Correlation-Driven Effects in Strongly Correlated Systems with Symmetry Protection and Disorder

This thesis explores the effects of strong correlations combined with additional interactions such as disorder and structural influences in nodal semimetals and correlated metals. Using Dynamical Mean Field Theory (DMFT) and Iterated Perturbation Theory (IPT) as a real-frequency solver, we analyze quasiparticle dynamics and d.c./a.c. transport properties. The quasi-particle and transport properties of a model describing interacting Dirac and Weyl semimetals has been investigated in the presence of local Hubbard repulsion U, where an explicit deviation from the linearity of the energy-momentum dispersion through an intermediate-energy scale has been introduced. The main focus is on the correlated phase of nodal semimetals. At the nodal point, the renormalization of spectral weight at a fixed temperature exhibits a weak dependence on the energy cutoff but is sensitive to the proximity to the Mott transition. Conversely, the scattering rate of quasi-particles and the resistivity display high-temperature exponents that crucially rely on $\Lambda$, leading to a crossover towards a conventional Fermi-liquid behaviour at finite temperature. Finally, by employing the Nernst-Einstein relation for conductivity, a corresponding density crossover as a function of the chemical potential has been identified. The Kondo effect has been found in our study of the nodal semimetals by analyzing charge compressibility and spin susceptibility. Within single-site DMFT this behaviour arise due to a divergent hybridization function in the auxiliary Anderson Impurity model for the lattice solution. The solution of the Anderson impurity model with divergent hybridization, reveals a spin susceptibility peak at low temperatures, reflecting a transition from Curie-Weiss to Pauli-like behavior. This peak is explained analitically by simplifying the impurity model with a Kondo dimer where an impurity is coupled with a site in the bath. The calculated compressibility matches the analytical solution, confirming our findings. In the correlated metallic phase of a single band Hubbard model the interplay between disorder and correlations in transport and quasiparticle properies is studied using a combination of IPT-DMFT and Coherent Potential Approximation (CPA). Interplay shows-up in a mutual, but non-symmetric, renormalization of scattering channels, leading to the breakdown of Matthiessen’s rule.