Longitudinal and anomalous Hall conductivity of a general two-band model

In the last decades, theoretical progress was made in describing transport phenomena that are based on so-called interband coherence effects, that is, going beyond independent quasiparticles. In recent years, there is increasing interest in such effects in multiband systems due to advances in experimental techniques.

In this talk, I present a microscopic approach to the longitudinal and the anomalous Hall conductivity for a general two-band model, which captures a broad spectrum of systems with very different and rich physics like Chern insulators, ferromagnets and spiral spin density waves. I present two criteria for a decomposition of the conductivity formulas into contributions with distinct physical interpretation and properties. This leads to various new insights and simplifications that I discuss in detail. The provided strategy in the derivation, the presented connection to concepts of quantum geometry and the generalization of well-known conductivity formulas for a scattering rate of arbitrary size may pave the way for future studies on transport phenomena that are based on interband coherence effects.

[1] Mitscherling, Phys. Rev. B 102, 165151 (2020)