Dr. Johannes Mitscherling - Interband contributions to the electrical conductivity: Quantum metric and Berry curvature

In a multiband system, not only the individual bands contribute to the electrical conductivity. It is well known that interband contributions are responsible for fascinating phenomena like the intrinsic anomalous Hall effect. In this talk, I will discuss the longitudinal and the anomalous Hall conductivity of a general two-band model including their interband contributions. I introduce a phenomenological relaxation rate of a very simple form but without any restriction in size, so that the band overlap due to band broadening and its impact on the interband contributions can be studied systematically. Within a microscopic approach, I propose a strategy to identify and disentangle the different interband contributions. We will see that the interband contributions are related to the quantum geometric tensor. We do not only recover the well-known Berry curvature contribution, which is responsible for the intrinsic anomalous Hall effect, but also identify a formerly unnoticed contribution based on the quantum metric, which vanishes in the limit of isolated bands. We will analyze the different contributions, discuss their properties, and see several examples.