Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1905.04965

Geometric classification of non-Hermitian topological systems through the singularity ring

Linhu Li·Ching Hua Lee·Jiangbin Gong
View original source ↗Read source document ↗Export metadata ↓

Abstract

This work unveils how geometric features of two-band non-Hermitian Hamiltonians can completely classify the topology of their eigenstates and energy manifolds. Our approach generalizes the Bloch sphere visualization of Hermitian systems to a ``Bloch torus'' picture for non-Hermitian systems, where a singularity ring (SR) captures the degeneracy structure of generic exceptional points. The SR picture affords convenient visualization of various symmetry constraints and reduces their topological characterization to the classification of simple intersection or winding behavior, as detailed by our explicit study of chiral, sublattice, particle-hole and conjugated particle-hole symmetries. In 1D, the winding number about the SR corresponds to the band vorticity measurable through the Berry phase. In 2D, more complicated winding behavior leads to a variety of phases that illustrate the richness of the interplay between SR topology and geometry beyond mere Chern number classification. Through a normalization procedure that puts generic 2-band non-Hermitian Hamiltonians on equal footing, our SR approach also allows for vivid visualization of the non-Hermitian skin effect.

Explore related subjects

cond-mat.mes-hallquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Linhu Li, Ching Hua Lee, Jiangbin Gong. 2019-05-13. Geometric classification of non-Hermitian topological systems through the singularity ring. https://doi.org/10.1103/physrevb.100.075403

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electrical Probing of Dark Excitons through Microwave Permittivity

Excitons in atomically thin semiconductors are almost always probed through their optical signatures, because the short lifetimes of these transient quasiparticles are generally assumed to preclude electrical detection. Here we show that photoexcited excitons in monolayer tungsten disulfide produce a large, optically tunable permittivity at gigahertz frequencies, and that the effect provides a contact-free electrical route to imaging dark excitons at the nanoscale. Using laser-illuminated microwave impedance microscopy, we find that high-purity encapsulated flakes exhibit a purely dielectric response resonant with the exciton spectrum, whereas defect-rich samples are governed by conventional photoconductivity. Spatial mapping of diffusion and sublinear power dependence identify long-lived dark excitons as the dominant contributors, and first-principles modelling of exciton polarizability reproduces the measured susceptibility. Our results establish excitons as optically tunable dielectric elements and introduce microwave microscopy as a direct electrical probe of dark-exciton transport with sub-100 nm resolution.

cond-mat.mes-hall↗
arXiv2026

Relation between the areal rate of Zitterbewegung and Berry curvature in two-band systems

We introduce the Zitterbewegung areal rate operator to study the relation between the orientation of trembling motion and band topology. Constructed from the oscillatory interband displacement and velocity, this operator distinguishes clockwise from anticlockwise motion. For a generic gapped two-band Hamiltonian in two dimensions, we show that the Zitterbewegung areal rate is proportional to the Berry curvature. The derivation uses only spectral projectors and is therefore gauge invariant. We also demonstrate that the Zitterbewegung areal rate operator is time-independent and a constant of motion at each momentum, although the displacement and velocity from which it is constructed oscillate in time. Its sign distinguishes anticlockwise from clockwise Zitterbewegung and coincides with the sign of the Berry curvature. For wave packets narrowly localized around the isolated massive Dirac points, the Zitterbewegung chirality equals the sign of the local Chern contribution. The Chern number can therefore be reconstructed from the orientations of the Zitterbewegung motion around the individual Dirac points.

cond-mat.mes-hall↗
arXiv2026

Substrate-driven topological engineering in plasmonic Su-Schrieffer-Heeger chains

We demonstrate the possibility of engineering the topological band structure of a plasmonic Su-Schrieffer-Heeger (SSH) chain through the interaction with its electromagnetic environment. We find that the long-range interaction of the in-plane modes of the SSH chain with the surface plasmon polaritons of a planar substrate introduces a band hybridization connected to a change of the Zak phase. On the other hand, the short-range interaction with the substrate introduces a band touching, again with a change in the Zak phase. Surprisingly, this second mechanism enables the emergence of topologically protected edge modes for parameters which correspond to the topologically trivial phase for an isolated plasmonic SSH chain. We study these mechanisms by changing the chain-substrate distance and the dimerization parameter. Finally, we discuss the robustness against disorder and, as one example, the impact of the observed effects on the near-field radiative heat transfer and the local density of states along the chain. Our findings pave the way to the engineering of edge modes in plasmonic topological configurations via the coupling to a plasmonic environment.

cond-mat.mes-hall↗