2009/10/26 by Sumanta Tewari, Jay D. Sau, S. Das Sarma · 1 citation
Physics and Astronomy · #Atiyah–Singer index theorem #Condensed matter physics #Degenerate energy levels #Dirac fermion #Dirac sea #Fermion #MAJORANA #Magnetic field #Majorana equation #Pairing #Physics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Superconductivity #Topological Materials and Phenomena #Zeeman effect #Zero mode #Zero-point energy #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1016/j.aop.2009.11.003
published as Annals Phys.325:219-231,2010 · 19 pages, 1 figure
arxiv created 2009/10/26 · openalex publication_date 2009/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum-space construction of the zero-mode solution presented here is complementary to the approximate real-space solution of the Bogoliubov-de Gennes equations at a vortex core [J. D. Sau et al., arXiv:0907.2239], proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.