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arXiv · 1904.07481

Non-Hermitian Majorana modes protect degenerate steady states

Simon Lieu
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Abstract

We introduce non-Hermitian generalizations of Majorana zero modes (MZMs) which appear in the topological phase of a weakly dissipative Kitaev chain coupled to a Markovian bath. Notably, the presence of MZMs ensures that the steady state in the absence of decoherence events is two-fold degenerate. Within a stochastic wavefunction approach, the effective Hamiltonian governing the coherent, non-unitary dynamics retains BDI classification of the closed limit, but belongs to one of four non-Hermitian "flavors" of the ten-fold way. We argue for the stability of MZMs due to a generalization of particle-hole symmetry, and uncover the resulting topological phase diagram. Qualitative features of our study generalize to two-dimensional chiral superconductors. The dissipative superconducting chain can be mapped to an Ising model in a complex transverse field, and we discuss potential signatures of the degeneracy.

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Simon Lieu. 2019-07-11. Non-Hermitian Majorana modes protect degenerate steady states. https://doi.org/10.1103/physrevb.100.085110

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