Topological states of matter are characterized by topological invariants, which are physical quantities whose values are quantized and do not depend on the details of the system (such as its shape, size and impurities). Of these quantities, the easiest to probe is the electrical Hall conductance, and fractional values (in units of e2/h, where e is the electronic charge and h is the Planck constant) of this quantity attest to topologically ordered states, which carry quasiparticles with fractional charge and anyonic statistics. Another topological invariant is the thermal Hall conductance, which is harder to measure. For the quantized thermal Hall conductance, a fractional value in units of κ0 (κ0 = π2kB2/(3h), where kB is the Boltzmann constant) proves that the state of matter is non-Abelian. Such non-Abelian states lead to ground-state degeneracy and perform topological unitary transformations when braided, which can be useful for topological quantum computation. Here we report measurements of the thermal Hall conductance of several quantum Hall states in the first excited Landau level and find that the thermal Hall conductance of the 5/2 state is compatible with a half-integer value of 2.5κ0, demonstrating its non-Abelian nature.Measurements of the thermal Hall conductance in the first excited Landau level of the quantum Hall effect show the existence of a state with non-Abelian excitations.

中文翻译：

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观察半整数热霍尔电导

物质的拓扑状态以拓扑不变量为特征，拓扑不变量是其值被量化且不依赖于系统细节（例如其形状、大小和杂质）的物理量。在这些量中，最容易探测的是霍尔电导，这个量的分数值（以 e2/h 为单位，其中 e 是电荷，h 是普朗克常数）证明了拓扑有序状态，它携带准粒子带分数电荷和任意统计。另一个拓扑不变量是热霍尔电导，它更难测量。对于量化的热霍尔电导，以 κ0 为单位的分数值（κ0 = π2kB2/(3h)，其中 kB 是玻尔兹曼常数）证明物质的状态是非阿贝尔状态。这种非阿贝尔态会导致基态简并并在编织时执行拓扑酉变换，这对于拓扑量子计算很有用。在这里，我们报告了对第一激发朗道能级中几个量子霍尔态的热霍尔电导的测量，发现 5/2 态的热霍尔电导与 2.5κ0 的半整数值兼容，证明其非阿贝尔性质。在量子霍尔效应的第一激发朗道能级中热霍尔电导的测量表明存在具有非阿贝尔激发的状态。