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.

Non-Hermitian skin clusters from strong interactions

“…Lately, intense research efforts have focused on non-Hermitian phenomena. Yet, the main avenues of non-Hermiticity -the non-Hermitian skin effect (NHSE) [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] and exceptional points [45][46][47][48][49][50][51][52][53][54][55][56][57][58] -are essentially singleparticle mechanisms based on first-quantized notions like non-Bloch eigenstates and single-particle band structure [29,[59][60][61][62][63][64][65]. It is thus timely to ask if strong interactions can open the door to even more exotic phenomena on top of the already rich non-Hermitian singleparticle background.…”

Designing non-Hermitian real spectra through electrostatics

“…To understand how, note that the complex deformation k → p(k) can be understood geometrically [Fig. 1c]: While the PBC spectrum (solid loop) traces out a loop E(k), k ∈ [0, 2π) in the complex E plane, the OBC spectrum (line of crests within the loop) is obtained by the ramping up |Im(p)| such that the PBC loop "shrinks" into its interior until it overlaps with itself i.e is degenerate everywhere [6,12,38,39]. In this OBC limit, the spectrum Ē traces out lines or curve segments connected to each other at branch points.…”

Unconventional node voltage accumulation in generalized topolectrical circuits with multiple asymmetric couplings

“…Nonhermicity has brought about a plethora of interesting new phenomena [1][2][3][4][5][6][7][8][9][10][11][12][13][14], of which the non-Hermitian skin-effect (NHSE) [15][16][17][18][19][20][21][22][23][24][25][26] (i.e, extreme localization of the eigenstates to a boundary) has galvanized various reformulations of the conventional concepts of the Brillouin zone (BZ) and bulk-boundary correspondence (BBC) [27,28]. While the BBC can already be broken with a single asymmetric non-Hermitian coupling, the more interesting interplay between multiple asymmetric non-Hermitian couplings has not been thoroughly explored.…”