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Time-dependent topological systems: A study of the Bott index

Toniolo, D; (2018) Time-dependent topological systems: A study of the Bott index. Physical Review B , 98 (23) , Article 235425. 10.1103/PhysRevB.98.235425. Green open access

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Abstract

The Bott index is an index that discerns among pairs of unitary matrices that can or cannot be approximated by a pair of commuting unitary matrices. It has been successfully employed to describe the approximate integer quantization of the transverse conductance of a system described by a short-range, bounded, and spectrally gapped Hamiltonian on a lattice on a finite two-dimensional torus and to describe the invariant of the Bernevig-Hughes-Zhang model even with disorder. This paper shows the constancy in time of the Bott index and the Chern number related to the time-evolved Fermi projection of a system described by a short-range, bounded, and time-dependent Hamiltonian that is initially gapped. The general situation of a ramp of a time-dependent perturbation is considered, a section is dedicated to time-periodic perturbations.

Type: Article
Title: Time-dependent topological systems: A study of the Bott index
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevB.98.235425
Publisher version: https://doi.org/10.1103/PhysRevB.98.235425
Language: English
Additional information: This is the published version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology
URI: https://discovery.ucl.ac.uk/id/eprint/10066758
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