Research Projects

Control of quantum systems using light (periodic drive) has been a fascinating area of research in condensed matter for a long time. The light (periodic drive) changes the quantum material in several ways. It induces non-trivial phases such as Floquet topological insulator, Floquet superconductivity, etc. Recently, multiple-frequency drives (particularly bi-circularly polarized light) have gained attention for their unique ability to alter even the lattice symmetry apart from discrete symmetry; the same is not possible with monochromatic light. It has a tremendous effect on the topology and transport properties of the quantum systems. It generates a photocurrent in a centrosymmetric material, which is also not possible using monochromatic light. It shows even more interesting phenomena like topological frequency conversion (one frequency gains energy at the cost of another frequency) when it is subjected to the quantum system, which is already in the topological phase. However, these studies are limited to frequencies with commensurate ratios. The study of nonlinear transport quantities such as photocurrents (injection or shift current) and their dependence on topological frequency conversion mechanisms in a driven (with multi-frequency light with incommensurate ratios) topological quantum system is untouched. In this project, we are going to unfold the effect of topological frequency conversion on nonlinear photocurrents in a multi-frequency driven (using both commensurate and incommensurate frequencies) topological nodal point(line) semimetal. In a topological nodal point(line) semimetal, the conduction band and valence band touch along the point(line) in the three-dimensional Brillouin zone. Electrons near the nodal point(line), which are also subjected to large Berry curvature as well as anomalous velocity, produce a large current. As a result of this, electrons near the nodal point(line) are expected to contribute significantly to nonlinear processes like frequency conversion, photocurrent generation, etc. Another aspect of the multifrequency drive (particularly with incommensurate frequencies) is the designing of the topological system in the pseudo lattice (also called Floquet lattice or frequency space with dimensions the same as the number of independent frequencies in the drive). For e.g., a two-dimensional BHZ model can be constructed by driving spin 1/2 particles with two elliptically polarized lights with an incommensurate frequency ratio. Quantize energy pumping between frequencies serves as a topological invariant that is analogous to charge conductance, which is the signature of the topology in the spatial lattice. However, these studies are limited only to topological insulators, the construction of topological nodal (point or line) semi-metal in the Floquet lattice is not explored.