Abstract
Asymmetric coupling amplitudes effectively create an imaginary gauge field, which induces a non-Hermitian Aharonov-Bohm (AB) effect. Nonzero imaginary magnetic flux invalidates the bulk-boundary correspondence and leads to a topological phase transition. However, the way of non-Hermiticity appearance may alter the system topology. By alternatively introducing the non-Hermiticity under symmetry to prevent nonzero imaginary magnetic flux, the bulk-boundary correspondence recovers and every bulk state becomes extended; the bulk topology of Bloch Hamiltonian predicts the (non)existence of edge states and topological phase transition. These are elucidated in a non-Hermitian Su-Schrieffer-Heeger model, where chiral-inversion symmetry ensures the vanishing of imaginary magnetic flux. The average value of Pauli matrices under the eigenstate of chiral-inversion symmetric Bloch Hamiltonian defines a vector field, the vorticity of topological defects in the vector field is a topological invariant. Our findings are applicable in other non-Hermitian systems. We first uncover the roles played by non-Hermitian AB effect and chiral-inversion symmetry for the breakdown and recovery of bulk-boundary correspondence, and develop new insights for understanding non-Hermitian topological phases of matter.
Highlights
The existence of gapless edge states of a system under the open boundary condition (OBC) is predictable from the change of topological invariants associated with the bulk topology of the system under the periodical boundary condition (PBC), known as the bulkboundary correspondence, which is ubiquitously applicable in Hermitian systems
Questions arise: Why does bulk-boundary correspondence fail in certain nonHermitian systems? What roles do non-Hermiticity and symmetry play in the breakdown of bulk-boundary correspondence? How to characterize the topological properties and understand the topological invariant without bulk-boundary correspondence?. In this Rapid Communication, we first report that chiralinversion symmetry plays an important role for the bulkboundary correspondence in the non-Hermitian system of a non-Hermitian SSH model with asymmetric coupling, which leads to a non-Hermitian Aharonov-Bohm (AB) effect with an imaginary magnetic flux under PBC and a non-Hermitian skin effect under OBC without chiral inversion symmetry
In contrast to a real magnetic flux that shifts k in the momentum space without varying the dispersion relation [140], the momentum changes to k + iφ [125,126,129] and the spectrum becomes fully complex affected by imaginary magnetic flux, which induces a topological phase transition with band touching degeneracy points split into pairs of band touching exceptional points (EPs) [Figs. 2(a) and 2(d)] [71] that exhibit different topology [145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161]
Summary
Nonzero imaginary magnetic flux invalidates the bulk-boundary correspondence and leads to a topological phase transition. By alternatively introducing the non-Hermiticity under symmetry to prevent nonzero imaginary magnetic flux, the bulk-boundary correspondence recovers and every bulk state becomes extended; the bulk topology of the Bloch Hamiltonian predicts the (non)existence of edge states and topological phase transition. These are elucidated in a non-Hermitian Su-Schrieffer-Heeger model, where chiral inversion symmetry ensures the vanishing of imaginary magnetic flux. We first uncover the roles played by the non-Hermitian AB effect and chiral inversion symmetry for the breakdown and recovery of bulk-boundary correspondence, and develop new insights for understanding the non-Hermitian topological phases of matter
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