Research

M.Sc. Project : I explored the nonlinear rotation of the polarization of light propagating in a 2D system. I used a density matrix framework to perturbatively calculate the induced polarization density, up to first and second order in the electric field strength. Using this I calculated the linear and non-linear optical conductivity. These conductivities go into Maxwell’s equations as material parameter inputs, for calculating the reflection and transmission coefficients of the optical beam interacting with the 2D material. I found that finite off-diagonal terms in the optical conductivity matrix induce Faraday and Kerr rotations in the reflected or transmitted optical beams . 

Third-order rectification in centrosymmetric metals: Rectification, the conversion of AC fields into DC currents, is crucial for optoelectronic applications such as energy harvesting and wireless communication. However, it is conventionally absent in centrosymmetric systems due to vanishing second-order optical responses. Here, we demonstrate significant rectification and photogalvanic currents in centrosymmetric metals via third-order nonlinear optical responses, driven by finite Fermi surface and disorder-induced contributions. We unveil distinct band geometric mechanisms---including Berry curvature quadrupole, Fermi surface injection, and shift effects---and classify all symmetry-allowed rectification responses. Using graphene as an example, we illustrate rectification tunability via light polarization and helicity, enabling rectification engineering in centrosymmetric materials for energy-efficient photodetection and terahertz applications.

Band Geometry Induced Third-Harmonic Generation: Third-harmonic generation (THG) is a key nonlinear optical process for ultrafast imaging, terahertz (THz) signal generation, and symmetry-sensitive probes, often dominating in centrosymmetric materials where lower-order responses vanish. Yet, the role of band geometry, Fermi surface effects, and disorder in enabling large and tunable THG remains poorly understood. Here, we develop a finite-frequency quantum kinetic theory of THG based on the density matrix formalism, deriving the third-harmonic conductivity tensor. Our framework isolates five distinct band-geometric contributions to interband and intraband processes, separates Fermi sea from Fermi surface terms, and incorporates disorder effects phenomenologically. We further provide a complete symmetry classification of THG for all 122 magnetic point groups. Applying the theory to the spin-split altermagnet RuO$_2$, we trace its THG response to specific geometric terms. These results establish a predictive foundation for designing materials with enhanced and tunable THG in the finite-frequency regime.

Band geometric transverse current driven by inhomogeneous AC electric field: We develop a semiclassical theory for electron wavepacket dynamics in the presence of an inhomogeneous AC electric field. While static electric-field gradients are known to generate charge transport governed by the quantum metric, we show that AC field gradients induce an additional geometric current that vanishes in the DC limit. This response originates from a novel band-geometric quantity, the higher-order connection (HOC) tensor, constructed from cubic products of interband Berry connections. We derive explicit expressions for the AC current and identify the symmetry conditions under which it arises. Remarkably, inhomogeneous AC fields can generate an anomalous Hall-like response even in nonmagnetic systems. Applying the theory to Bernal-stacked bilayer graphene, we demonstrate that the HOC-induced response produces measurable Hall currents peaking at band edges. These results establish inhomogeneous AC fields as a powerful probe of higher-order band geometric quantities beyond Berry curvature and the quantum metric.