Thouless pumping in quasi-periodic lattices is governed by an emergent effective potential that produces a universal geometry-induced drift velocity determined by the quasi-Brillouin zone, reducing to an explicit formula for Chern numbers in periodic cases.
Vanderbilt,Berry phases in electronic structure the- ory: electric polarization, orbital magnetization and topo- logical insulators(Cambridge University Press, 2018)
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Thouless pumps and universal geometry-induced drift velocity in multi-sliding quasi-periodic lattices
Thouless pumping in quasi-periodic lattices is governed by an emergent effective potential that produces a universal geometry-induced drift velocity determined by the quasi-Brillouin zone, reducing to an explicit formula for Chern numbers in periodic cases.