Probing Tensor Monopoles and Gerbe Invariants in Three-Dimensional Topological Matter

Fuente: arXiv
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Main Authors: Jankowski, Wojciech J., Slager, Robert-Jan, Palumbo, Giandomenico
Format: Preprint
Published: 2025
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author Jankowski, Wojciech J.
Slager, Robert-Jan
Palumbo, Giandomenico
author_facet Jankowski, Wojciech J.
Slager, Robert-Jan
Palumbo, Giandomenico
contents 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 $\mathbb{Z}$-quantized bulk magnetoelectric and nonlinear optical phenomena. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_22116
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Probing Tensor Monopoles and Gerbe Invariants in Three-Dimensional Topological Matter
Jankowski, Wojciech J.
Slager, Robert-Jan
Palumbo, Giandomenico
Mesoscale and Nanoscale Physics
Optics
Quantum Physics
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 $\mathbb{Z}$-quantized bulk magnetoelectric and nonlinear optical phenomena. 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.
title Probing Tensor Monopoles and Gerbe Invariants in Three-Dimensional Topological Matter
topic Mesoscale and Nanoscale Physics
Optics
Quantum Physics
url https://arxiv.org/abs/2507.22116