Gurarie V
Physics Department, University of Colorado, Boulder, CO 80309, USA.
J Phys Condens Matter. 2015 Feb 25;27(7):075601. doi: 10.1088/0953-8984/27/7/075601. Epub 2015 Jan 28.
Hall conductance of noninteracting fermions filling a certain number of Landau levels can be written as a topological invariant. A particular version of this invariant when expressed in terms of the single particle Green's functions directly generalizes to cases when interactions are present including those of fractional Hall states, although in those cases this invariant no longer corresponds to Hall conductance. We argue that when evaluated for both integer and fractional Hall states this invariant gives twice the total orbital spin of fermions which in turn is closely related to the Hall viscosity, a quantity characterizing the integer and fractional Hall states which recently received substantial attention in the literature.
填充一定数量朗道能级的无相互作用费米子的霍尔电导可以写成一个拓扑不变量。当用单粒子格林函数表示时，这个不变量的一个特定版本可以直接推广到存在相互作用的情况，包括分数量子霍尔态的情况，尽管在这些情况下这个不变量不再对应于霍尔电导。我们认为，当对整数和分数量子霍尔态进行评估时，这个不变量给出了费米子总轨道自旋的两倍，而总轨道自旋又与霍尔粘度密切相关，霍尔粘度是一个表征整数和分数量子霍尔态的量，最近在文献中受到了广泛关注。
