Hexagonal warping effect on Majorana zero modes at the ends of superconducting vortex lines in doped strong 3D topological insulators

  • Chuang Li
  • Lun-Hui HuEmail author
  • Fu-Chun ZhangEmail author


In a superconducting topological insulator, a superconducting vortex line can trap a one-dimensional topological band with localized Majorana zero modes at the ends. Here, we study the effect of hexagonal warping and its corresponding symmetry-breaking effect on vortex phase transition. We perform both analytical calculations based on a semiclassical formula and numerical calculations based on full quantum mechanics using the Bogoliubov-de Gennes equation. We find that the hexagonal warping term extends the topological region of the vortex line as the chemical potential changes and leads to MZMs, even in the absence of topological surface states.

Key words

topological insulator topological superconductor vortex phase transition Majorana zero modes hexagonal warping 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsZhejiang UniversityHangzhouChina
  2. 2.Kavli Institute for Theoretical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.Department of PhysicsUniversity of CaliforniaSan DiegoUSA
  4. 4.CAS Center for Excellence in Topological Quantum ComputationUniversity of Chinese Academy of SciencesBeijingChina
  5. 5.Collaborative Innovation Center of Advanced MicrostructuresNanjing UniversityNanjingChina

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