Abstract

There has recently been a huge renewed interest in the literature to the study of currents generated in solids by external electrical and magnetic fields, especially in relation with topology, Berry curvature and Weyl points. The responses of interest include nonlinear anomalous Hall effect, crystal Hall effect, planar Hall effect, unidirectional magnetoresistance and electrical magnetochiral anisotropy among others. In this talk I would like to show how all these responses are classified according to their properties with respect to the inversion and time-reversal symmetry, and how they can be systematically described by the Boltzmann equations modified by Berry curvature and intrinsic magnetic moment of Bloch states – the so-called “Berry-Boltzmann” equations. In addition the different terms contributing to the conductivity tensors are classified due to there microscopic origin as being classical or due to Berry curvature and/or intrinsic magnetic moment. I will also discuss what we should call “Hall” and “Ohmic” conductivities in the nonlinear responses, and how they may be extracted from a particular conductivity tensor. If time permits, I will also address some aspects of ab initio evaluation of such responses within Wannier functions formalism, and how we implement it in the WannierBerri code.