Thermal Hall response: violation of gravitational analogues and Einstein relations
Jinhong Park, Omri Golan, Yuval Vinkler-Aviv, Achim Rosch
备注：
In the latest version, we have added the part to include phonon baths for internal equilibration and a more realistic way to imprint a temperature profile onto the system. 17 pages (5 pages for the main text and 12 pages for the supplementary material), 8 figures (4+4)
The response of solids to temperature gradients is often described in terms of a gravitational analogue: the effect of a space-dependent temperature is modeled using a space dependent metric. We investigate the validity of this approach in describing the bulk response of quantum Hall states and other gapped chiral topological states. To this end, we consider the prototypical Haldane model in two different cases of (i) a space-dependent electrostatic potential and gravitational potential and (ii) a space-dependent temperature and chemical potential imprinted by a weak coupling to non-interacting electron baths and phonons. We find that the thermal analogue is \textit{invalid}; while a space dependent gravitational potential induces transverse energy currents proportional to the third derivative of the gravitational potential, the response to an analogous temperature profile vanishes in limit of weak coupling to the thermal bath. Similarly, the Einstein relation, the analogy between the electrostatic potential and the internal chemical potential, is not valid in such a setup.
Anomalous thermoelectric Hall response of interacting 2D Dirac fermions
Department of Physics and Astronomy, University of Manchester（曼彻斯特大学物理与天文系）；Department of Physics, The Hong Kong University of Science and Technology（香港科技大学物理系）
Luttinger's Theorem Violation and Green's Function Topological Invariants in a Fractional Chern Insulator
International Solvay Institutes（国际索尔维研究所）；Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.)（布鲁塞尔自由大学非线性现象与复杂系统中心）；Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；T.C.M. Group, Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室TCM组）；Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（巴黎高等师范学院-PSL大学-索邦大学卡斯勒布罗塞尔实验室）
