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Integer-graded reciprocal skin effect from internal rotation

Kin Hung Fung1,* and C. T. Chan1,2

  • *Contact author: funguiuc@gmail.com
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APS Open Sci. 1, 000178 – Published 21 October, 2026

DOI: https://doi.org/10.1103/9y8d-bj4j

Abstract

A prominent class of reciprocal non-Hermitian skin effects has a Z2 topological classification, characterized by a parity invariant protected by reciprocity. We show that conserved internal rotation refines this classification into an unbounded integer-graded hierarchy. Every angular momentum channel is an exactly solvable asymmetric chain with its own integer point-gap winding, while conjugate channels accumulate at opposite edges so that reciprocity is preserved globally. For conserved channels, the classification contains one integer per conjugate pair, with the number of independent integers determined by the internal multiplet. Half-integer spin realizes the symplectic class AII†, whose Z2 index is recovered as the parity of the grading. Conjugate-channel mixing destroys the grading and can leave a critical, scale-free skin effect. A cyclic three-site lattice and a passive array of lossy resonators provide minimal realizations.

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Outline

Information

APS Open Sci. 1, 000178– Published 21 October, 2026
Vol. 1
  • Received 11 August 2026
  • Revised 1 October 2026
  • Accepted 6 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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