The interplay between electron correlations and spin-orbit coupling is fundamental to understanding quantum materials. It is of great interest due to the emergence of novel quantum phases and exotic properties. Spin-orbit coupling, a relativistic effect, can lead to spin-dependent hopping in metals and introduce anisotropic exchange interactions in Mott insulators, fundamentally changing their physical behaviour and leading to phenomena such as topological insulators, unconventional superconductivity, and quantum spin liquids.

 

This PhD project aims to investigate these complex systems from a microscopic perspective. By constructing symmetry-allowed Hamiltonians using the formalism of magnetic space groups and double groups, we aim to gain new insights into the underlying physics of these materials. We will study how these materials respond to electric and magnetic fields via magnetoelectric coupling induced by spin-orbit interactions, possibly in collaboration with experimentalists.