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arXiv · 2105.05428

Diophantine equation for the Rice-Mele model: Topological aspect of filling numbers and associated spatial pump

K. Asaga·T. Fukui
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Abstract

We introduce a long-period generic spatial modulation into a typical model of the Thouless pump, namely, the Rice--Mele (RM) model, to examine the lattice analog of the fermion charge in quantum field theory. We derive a Diophantine equation relating the fermion charge and the pumped charge, which leads to the one-dimensional (1D) analog of the Streda formula in the quantum Hall effect (QHE). This formula implies that an adiabatic change of the periodicity of the spatial modulation yields a spatial charge pump such that the rightmost charge is pumped to the right by the Chern number compared with the leftmost charge. This causes a change in the length of the fermion chain by an integer, thus providing the opportunity for direct measurement of the Streda formula in 1D systems.

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K. Asaga, T. Fukui. 2021-05-12. Diophantine equation for the Rice-Mele model: Topological aspect of filling numbers and associated spatial pump. https://doi.org/10.7566/jpsj.90.093702

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