Topological phase in Kitaev chain with spatially separated pairing processes

TL;DR

This paper explores how spatially separated pairing processes affect topological phases in the Kitaev chain, revealing real spectra, quantized Zak phases, and robust edge modes despite complex energy branches.

Contribution

It introduces a model with separated pair creation and annihilation, analyzing its topological properties using a non-Hermitian Hamiltonian and revealing novel edge state features.

Findings

Real energy spectra in the pair excitation subspace

Quantized Zak phases characterize different topological phases

Edge modes with zero energy obey bulk-boundary correspondence

Abstract

The dynamic balance between pair creation and annihilation processes takes a crucial role to the topological superconductivity in Kitaev model. Here we study the effect of spatial separation of creation and annihilation terms, i.e., sources and drains of pair are arranged alternatively. In this regard, a non-Hermitian Hamiltonian is naturally considered, which may possess complex energy branches. However, when the Bardeen-Cooper-Schrieffer pair (BCS)-like pair excitation is only considered, the spectrum in such a subspace is fully real. In particular, the Zak phases extracted from the pair wave function are quantized and therefore able to characterize the different phases regardless of the breaking of time reversal symmetry. For open chain system, the corresponding Majorana lattice is investigated. We find that although there are complex modes, all the edge modes have zero energy and obey the bulk-boundary correspondence. This results in the Kramerlike degeneracy of both the real and complex levels as a signature of the topologically non-trivial phase.