Vorträge in der Woche 04.04.2022 bis 10.04.2022

Donnerstag, 07.04.2022: A new approach to transport coefficients in the quantum spin Hall effect and to purely linear response of the quantum Hall current

Dr. Giovanna Marcelli (SISSA, Italy)

Using recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost-stationary state, we derive general formulas for spin conductivity and show that the Kubo formula for the Hall conductivity remains valid beyond the linear response regime. For the spin transport, we consider both the choice of the conventional and of the proper spin current operator, and we isolate a subclass of discrete periodic models (including the Kane-Mele model) where the conventional and the proper spin conductivity agree. These results are proved in the following framework, including both discrete and continuum models: the perturbation to a periodic spectrally gapped equilibrium one-particle Hamiltonian is modeled by a linear potential. This seminar is based on joint works with D. Monaco, G. Panati and S. Teufel.

Donnerstag, 07.04.2022: TBA

Prof. Dr. Robert Wald (University of Chicago, USA)

Donnerstag, 07.04.2022: Topology vs localization in synthetic dimensions

Dr. Domenico Monaco (Sapienza, Italy)

The recent development of quantum simulators using optical lattices and ultracold atoms have made it possible to model higher-dimensional quantum systems in the lab, by exploring so-called synthetic dimensions. This is of particular relevance to the investigation of new exotic phases of topological matter: for example, a four-dimensional (4D) analogue of the quantum Hall effect (QHE) has been effectively probed. The topology of 4D quantum systems features an integer, called the second Chern number, which is responsible for this effect in a similar way to how the "usual" first Chern number controls the two-dimensional QHE. In this talk, I will show how the second Chern number arises as an obstruction to the existence of orthonormal bases of localized Wannier functions in 4D crystals, and how relaxing the orthonormality constraint requiring only a Parseval frame removes this topological obstruction.