Quantized Thouless pumps in periodic systems, set by Chern numbers or Wannier-center winding, are by now fairly well established, whereas their quasiperiodic extensions still require further clarification. Here, we develop a general quantitative paradigm for bulk Thouless pumps in continuous models with spacetime quasiperiodicity, applicable to arbitrary spatial dimensions. Within this framework, the bulk pumping turns out to be governed by an emergent long-wavelength effective potential. Based on this mechanism, we obtain our main result, a universal relation between topological drift and the geometry of the quasi-Brillouin zone. Reduced to periodic systems, our result gives an explicit and compact formula, which enables us to directly calculate Chern numbers by microscopic data. These proposals are corroborated by simulations of one- and two-dimensional continuous moiré-type spacetime quasiperiodic lattices, which exhibit stable, localized, directional drift in excellent agreement with the theory.

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• Berry curvature
• Chern number
• Quantum transport
• Transport phenomena
• Band structure methods