Symplectic Hopf Insulator: Delicate Topology in Bosonic Bogoliubov-de Gennes Systems

Abstract:Recent advances in topological phases have highlighted the role of symplectic (Krein-space) topology in the classification of bosonic Bogoliubov-de Gennes (BBdG) systems. In this work, we construct a BBdG realization of Hopf topology, which we dub the symplectic Hopf insulator, starting from a microscopic Bose-Hubbard generalization of the Moore-Ran-Wen model with weak on-site interactions treated within a Bogoliubov approximation. The resulting BBdG system admits a symplectic Hopf invariant, which we show to be integer-quantized for isolated bands. We establish that this topology is intrinsically delicate, requiring exactly two bosonic modes per unit cell, while remaining robust against weak interactions over a range of mass parameters. Upon terminating the three-dimensional insulator at a boundary, we find topologically protected in-gap surface states at finite excitation energy, whose protection is itself delicate. Our results establish the symplectic Hopf insulator as a robust yet delicate topological phase in weakly interacting bosonic systems lying beyond the tenfold-way classification.

7 + 12 pages + 3 + 0 figures. Comments are welcome

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)

arXiv:2609.10541 [cond-mat.mes-hall]

(or arXiv:2609.10541v2 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2609.10541 Focus to learn more arXiv-issued DOI via DataCite

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