Topological phase transition independent of system non-Hermiticity

Abstract

Non-Hermiticity can vary the topology of system, induce topological phase transition, and even invalidate the conventional bulk-boundary correspondence. Here, we show the introducing of non-Hermiticity without affecting the topological properties of the original chiral symmetric Hermitian systems. Conventional bulk-boundary correspondence holds, topological phase transition and the (non)existence of edge states are unchanged even though the energy bands are inseparable due to non-Hermitian phase transition. Chern number for energy bands of the generalized non-Hermitian system in two dimension is proved to be unchanged and favorably coincides with the simulated topological charge pumping. Our findings provide insights into the interplay between non-Hermiticity and topology. Topological phase transition independent of non-Hermitian phase transition is a unique feature that beneficial for future applications of non-Hermitian topological materials. *

Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems

“…In the topological classification discussed in Refs. [36], the NH chiral-symmetric Hamiltonians are discussed and the topological invariant and bulk-boundary correspondence has been established [36,71]. They can also be considered in the framework of pseudo-Hermitian Hamiltonians because iH k is a pseudo-Hermitian matrix.…”

Untying links through anti-parity-time-symmetric coupling

“…The linking number associated with this phase is L = 0 and the band is topologically trivial. Notably, the anti-PT -symmetric coupling induces the topological phase transition at the EP, which dramatically differs from the topological phase transitions in other non-Hermitian systems with PTsymmetric gain and loss [28][29][30][31][32][33][34], as well as in non-Hermitian systems with asymmetric coupling strengths [54][55][56][57][58][59], where topological phase transition is irrelevant to the EP. Counterintuitively, increasing the dissipation can create nontrivial topology instead of behaving destructively: more dissipation reduces the strength of the anti-PT -symmetric coupling, tying vector field link and increasing the linking number.…”

“…Photonic crystal is an excellent platform for the study of topological physics [6]. The non-Hermitian quasicrystal [21,22], high-order topological phase [23][24][25][26][27], robust edge state [28][29][30][31][32][33][34][35][36], and topological lasing [37][38][39][40][41][42][43] in photonic crystals were discovered. Here, we consider a photonic crystal lattice as schematically illustrated in Fig.…”

Topological Phase Transition of Non‐Hermitian Crosslinked Chain

“…[ 18 ] It was found that non‐Hermitian Aharonov–Bohm effect is essential for the validation of conventional bulk‐boundary correspondence in non‐Hermitian realm, and the inversion or combined inversion symmetry is critical for restoring conventional bulk‐boundary correspondence. [ 40–42 ] The topology of real‐energy gapless phase resulting from exceptional point has been discussed in ref. [43].…”