Topologically quantized current in quasiperiodic Thouless pumps

Pasquale Marra,Muneto Nitta

doi:10.1103/physrevresearch.2.042035

Pasquale Marra, Muneto Nitta

Open Access

https://doi.org/10.1103/physrevresearch.2.042035

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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, 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 timescale, 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.

Highlights

The hallmark of topological states of matter is the exact quantization of a physical observable in terms of a conserved quantity, the topological invariant [1,2]
We describe the experimental fingerprint of the quasiperiodic topological state, which reveals itself in the charge transport and adiabatic evolution of the center of mass of the atomic cloud
Whereas in the commensurate case the current is not constant and the pumped charge is quantized only at exact multiples of the pumping cycle, we find that the quasiperiodic nontrivial state is characterized by a steady and topologically quantized pumping current, independently from the duration of the pumping process

Summary

Introduction

The hallmark of topological states of matter is the exact quantization of a physical observable in terms of a conserved quantity, the topological invariant [1,2]. When the superlattice is adiabatically and periodically varied in time t, the charge pumped through the atomic cloud is quantized in terms of the topological invariant, i.e., the Chern number [2]. We will operatively define the Chern number by taking the limit of an ensemble of periodic and topologically equivalent states which progressively approximate quasiperiodicity.

Results

Conclusion