This thesis presents studies of different schemes to probe and manipulate quantum matter using light with an aim to discover novel routes to efficiently control the properties of quantum materials. A special focus is placed on developing new schemes utilizing light-matter interactions (1) to modify exchange interactions in magnetic insulators, and (2) to probe and modify band topology in quantum matter.
In part II, new schemes are presented to probe local band topology of Bloch bands. First, we study the effects of time-dependent band topology on adiabatic evolution of a Bloch wavepacket. We find that it results in an electric-field analog in semi-classical equation of motion, and can be demonstrated in a honeycomb lattice by varying the sublattice offset energy. We then extend these methods to include non-adiabatic processes, and found interesting connections between the anomalous drift during band excitation and a quantum geometric quantity known as shift-vector. We generalize the concept of shift-vector to include different kinds of band transition protocols beyond light-induced dipole transitions. The idea of electric-field analog and the shift-vector are then combined to develop a novel charge pumping scheme. Motivated by these interesting consequences of band topology in non-adiabatic processes, we study shift-current response in moiré materials, and find that the highly topological nature of flat bands along with their very large unit cells significantly enhances these shift-vector related effects. This response also displays a strong dependence on interaction-induced changes in the band structure and quantum geometric quantities. These results suggest that shift-current response can possibly serve as a very reliable probe for interactions in twisted bilayer graphene. In addition to studying consequences of band topology on single-particle transport, we also consider Berry curvature effects on exciton transport. We find that the non-trivial band topology of underlying electron and hole bands allows us to manipulate excitons with a uniform electric field. We examine the conditions necessary to observe such transport and propose that transition metal dichalcogenide heterobilayers with moiré structure can prove an ideal platform for these effects.
In part III, we propose novel drive protocols based on manipulating orbital and lattice degrees of freedom in quantum materials with light. We found that light induced changes in orbital hybridization and their electronic energies results in a significant change in exchange interactions in quantum magnets. We also accounted for the role of ligands in periodically driven quantum magnets, and found that the predictions made by the minimal model based on direct-hopping can be wrong in certain regimes of drive parameters. This understanding of light induced modifications in ligand-mediated exchange interactions was used to explain the phase shift observed in coherent phonon oscillations of CrSiTe₃ upon the onset of short-range spin correlations. We also demonstrate that light induced coherent lattice vibrations can provide a new route to realize space-time symmetry protected topological phases. Our results suggest that manipulating additional degrees of freedom (not included in commonly employed minimal models of periodically driven systems) with light can provide novel routes for ultrafast control of quantum materials.</p
