Non-adiabatic breaking of topological pumping

TL;DR

This paper investigates how non-adiabatic effects cause deviations from the quantized charge in topological Thouless pumping, revealing that the phenomenon is not inherently robust beyond the adiabatic limit and depends on the driving protocol.

Contribution

It demonstrates that topological Thouless pumping deviates from quantization under non-adiabatic conditions, providing a detailed analysis of the frequency dependence and protocol tailoring needed.

Findings

Deviation from quantization is quadratic in driving frequency

Charge pumped per period shows non-analytic behavior

Careful protocol design can recover exponential accuracy

Abstract

We study Thouless pumping out of the adiabatic limit. Our findings show that despite its topological nature, this phenomenon is not {generically} robust to non-adiabatic effects. Indeed we find that the Floquet diagonal ensemble value of the pumped charge shows a deviation from the topologically quantized limit which is quadratic in the driving frequency {for a sudden switch-on of the driving}. This is reflected also in the charge pumped in a single period, which shows a non-analytic behaviour on top of an overall quadratic decrease. Exponentially small corrections are recovered only with a careful tailoring of the driving protocol. We also discuss thermal effects and the experimental feasibility of observing such a deviation.