Exceptional point description of one-dimensional chiral topological superconductors/superfluids in BDI class

Abstract

We show that certain singularities of the Hamiltonian in the complex wave vector space can be used to identify topological quantum phase transitions for $1D$ chiral topological superconductors/superfluids in the BDI class. These singularities fall into the category of the so-called exceptional points ($EP$'s) studied in the context of non-Hermitian Hamiltonians describing open quantum systems. We also propose a generic formula in terms of the properties of the $EP$'s to quantify the exact number of Majorana zero modes in a particular chiral topological superconducting phase, given the values of the parameters appearing in the Hamiltonian. This formula serves as an alternative to the familiar integer ($\mathbb{Z}$) winding number invariant characterizing topological superconductor/superfluid phases in the chiral BDI class.

minor typos corrected; journal version

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Cited by in corpus (16)

• New topological invariants in non-Hermitian systems
• Symmetry and Higher-Order Exceptional Points
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• Optimized heat transfer at exceptional points in quantum circuits
• Circular dichroism as a probe for topology in three-dimensional semimetals
• Numerical calculation of the complex berry phase in non-Hermitian systems
• Signatures of two- and three-dimensional semimetals from circular dichroism
• Enhanced eigenvector sensitivity and algebraic classification of sublattice-symmetric exceptional points
• Acceleration toward polarization singularity inspired by relativistic ExB drift
• Majorana fermions in finite-size strips with in-plane magnetic fields
• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Counting Majorana bound states using complex momenta
• Symmetry-breaking signatures of multiple Majorana zero modes in one-dimensional spin-triplet superconductors
• Transport across a system with three p-wave superconducting wires: effects of Majorana modes and interactions
• Non-Hermitian generalizations of the Yao-Lee model augmented by SO(3)-symmetry-breaking terms
• Characterizing topological pumping of charges in exactly solvable Rice-Mele chains of the non-Hermitian variety