Microscopic theory of magnetoconductivity at low magnetic fields in terms of Berry curvature and orbital magnetic moment

Using a microscopic theory for the magnetoconductivity at low magnetic fields, we show how all components of the conductivity tensor can be calculated in the low scattering rate limit. In the lowest order of the scattering rate, we recover the result of the semiclassical Boltzmann transport theory. At higher order, we get corrections containing the Berry curvature and the orbital magnetic moment. We use this formalism to study the linear longitudinal magnetoconductivity in tilted Weyl semimetals. We discuss how our result is related to the semiclassical Boltzmann approach and show the differences that arise compared to previous studies related to the orbital magnetic moment.