Conclusions and Prospects

Abstract

As a conclusion of the thesis, we briefly summarize the results presented in the previous chapters, which include the renormalization group analysis of the long-range electron-electron interaction in $(3+1)$ dimensional Dirac systems and two-dimensional tilted Dirac cones, a generalization of the Hund’s rule to a two-site model of $t_{2g}$ orbitals, and the classification of topological crystalline insulators protected by mirror symmetry in the presence of interactions.