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Phys Rev Lett. 2017 Jul 28;119(4):047001. doi: 10.1103/PhysRevLett.119.047001. Epub 2017 Jul 27.

Generic Theory for Majorana Zero Modes in 2D Superconductors.

Chan C1,2, Zhang L1,2, Poon TFJ1,2, He YP1,2, Wang YQ1,2, Liu XJ1,2,3.

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International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.
Collaborative Innovation Center of Quantum Matter, Beijing 100871, China.
Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China.


It is well known that non-Abelian Majorana zero modes (MZM) are located at vortex cores in a p_{x}+𝒾p_{y} topological superconductor, which can be realized in a 2D spin-orbit coupled system with a single Fermi surface and by proximity coupling to an s-wave superconductor. Here we show that the existence of non-Abelian MZMs is unrelated to the bulk topology of a 2D superconductor, and propose that such exotic modes can result in a much broader range of superconductors, being topological or trivial. For a generic 2D system with multiple Fermi surfaces that is gapped out by superconducting pairings, we show that at least a single MZM survives if there are only an odd number of Fermi surfaces of which the corresponding superconducting orders have vortices; such a MZM is protected by an emergent Chern-Simons invariant, irrespective of the bulk topology of the superconductor. This result enriches new experimental schemes for realizing non-Abelian MZMs. In particular, we propose a minimal scheme to realize the MZMs in a 2D superconducting Dirac semimetal with trivial bulk topology, which can be well achieved based on recent cold-atom experiments.

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