correl23 — Autumn School on Correlated Electrons: Orbital Physics in Correlated Matter

In a classic paper 50 years ago, Kugel and Khomskii demonstrated that in strongly-correlated systems orbital ordering can arise from a purely electronic super-exchange mechanism and not just the conventional co-operative Jahn-Teller effect. This work opened the field of orbital physics — a field which, since then, is undergoing continuous growth. It was understood that, beside orbital ordering, super-exchange can give rise to the orbital analogue of spin-liquid states. It was shown that the directional character of the orbitals can introduce anisotropic super-exchange interactions, which, in a simplified setting, are described by compass models, a prototype for the Kitaev model. This opened new avenues of its own. More surprising phenomena arise from the entanglement of spin and orbital degrees of freedom. New developments aim at dynamically tuning orbital occupations by pushing the system out of equilibrium, and at orbital-controlled electronics.

The goal of this year’s school is to provide students with an overview of the state-of-the art in the field of orbital physics in strongly correlated systems and the techniques used to investigate them. After introducing fundamental models and effects, lectures will focus on these effects in real materials, with introductions to crystallography and symmetries, methods for building minimal tight-binding Hamiltonians, the Jahn-Teller effect, and Coulomb-enhancements of the Jahn-Teller effect. Advanced lectures will address orbital ordering, orbital liquids and Kitaev materials, as well as theoretical approaches, from self-interaction corrected density functionals to dynamical mean-field theory and beyond. Experimental lectures will present probes of spin, orbital, and charge degrees of freedom, techniques to image orbitals and orbital ordering, as well as orbitally-controlled transport phenomena.

Topics: Orbital physics, orbital ordering, multi-orbital Hubbard model, strong-correlations, DMFT, Jahn-Teller, group theory, Kitaev materials, Mott transition, quantum Montecarlo, spin and orbital liquid, theory and experiments