iron-Based Super-conductor. Nature Physics, 15, 1181. [Google Scholar] [CrossRef] 
[22] Chen, C., Liu, Q., Zhang, T.Z., Li, D., Shen, P.P., Dong, X.L., Zhao, Z.X., Zhang, T. and Feng, D.L. (2019) Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor (Li0.84Fe0.16)OHFeSe. Chinese Physics Letters, 36, Article ID: 057403. [Google Scholar] [CrossRef] 
[23] Liu, W.Y., Gao, L., Zhu, S.Y., Kong, L.Y., Wang, G.W., Papaj, M., Zhang, P., Liu, Y.B., Chen, H., Li, G., Yang, F.Z., Kondo, T., Du, S.X., Cao, G.H., Shin, S., Fu, L., Yin, Z.P., Gao, H.J. and Ding, H. (2020) A New Majorana Platform in an Fe-As Bilayer Su-perconductor. Nature Communications, 11, Article No. 5688. [Google Scholar] [CrossRef] [PubMed]
[24] Wang, Z.Y., Rodriguez, J.O., Jiao, L., Howard, S., Graham, M., Gu, G.D., Hughes, T.L., Morr, D.K. and Madhavan, V. (2020) Evidence for Dispersing 1D Majorana Channels in an Iron-Based Superconductor. Science, 367, 104-108. [Google Scholar] [CrossRef] [PubMed]
[25] Zhao, W.H., Ding, L.L., Zhou, B.W., et al. (2021) Phase Dia-grams of Superconducting Topological Surface States. Condensed Matter Physics, 24, 43701. [Google Scholar] [CrossRef] 
[26] Gygi, F. and Schl, M. (1991) Self-Consistent Electronic Structure of a Vortex Line in a Type-II Superconductor. Physical Review B, 43, 7609-7621. [Google Scholar] [CrossRef] 
[27] Hu, L.-H., Wu, X.X., Liu, C.-X. and Zhang, R.-X. (2021) Competing Vortex Topologies in Iron-Based Superconductors. Physical Review Letters, 129, Article ID: 277001. [Google Scholar] [CrossRef] 

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