Topological properties in many electron models
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In recent years, novel phases of matter in condensed matter physics have received intensive study. Among these, topological phases in many-electron systems have received enormous amounts of attention. These are phases where topology plays an essential role in explaining the physical properties of matter. In this thesis, we first present the numerical study on the interacting topological phases present in the Hubbard-type models based on the pyrochlore iridates thin films where we go beyond the Hatree-Fock approximtion by applying the cellular dynamical mean-field theory (CDMFT) to better understand the interplay between strong spin-orbit coupling and the electron correlation effects in realizing interacting topological phases. Then the focus is shifted towards the results on the thermoelectric transport coefficients in the novel double-Weyl semi-metals, where we systematically studied the influence of electron-electron interaction and disorder scattering on the electronic transport properties in both the absence and the presence of a static magnetic field. Finally, we investigate how a periodically driven laser field is applied to engineering the electronic band structures and altering the electrical transport dominated by the semi-Dirac dispersion in equilibrium.