Quantized classical response from spectral winding topology

Abstract

Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge states as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green’s function, and shows up in steady-state response, without invoking a conventional linear response theory. Specifically, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits

“…But the SS phase is due to nontrivial skin effect in both directions, and occurs when the spectral winding in the complex eigenvalue plane is nontrivial. As such, it is not due to topological in the bandstructure sense, but in the spectral winding 11 . Moreover, when we change the edge of system to be perpendicular to the one diagonal direction, the large amplitude of the summed squared eigenmode amplitude still emerges at the corner of SS model.…”

Non-Hermitian Pseudo-Gaps

“…Our work shows how the combination of these two fundamental features create pseudo-gaps with arbitrarily low DOS, going beyond previous theoretical [21][22][23][24][25] and experimental [26,27,[67][68][69][70][71][72] works where adiabatic continuity between the periodic and open boundary condition (PBC and OBC) spectra is generally assumed. As such, besides reformulating major notions like topological bulk-boundary correspondences and criticality [21,24,28,53,57], the NHSE here also raises funda- mental questions on the nature of topological band gaps, with implications like quasi-particle fractionalization.…”

“…It exists because NH systems are special in at least two fundamental ways. Firstly, their spectrum is not constrained to be real, and can thus acquire geometric and topological features in the complex energy plane, such as point-gapped loops without Hermitian analog [21][22][23][24][25][26][27]. Secondly, with point gaps, NH lattices also experience the non-Hermitian skin effect (NHSE) marked by dramatic boundary mode accumulation with universal spectral flow in the complex energy plane [28][29][30][31][32].…”

Non-Hermitian Squeezed Polarons

“…1a), for instance, are edge-localized and asymmetrically propagating, but they originate from nontrivial Chern topology, which is already completely well-defined in the singleparticle context. Non-Hermitian boundary-localized skin states [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] (Fig. 1b) are also essentially single-particle phenomena, with their robustness stemming from the directed non-Hermitian "pumping" in non-reciprocal lattices.…”