Theory of Topological Electric and Thermoelectric Transport in Skyrmion Materials I

The Hall resistivity of chiral magnets is commonly analyzed as the sum of three terms: an anomalous Hall effect arising from spin-orbit coupling, a topological Hall signal deriving from a nonzero skyrmion density, and an ordinary Hall effect proportional to the external magnetic field. The theoretical justification for such a decomposition has long remained an open problem. Using a controlled semiclassical approach that includes all phase-space Berry curvatures [1], we show that the solution of the Boltzmann equation leads to a Hall resistivity that is just the sum of an intrinsic anomalous term arising from momentum-space curvature and a topological term related to the real-space curvature, in addition to the ordinary Hall effect. We generalize these results to calculate thermoelectric transport coefficients in chiral magnets in the next presentation.

[1] N. Verma, Z. Addison, M. Randeria, arXiv:2203.07356 (2022) to appear in Science Adv.