2019/10/31 by I. V. Fialkovsky, M. Suleymanov, Xi Wu +2
Physics and Astronomy · #cond-mat.mes-hall
paper · pdf · doi:10.1088/1402-4896/ab7ce4
published as Physica Scripta 95 (6), 064003 (2020) · Latex, 11 pages, proceedings of ICNFP2019, misprints corrected. arXiv admin note: text overlap with arXiv:1905.11097
arxiv created 2021/04/27 · arxiv updated 2021/04/28
It is well known that the quantum Hall conductivity in the presence of constant magnetic field is expressed through the topological TKNN invariant. The same invariant is responsible for the intrinsic anomalous quantum Hall effect (AQHE), which, in addition, may be represented as one in momentum space composed of the two point Green's functions. We propose the generalization of this expression to the QHE in the presence of non-uniform magnetic field. The proposed expression is the topological invariant in phase space composed of the Weyl symbols of the two-point Green's function. It is applicable to a wide range of non-uniform tight-binding models, including the interacting ones.