Topologically quantized current in quasiperiodic Thouless pumps

Abstract

Thouless pumps are topologically nontrivial states of matter with quantized charge transport, which can be realized in atomic gases loaded into an optical lattice. This topological state is analogous to the quantum Hall state. However, contrarily to the exact and extremely precise and robust quantization of the Hall conductance, the pumped charge is strictly quantized only when the pumping time is a multiple of a characteristic time scale, i.e., the pumping cycle duration. Here, we show instead that the pumped current becomes exactly quantized, independently from the pumping time, if the system is led into a quasiperiodic, incommensurate regime. In this quasiperiodic and topologically nontrivial state, the Bloch bands and the Berry curvature become flat, the pumped charge becomes linear in time, while the current becomes steady, topologically quantized, and proportional to the Chern number. The quantization of the current is exact up to exponentially small corrections. This has to be contrasted with the case of the commensurate (nonquasiperiodic) regime, where the current is not constant, and the pumped charge is quantized only at integer multiples of the pumping cycle.

Effect of disorder on topological charge pumping in the Rice-Mele model

“…These experiments observe quantized pumping over a number of cycles despite the fact that finite particle numbers and inhomogeneous systems were considered. Current theoretical efforts investigate the stability of charge pumps in optical lattices in genuine many-body systems [6][7][8][9][10][11][12][13][14][15][16][17], in noninteracting systems with disorder [18][19][20][21][22][23], with dissipation [24], or as a proximity effect [25].…”

Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving

“…Introduction.-Topological order in static systems can underlie the quantization of non-equilibrium responses in slowly driven systems with fewer dimensions. A wellknown example is the Thouless charge pump, a slowly and periodically driven insulating wire, which transmits charge at a quantized rate [1][2][3][4][5][6]. Fourier transforming the drive produces a static frequency lattice with one spatial and one synthetic dimension in the presence of a weak electric field.…”