Executive Summary : | This project combines topology and strong correlations in modern-day condensed matter physics, with a key parameter being spin-orbit coupling (SOC) of electrons combining with Coulomb interactions to generate strongly correlated topological phases. Heavy-fermion systems, such as rare-earth materials, are paradigmatic settings hosting these ingredients on equal footing. The project theoretically models these systems, which contain a localized interacting orbital and an itinerant sea of conduction electrons that hybridize. The SOC in these systems introduces a non-trivial topological structure, manifested in the structure of the hybridization between the heavy or localized electrons with the itinerant electrons. The complex interplay of strong Coulomb repulsions between the electrons and their SOC can lead to quantum critical phase transitions. The project goes beyond mean-field theories to capture phase transitions in the true many-body sense using a minimal many-body framework based on a local picture of strong correlations called dynamical mean-field theory. This method is non-perturbative, crucial for addressing quantum phase transitions, and can be easily extended to incorporate effects due to inhomogeneities or combine with material-specific calculations.
The project will first solve the SOC, heavy-fermion model for different parameters at zero and finite temperatures and evaluate the spectral functions. The Green's functions will be used to uncover the topological character of the phases, and a recently developed method by the PI will be compared with the former characterization. The transport and thermodynamic properties of these phases will be calculated and compared with experimental observations. |