Advent of new-generation materials, with flat topological bands and ultranarrow band gaps (in the order of 1 meV), poses challenges on their precise characterization. We uncover a useful connection between the integrated current noise $S\left(\omega \right)$ and the topological band gap in dispersionless quantum states, $\int d\omega [{\mathcal{S}}_{xx}^{\text{flat}}+{\mathcal{S}}_{yy}^{\text{flat}}]=C{e}^2{\mathrm{\Delta }}^2$ (in units $\hslash =1$), where $C$ is the Chern number, $e$ is electric charge, and $\mathrm{\Delta }$ is the topological band gap. This relationship may serve as a working principle for experimental probe of topological band gaps in flat band materials. Possible applications include moiré systems, such as twisted bilayer graphene and twisted transition metal dichalcogenides, where a band gap measurement in meV regime presents an experimental challenge.

中文翻译：

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通过量子噪声测量超窄拓扑带隙


具有平坦拓扑带和超窄带隙（1 meV 量级）的新一代材料的出现，对其精确表征提出了挑战。我们发现了积分电流噪声 $S\left(\omega \right)$ 与无色散量子态中的拓扑带隙 $\int d\omega [{\mathcal{S}}_{xx}^{\text{flat}}+{\mathcal{S}}_{yy}^{\text{flat}}]=C{e}^2{\mathrm{\Delta }}^2$ （以单位 $\hslash =1$ 为单位）之间的有用联系，其中 $C$ 是陈数， $e$ 是电荷， $\mathrm{\Delta }$ 是拓扑带隙。这种关系可以作为平带材料拓扑带隙实验探测的工作原理。可能的应用包括莫尔系统，例如扭曲双层石墨烯和扭曲过渡金属二硫属化物，其中兆伏级带隙测量提出了实验挑战。