Local and non-local correlations in Topological Insulators and Weyl Semimetals

In the context of solid state physics, topological insulators and semimetals show nontrivial conduction properties and responses as a consequence of the peculiarities of their band structure. Recently, the study of the interplay between strong electronic interaction and topology has uncovered a series of novel phenomena. In this thesis we study, in the framework of Dynamical Mean-Field Theory, the effects of correlation on a microscopic Weyl semimetal model derived from the Bernevig-Hughes-Zhang Hamiltonian, uncovering a discontinuous topological phase transition with nonlocal annihilation of the gapless Weyl points. We also study the role of nonlocal correlation effects on the two-dimensional BHZ model, assessing the possible modifications they provide to the local DMFT picture.