Topological phases in Kitaev chain with imbalanced pairing

TL;DR

This paper explores the effects of non-Hermitian imbalanced pairing on the topological phases of the Kitaev chain, demonstrating the robustness of topological invariants and Majorana modes despite non-Hermiticity.

Contribution

It introduces a systematic analysis of a non-Hermitian Kitaev chain with imbalanced pairing, revealing the persistence of topological phases and edge modes under such conditions.

Findings

Topological phases remain robust with imbalanced pairing.

Extended Zak phase characterizes gapped phases in the non-Hermitian system.

Majorana edge modes exist within the unbroken time-reversal symmetric region.

Abstract

We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. Exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of groundstates occur, associating with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist for the open chain within unbroken time-reversal symmetric region, demonstrating the bulk-edge correspondence in such a non-Hermitian system.