Density-functional-theory calculations of currents in real materials and the study of topological & geometrical natures of band states

We have explored charge and spin currents in real materials using ab initio computational methods, grounded in Time-Dependent Density Functional Theory (TDDFT) and Time-Dependent Current Density Functional Theory (TDCDFT). While our research has examined various Berry curvature characteristics in solid-state systems, our primary focus is on uncovering the topological and geometrical properties of band states in the real-time dynamics of real materials. For instance, we show that quantum anomalous Hall conductivity and quantum spin Hall conductivity in bulk topological insulators can be directly computed via ab initio evaluations of charge and spin currents, respectively. In this talk, we also present our recent advances in the study of one-dimensional structures, with a particular attention to how the intricate interplay between the topology, chirality, and correlation gives rise to unique spin, orbital, and charge dynamics.