论文标题
拓扑量化的准泵中的电流
Topologically quantized current in quasiperiodic Thouless pumps
论文作者
论文摘要
无需泵是物质的拓扑状态，具有量化的电荷运输，可以用加载到光学晶格中的原子气体实现。这种拓扑状态类似于量子厅状态。但是，与霍尔电导的确切，非常精确且可靠的量化相反，仅当泵送时间是特征时间尺度的倍数时，即泵送循环持续时间才能严格量化。在这里，我们表明，如果系统被带入准二级，不稳定的状态，则泵送电流已完全量化，独立于泵送时间。在这种准膜状和拓扑的状态下，Bloch带和浆果曲率变得平坦，泵电荷及时变线，而电流变得稳定，拓扑量化，并且与Chern数字成比例。电流的量化精确到指数较小的校正。这必须与相应的（非quasiperiodic）状态的情况形成鲜明对比，该状态不恒定，并且仅在泵送循环的整数倍数下对泵电荷进行量化。
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.
