Topological phases in a Kitaev chain with imbalanced pairing

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.

Edge States and Topological Invariants of Non-Hermitian Systems

“…(5) gives t 1 ≈ ±1.20. Note that any H(k)-based topological invariants [48][49][50][51][52][53][54][55][56] can jump only at t 1 = ±t 2 ± γ/2, where the gap of H(k) closes. A bulk eigenstate |ψ l of HermitianH is extended, therefore, H's eigenstate |ψ l = S |ψ l is exponentially localized at an end of the chain when γ 0.…”

“…Non-Bloch topological invariant.-The bulk-boundary correspondence is fulfilled if we can find a bulk topological invariant that determines the edge modes. Previous constructions take H(k) as the starting point [48][49][50][51][52][53][54][55][56], which should be revised in view of the non-Hermitian skin effect. The usual Bloch waves carry a pure phase factor e ik , whose role is now played by β.…”

Non-Hermitian Chern Bands

“…As demonstrated numerically [46,53,54,56], the bulk spectra of one-dimensional (1D) open-boundary systems dramatically differ from those with periodic boundary condition, suggesting a breakdown of bulk-boundary correspondence. This issue has been resolved[56] in 1D non-Hermitian Su-Schrieffer-Heeger (SSH) model: The topological end modes are determined by the non-Bloch winding number[56] instead of topological invariants defined by Bloch Hamiltonian [45][46][47][48][49][50][51][52], which suggests a generalized bulk-boundary correspondence [56].However, the general implications of these results based solely on a simple 1D model remain to be understood (e.g., Is the physics specific to 1D?). Moreover, the topology of this 1D model requires a chiral symmetry [85], which is often fragile in real systems.…”

Symmetry-protected localized states at defects in non-Hermitian systems

“…C and T symmetries are unified by non-Hermiticity, which allows topological phases in high dimensions. The interplay between topology and non-Hermiticity leads to rich topological features with no Hermitian counterpart [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. In particular, the conventional bulk-boundary correspondence breaks down in non-Hermitian systems and new topological invariants like non-Bloch topological invariant and vorticity must be introduced to understand the underlying topological properties.…”