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  • Letter
  • Open Access

Probing tensor monopoles and gerbe invariants in three-dimensional topological matter

Wojciech J. Jankowski1,*, Robert-Jan Slager1,2, and Giandomenico Palumbo3,4,†

  • *Contact author: wjj25@cam.ac.uk
  • †Contact author: giandomenico.palumbo@gmail.com
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Phys. Rev. B 114, L291105 – Published 12 November, 2026

DOI: https://doi.org/10.1103/xcx4-prvh

Abstract

We show that momentum-space tensor monopoles corresponding to nontrivial vector bundle generalizations, known as bundle gerbes, can be realized in bands of three-dimensional topological matter with nontrivial Hopf invariants. We provide a universal construction of tensor Berry connections in these topological phases, demonstrating how obstructions therein lead to Z-quantized bulk magnetoelectric and nonlinear optical phenomena in the presence of spacetime inversion (PT) symmetry. We then pinpoint that these quantum effects are supported by intraband and interband torsion leading to nontrivial Dixmier-Douady classes in most known Hopf phases and in more general topological insulators realizing gerbe invariants falling beyond the tenfold classification of topological phases of matter. We furthermore provide an interacting generalization upon introducing many-body gerbe invariants by employing twisted boundary conditions. This opens an avenue to study gerbe invariants realized through higher-dimensional charge fractionalizations that can be electromagnetically probed.

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Phys. Rev. B 114, L291105– Published 12 November, 2026
  • Received 11 August 2025
  • Revised 10 November 2025
  • Accepted 23 October 2026
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