Quench topology of Chern insulators

Date

2023-6

Author

Kum, Özgün

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We show evidence which suggests that the quench dynamics of general N -level Chern insulators can be topologically characterised by a linking number that is related to the equilibrium topology of the insulator. Recently, it was demonstrated that the intuitive picture of the Chern number in terms of the wrapping of a sphere, that famously exists in two-level systems, can be generalised to N-level systems, where it corresponds to the wrapping of N − 1 spheres that are nested in one another. The exterior sphere in this nested structure plays a dominant role in determining the Chern number. Inspired by a previous work which focuses on the quench dynamics of two-level systems, we make use of the dominant role played by the exterior sphere and use its surface vector as a Hopf map. For a topologically trivial initial Hamiltonian, the homotopy classes of such maps give rise to the homotopy group π3(S2) = Z, and is used in the characterisation of the quenched topological phase. The topological index is the Hopf invariant and is equal to the linking number of the preimages of the Hopf map.

Subject Keywords

Quench dynamics, Chern insulator, Hopf map, Hopf invariant

URI

https://hdl.handle.net/11511/104440

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Graduate School of Natural and Applied Sciences, Thesis