Séminaire de Max Lein

The Fermi surface characterizes the states that dominate conductivity properties in metals. Even though it can be measured in experiment, its definition rests on a description via an effective one-electron model moving in a perfectly periodic potential. However, in real metals one has random impurities and electron-electron interactions, and the external electromagnetic fields, which are necessary to drive a current, destroy the perfect periodicity. So the question how one can generalize the notion of Fermi surface in the presence of some of these effects. We propose a generalization of the notion of Fermi surface based on semiclassical arguments, which can deal with external electromagnetic fields.

Semiclassical equations have proven very successful in characterizing the properties of metals, an idea going back to Lifshitz in the late 1950s. In a decades-long effort, researchers like Dynnikov, Maltsev, Novikov and co-workers have classified semiclassical trajectories on Fermi surfaces in the presence of strong magnetic fields. Crucially they find that regular and chaotic trajectories contribute differently to the overall conductivity as chaotic trajectories tend to move more slowly on a macroscopic level.

However, Dynnikov et al. only used the leading-order equations. In the study of topological insulators the subleading equation have proven crucial in explaining non-zero conductivity, and our work sets the stage for investigating whether the subleading terms change the conclusions by Dynnikov et al. Specifically, the subleading terms could turn regular trajectories into chaotic ones and vice versa.

Joint work with Giuseppe De Nittis (Catholic University of Santiago de Chile) and Marcello Seri (University of Groningen)