Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals

Abstract

We study non-Hermitian spatial symmetries -- a class of symmetries that have no counterparts in Hermitian systems -- and study how normal and exceptional semimetals can be stabilized by these symmetries. Different from internal ones, spatial symmetries act nonlocally in momentum space and enforce global constraints on both band degeneracies and topological quantities at different locations. In deriving general constraints on band degeneracies and topological invariants, we demonstrate that non-Hermitian spatial symmetries are on an equal footing with, but are essentially different from Hermitian ones. First, we discover the nonlocal Hermitian conjugate pair of exceptional or normal band degeneracies that are enforced by non-Hermitian spatial symmetries. Remarkably, we find that these pairs lead to the symmetry-enforced violation of the Fermion doubling theorem in the long-time limit. Second, with the topological constraints, we unravel that certain exceptional manifold is only compatible with and stabilized by non-Hermitian spatial symmetries but is intrinsically incompatible with Hermitian spatial symmetries. We illustrate these findings using two three-dimensional models of a non-Hermitian Weyl semimetal and an exceptional unconventional Weyl semimetal. Experimental cold-atom realizations of both models are also proposed.

Major revision, with new content included. Published version

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Cited by in corpus (19)

• Non-Hermitian Topological Phases: Principles and Prospects
• Universal scalefree non-Hermitian skin effect near the Bloch point
• Non-Hermitian Dirac cones with valley-dependent lifetimes
• Making topologically trivial non-Hermitian systems nontrivial via gauge fields
• Hermitian Topologies originating from non-Hermitian braidings
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Effective impurity behavior emergent from non-Hermitian proximity effect
• General theory for infernal points in non-Hermitian systems
• Real spectra in one-dimensional single-band non-Hermitian Hamiltonians
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points
• Nodal phases in non-Hermitian wallpaper crystals
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Spin-dependent gain and loss in photonic quantum spin Hall systems
• Discriminant indicator with generalized rotational symmetry
• Instanton-Induced Supersymmetry Breaking in Topological Semimetals
• Exceptional Non-Hermitian Topology Associated with Non-Toroidal Brillouin Zones
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Continuum Landau surface states in a non-Hermitian Weyl semimetal