Hidden Symmetry Decoupling of Majorana Fermions

Abstract

Multiple zero-energy Majorana fermions (MFs) with spatially overlapping wave functions can survive only if their splitting is prevented by an underlying symmetry. Here we show that, in quasi-one-dimensional (Q1D) time reversal invariant topological superconductors (class DIII), a realistic model for superconducting lithium molybdenum purple bronze and certain families of organic superconductors, multiple Majorana-Kramers pairs with strongly overlapping wave functions persist at zero energy even in the absence of an easily identifiable symmetry. We find that similar results hold in the case of Q1D semiconductor-superconductor heterostructures (class D) with transverse hopping t_{perp} much smaller than longitudinal hopping t_x. Our results, explained in terms of special properties of the Hamiltonian and wave functions, underscore the importance of hidden accidental symmetries in topological superconductors.

4+ pages, 3 figures

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• Majoranas with and without a 'character': hybridization, braiding and Majorana number
• Effective model for Majorana modes in graphene
• Majorana fermions in topological insulator nanowires: from single superconducting nanowires to Josephson junctions
• Symmetry-breaking signatures of multiple Majorana zero modes in one-dimensional spin-triplet superconductors
• Hidden chiral symmetries in BDI multichannel Kitaev chains
• Topological superconductivity and fractional Josephson effect in quasi-one dimensional wires on a plane
• One-dimensional p-wave superconductor toy-model for Majorana fermions in multiband semiconductor nanowires