Topological phases in thin films of pyrochlore iridates along the (111) direction

Topological states in (quasi) two-dimensional systems have attracted a lot of attention, both theoretically and experimentally, since the discovery of quantum Hall effect. In this thesis, we first introduce the ruby lattice which is able to host an extremely flat topologically non-trivial band. This helps to realize integer and fractional quantum Hall effect in lattices. We then study the thin films of pyrochlore iridates grown along the (111) direction. We first investigate a semi-empirical model described by a multi-band Hubbard model. Using Hartree-Fock approximation, our phase diagrams predict that the bilayer and triangular-Kagome-triangular trilayer structures are the most favorable for topological phases. We then check those structures with firstprinciples calculations, and find they are able to support the Z₂ topological metallic phase and Chern metallic phase. We study in detail the extended nature of 5d orbitals. As a consequence, the charge-density wave caused by nearest-neighbor interaction may serve as a possible way to turn these topological metallic phases into their insulating counterparts.