Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries

Abstract

We study a topological band degeneracy in non-Hermitian systems with parity-time (P T ) and parity-particle-hole (CP ) symmetries. In d-dimensional non-Hermitian systems, it is shown that (d − 1)-dimensional exceptional surfaces can appear from band touching thanks to P T or CP symmetry. We investigate the topological stability and zero-gap quasiparticles for the exceptional surfaces due to the band degeneracy. We also demonstrate the band degeneracy by using lattice models of a topological semimetal and a superconductor.

Chiral-symmetry protected exceptional torus in correlated nodal-line semimetals

“…As pointed out in Ref. 79, P T symmetry may induce SPETs for the NLSMs with gain and loss, which indicates the presence of SPETs for corresponding correlated systems. We stress, however, that the crucial difference from the P T symmetric case is that for our system with many-body chiral symmetry, the low energy excitations induced by the SPETs appear strictly at the Fermi level, which enhances the magnetic susceptibility.…”

“…We stress that the chiral symmetry is essential for the above behaviors. Recently, the emergence of SPETs with P T symmetry has been reported by analyzing a noninteracting non-Hermitian Hamiltonian 79 . In contrast to such a case, SPETs with chiral symmetry are fixed to the Fermi level, which induces the Fermi volumes (i.e., low energy excitations enclosed by SPETs) in the Brillouin zone 89 .…”

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

“…The nontrivial bulk topology in Hermitian systems can * wuyajie@xatu.edu.cn † Junpeng.Hou@utdallas.edu be detected by defects, such as edges, π-flux, dislocations and vortices [48][49][50][51][52][53]. When it comes to non-Hermitian systems, stable edge states could also exist at the interface between topological and trivial phases [54][55][56][57][58][59][60][61][62]. These topological states, originated from bulk topologies, are immune to local symmetry-preserved perturbations.…”

Non-Hermitian Exceptional Landau Quantization in Electric Circuits

“…Important developments have recently been focused on the classification of new phases [16][17][18][19][20][21][22], the anomalous bulk-boundary correspondence and skin effect [23][24][25][26][27][28][29][30][31][32], and the bulk Fermi arc and line structures [12,15,33,34]. Of particular importance are the generic exceptional degeneracies -exceptional point (EP) in two dimensions (2D) and exceptional ring (ER) in three dimensions (3D) -in the complex energy spectrum where two resonances match at once in position and width [35][36][37][38][39][40]. Signatures of these have been experimentally observed in microwave cavities [41,42], exciton-polariton systems [43], and photonic lattices [44,45].…”