Seminars

Electrical conductivity formulas for a general two-band model and their application

The electrical conductivity is one of the key property of solids and as such of ongoing interest for both theory and experiment. The concept of bands has proven to be veryuseful in the theoretical description of the conductivity. In recent years, there is increasing interest in transport phenomena that are intrinsically linked to the presence of multiple bands. 

In this talk, I derive and discuss the longitudinal and the (anomalous) Hall conductivity for a general two-band model within a microscopic Matsubara Green's function approach.The model captures a broad variety of physical systems ranging from systems with magnetic order like Neel antiferromagnetism and spiral spin density waves to systems that have topological properties like, for instance, a Chern insulator. I focus on a transparentand physically motivated decomposition of the conductivity formulas by introducing two criteria: intra- and interband contributions as well as symmetric and antisymmetric contributions under the exchange of the current and the electric field directions. I discussthe unique properties of the different contributions including their deep connection to quantum geometry, namely the quantum metric and the Berry curvature. The derived formulas are obtained for a relaxation rate that is constant and equal for both bands butarbitrary in size. This allows us to study the scaling behavior of the different contributions. I discuss a generalization of the Thouless-Kohmoto-Nightingale-Nijs (TKNN) formula for the quantum anomalous Hall effect for a finite relaxation rate beyond theclean limit.