2019/04/30 by Simon Lieu · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Degeneracy (biology) #Degenerate energy levels #Dissipative system #Hamiltonian (control theory) #Hermitian matrix #Ising model #MAJORANA #Mathematics #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum decoherence #Quantum mechanics #Superconductivity #Topological Materials and Phenomena #Wave function #cond-mat.mes-hall #cond-mat.quant-gas #quant-ph
paper · pdf · doi:10.1103/physrevb.100.085110
published as Phys. Rev. B 100, 085110 (2019) · 7 pages, 6 figures, PRB in press
arxiv created 2019/07/11 · openalex publication_date 2019/08/02 · arxiv updated 2019/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 twofold degenerate. Within a stochastic wave-function approach, the effective Hamiltonian governing the coherent nonunitary dynamics retains BDI classification of the closed limit but belongs to one of four non-Hermitian ``flavors'' of the tenfold 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 paper 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.