Grant: Discovery Grants Program - Individual

Low dimensional systems are interesting class of systems exhibiting novel quantum phenomena. Some examples that has created a lot of buzz are unconventional superconductors and Graphene-based materials. They offer great promise for the future by aiding in discovery on novel quantum phases (involving magnetism, density waves, superconductivity and even coexistence amongst them); and replacing electronics with Spintronics: a more efficient means to transfer information. Another unavoidable ingredient in low dimensional systems is the spin-orbit coupling that breaks parity. When combined with superconductivity it can lead to exotic excitations like Majorana fermions which are essential for quantum computing. However, much of the excitement has been at the level of single-particle physics. This does not allow us to exploit the benefits of the quantum world to the fullest potential. To do that one needs to understand the role of many-body correlations in such systems. This research program is designed to achieve precisely that in a very systematic manner by studying collective excitations in various low-dimensional systems. Collective excitations in general have the potential to tell us a great deal about a system provided we are equipped with a theory that can appropriately handle correlations. As part of this program, we will investigate the role of electronic correlations on spin-orbit coupled single/bilayer Graphene grown on transition metal dichalcogenides. It provides us with the opportunity to investigate collective excitations from non-spin degrees of freedom like sublattice, valley, and layer. We will further investigate collective excitations in the various quantum phases expected around the unconventional superconductivity phase like nematic, coexistence of nematic with superconductivity, magnetic and its coexistence with superconductivity. We will also provide the theory of Raman spectrum in all of these phases. Experimentally tracking the modes across the phase-boundaries using our theoretical model will provide improved insight into the nature of correlations present in the system. This program is designed to develop theoretical tools to handle many-body correlations in spin-orbit coupled systems: an important step forward in studying more complex phases of matter and incorporating many-body effects into fields like Spintronics and quantum computation. Several groups stand to benefit from the output of this program: it directly impacts groups working on Graphene-based devices; the high Tc community can benefit from the fact that different pairing mechanisms that predict similar ground-states, can now be distinguished as the collective excitations are different in each case; many of the conclusions we form in this program can also be tested using cold-atom set-ups thereby encouraging experiments in that field; the knowledge of collective excitations is also a stepping stone towards gauging the properties of non-equilibrium systems.