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  • Open Access

Floquet generation of hybrid-order topology and Z2-like bipolar localization

Koustav Roy1,*,†, Latu Kalita1,*,‡, B. Tanatar2,§, and Saurabh Basu1

  • *These authors contributed equally to this work.
  • †Contact author: koustav.roy@iitg.ac.in
  • ‡Contact author: latukalita591@gmail.com
  • §Contact author: tanatar@fen.bilkent.edu.tr
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Phys. Rev. Research 8, 043094 – Published 26 October, 2026

DOI: https://doi.org/10.1103/rlrh-clk2

Abstract

Periodic driving offers a powerful tool to engineer topological phases and even induce phase transitions that are inaccessible in static settings. In this work, we demonstrate that a suitable driving protocol applied to the Benalcazar-Bernevig-Hughes model, a canonical quadrupolar insulator with a π-flux-induced projective PT symmetry, gives rise to a hybrid-order topological phase in which the dispersive first-order edge states and localized higher-order corner modes are shown to coexist at distinct quasienergies. Further, extending the scenario to nonreciprocal-hopping-induced non-Hermiticity, we uncover a Z2-like skin effect characterized by a sharp transition from a unipolar to a bipolar eigenstate-localized phase. Remarkably, this phenomenon, which is established as a prerogative for spinful systems, emerges here purely from the interplay between the embedded gauge structure and Floquet-renormalized symmetry constraints, without invoking physical spin degrees of freedom. Further, the broken bulk-boundary correspondence in this driven non-Hermitian setting can be restored via computing the two-dimensional generalized Brillouin zone, which we construct through a symmetry-reduced mapping onto an effective one-dimensional problem. The resulting non-Bloch invariants faithfully capture both the higher-order topology and the unipolar to bipolar transition. These findings reveal periodic driving as a versatile and controllable handle for sculpting the interplay of higher-order topology, symmetry transmutation, and non-Hermitian skin physics in a single unified platform.

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Phys. Rev. Research 8, 043094– Published 26 October, 2026
  • Received 30 March 2026
  • Accepted 2 October 2026
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