Srivastav Saurabh Kumar, Kumar Ravi, Spånslätt Christian, Watanabe K, Taniguchi T, Mirlin Alexander D, Gefen Yuval, Das Anindya
Department of Physics, Indian Institute of Science, Bangalore, 560012, India.
Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, S-412 96, Göteborg, Sweden.
Nat Commun. 2022 Sep 3;13(1):5185. doi: 10.1038/s41467-022-32956-z.
To determine the topological quantum numbers of fractional quantum Hall (FQH) states hosting counter-propagating (CP) downstream (N) and upstream (N) edge modes, it is pivotal to study quantized transport both in the presence and absence of edge mode equilibration. While reaching the non-equilibrated regime is challenging for charge transport, we target here the thermal Hall conductance G, which is purely governed by edge quantum numbers N and N. Our experimental setup is realized with a hexagonal boron nitride (hBN) encapsulated graphite gated single layer graphene device. For temperatures up to 35 mK, our measured G at ν = 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime (N + N)κT, where κT is a quanta of G. With increasing temperature, G decreases and eventually takes the value of the equilibrated regime ∣N - N∣κT. By contrast, at ν = 1/3 and 2/5 (without CP modes), G remains robustly quantized at NκT independent of the temperature. Thus, measuring the quantized values of G in two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.
为了确定承载反向传播（CP）下游（N）和上游（N）边缘模式的分数量子霍尔（FQH）态的拓扑量子数，研究边缘模式平衡存在和不存在时的量子化输运至关重要。虽然对于电荷输运而言，达到非平衡状态具有挑战性，但我们在此以热霍尔电导率G为目标，它完全由边缘量子数N和N决定。我们的实验装置是用六方氮化硼（hBN）封装的石墨栅极单层石墨烯器件实现的。对于高达35 mK的温度，我们在ν = 2/3和3/5（具有CP模式）下测量的G与非平衡状态（N + N）κT的量子化值匹配，其中κT是G的量子。随着温度升高，G减小并最终取平衡状态∣N - N∣κT的值。相比之下，在ν = 1/3和2/5（没有CP模式）时，G在NκT处保持稳健的量子化，与温度无关。因此，通过测量两种状态下G的量子化值，我们确定了边缘量子数，这为寻找奇异非阿贝尔FQH态的拓扑序开辟了一条新途径。
