Non-Hermitian Pseudo-Gaps

Abstract

The notion of a band gap is ubiquitous in the characterization of matter. Particularly interesting are pseudo-gaps, which are enigmatic regions of very low density of states that have been linked to novel phenomena like high temperature superconductivity. In this work, we discover a new non-Hermitian mechanism that induces pseudo-gaps when boundaries are introduced in a lattice. It generically occurs due to the interference between two or more asymmetric pumping channels, and possess no analog in Hermitian systems. Mathematically, it can be visualized as being created by divergences of spectral flow in the complex energy plane, analogous to how sharp edges creates divergent electric fields near an electrical conductor. A non-Hermitian pseudo-gap can host symmetry-protected mid-gap modes like ordinary topological gaps, but the mid-gap modes are extended instead of edge-localized, and exhibit extreme sensitivity to symmetry-breaking perturbations. Surprisingly, pseudo-gaps can also host an integer number of edge modes even though the pseudo-bands possess fractional topological windings, or even no well-defined Chern number at all, in the marginal case of a phase transition point. Challenging conventional notions of topological bulk-boundary correspondences and even the very concept of a band, pseudo-gaps post profound implications that extend to many-body settings, such as fractional Chern insulators.

16 pages and 10 figures in total. Comments are welcome

References in corpus (16)

• Topological Origin of Non-Hermitian Skin Effects
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Magnetic order in the pseudogap phase of high-$T_C$ superconductors
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Topological phase transition in non-Hermitian quasicrystals
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• Axion topological field theory of topological superconductors
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Composite-Fermion Theory for Pseudogap, Fermi Arc, Hole Pocket, and Non-Fermi-Liquid of Underdoped Cuprate Superconductors
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• Floquet edge states in a harmonically driven integer quantum Hall system
• Weyl-type topological phase transitions in fractional quantum Hall like systems
• Universal driving protocol for symmetry-protected Floquet topological phases

Cited by in corpus (17)

• Non-Hermitian skin clusters from strong interactions
• Dimensional transmutation from non-Hermiticity
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Designing non-Hermitian real spectra through electrostatics
• Zoology of non-Hermitian spectra and their graph topology
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Non-Hermitian Squeezed Polarons
• System size dependent topological zero modes in coupled topolectrical chains
• Non-Hermitian boundary spectral winding
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Direction reversal of non-Hermitian skin effect via coherent coupling
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Real Non-Hermitian Energy Spectra Without Any Symmetry
• Observation of non-local impedance response in a passive electrical circuit
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Anomalous hybridization of spectral winding topology in quantized steady-state responses
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension