Unraveling non-Hermitian pumping: Emergent spectral singularities and anomalous responses

Ching Hua Lee, Linhu Li, Ronny Thomale, and Jiangbin Gong
Phys. Rev. B 102, 085151 – Published 27 August 2020

Abstract

Within the expanding field of non-Hermitian physics, non-Hermitian pumping has emerged as a key phenomenon, epitomized through the skin effect via extensive boundary mode accumulation modifying the conventional Bloch picture. Beyond redefining bulk-boundary correspondences, we show that non-Hermitian pumping induces an unprecedented type of spectral topology: It admits a classification in terms of graph topology, which is distinct from conventional topological classifications of the eigenstate or energy Riemann surface. Each topological class is characterized by a conformally invariant configuration of spectral branching singularities, with gap-preserving transitions giving rise to emergent band geometry and Berry curvature discontinuities physically manifested as anomalous response kinks. By placing all Hermitian and non-Hermitian lattice Hamiltonians on equal footing, our comprehensive framework also enables the first analytic construction of topological phase diagrams in the presence of multiple nonreciprocal coupling scales, as prototypically demonstrated for the extended non-Hermitian Chern and Kitaev models. Based on general algebraic geometry properties of the energy dispersion, our framework can be directly generalized to multiple bands, dimensions, and even interacting systems. Overall, it reveals the conspiracy of band representations, spectral topology, and complex geometry as it unfolds in directly measurable quantities.

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  • Received 4 February 2020
  • Revised 31 July 2020
  • Accepted 5 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.085151

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ching Hua Lee1,*, Linhu Li1, Ronny Thomale2, and Jiangbin Gong1

  • 1Department of Physics, National University of Singapore, Singapore, 117542
  • 2Institute for Theoretical Physics and Astrophysics, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany

  • *phylch@nus.edu.sg

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Vol. 102, Iss. 8 — 15 August 2020

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