Robust zero modes in non-Hermitian systems without global symmetries
arXiv:2311.01566 · doi:10.1103/PhysRevLett.131.223801
Abstract
We present an approach to achieve zero modes in lattice models that do not rely on any symmetry or topology of the bulk, which are robust against disorder in the bulk of any type and strength. Such symmetry-free zero modes (SFZMs) are formed by attaching a single site or small cluster with zero mode(s) to the bulk, which serves as the "nucleus" that expands to the entire lattice. We identify the requirements on the couplings between this boundary and the bulk, which reveals that this approach is intrinsically non-Hermitian. We then provide several examples with either an arbitrary or structured bulk, forming spectrally embedded zero modes in the bulk continuum, midgap zero modes, and even restoring the "zeroness" of coupling or disorder-shifted topological corner states. Focusing on viable realizations using photonic lattices, we show that the resulting SFZM can be observed as the single lasing mode when optical gain is applied to the boundary.
arXiv comment5 pages, 5 figures
References in corpus (34)
- Topological Insulators
- Topological insulators and superconductors
- Classification of topological quantum matter with symmetries
- New directions in the pursuit of Majorana fermions in solid state systems
- Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
- Quantized Electric Multipole Insulators
- Symmetry and Topology in Non-Hermitian Physics
- Anomalous edge state in a non-Hermitian lattice
- Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
- Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
- Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
- Corner states of light in photonic waveguides
- Topological Hybrid Silicon Microlasers
- Topologically protected midgap states in complex photonic lattices
- Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
- Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
- Observation of higher-order non-Hermitian skin effect
- Random-matrix theory of Majorana fermions and topological superconductors
- Robust light transport in non-Hermitian photonic lattices
- Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
- Exceptional rings in two-dimensional correlated systems with chiral symmetry
- Non-Hermitian Morphing of Topological Modes
- Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
- Antisymmetric PT-photonic structures with balanced positive and negative index materials
- Synthetic parity-time symmetry breaking in a single microcavity
- Defect states emerging from a non-Hermitian flat band of photonic zero modes
- Symmetry-protected zero-mode laser with a tunable spatial profile
- Bound states in the continuum in PT-symmetric optical lattices
- Non-Hermitian physics without gain or loss: the skin effect of reflected waves
- Chiral symmetry in non-Hermitian systems: product rule and Clifford algebra
- Pseudo-chirality: a manifestation of Noether's theorem in non-Hermitian systems
- Symmetry-protected localized states at defects in non-Hermitian systems
- Non-Hermitian gauged laser arrays with localized excitations: Anomalous threshold and generalized principle of selective pumping
- Linear localization of zero modes in weakly coupled non-Hermitian reservoirs