In this thesis we employ various mean-field approaches to study the shortrange
interaction effects in topological insulators. We start with the Kane-Mele
model on the decorated honeycomb lattice and study the stability of topological
insulator phase against different perturbations. We establish an adiabatic connection
between a noninteracting topological insulator and a strongly interacting spin liquid
in its Majorana fermion representation.
We use the Hartree-Fock mean-field approach, slave-rotor approach and
slave-boson approach to study correlation effects related to topological insulators.
With the spontaneous symmetry breaking mechanism, we can have an interaction driven topological insulator with extended Hubbard models on the kagome lattice
and decorated honeycomb lattice. For the interplay among spin-orbit coupling,
distortion and correlation effect in transition metal oxides, we use the slave-rotor
mean-field approach to study its phase transition. We identify regimes where a
strong topological Mott insulator and a weak topological insulator reside due to the
strong Coulomb interaction and distortion. This is relevant to experiments with the
transition metal oxides as they hold promise to realize topological insulators. To
study the doping effects and a possible spin liquid in Kane-Mele-Hubbard model
on the honeycomb lattice, we employ the slave-boson mean-field approach which is
appropriate for the intermediate interaction strength. We compare our results with
those obtained from other methods. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/19453 |
| Date | 14 February 2013 |
| Creators | Wen, Jun, doctor of physics |
| Source Sets | University of Texas |
| Language | en_US |
| Detected Language | English |
| Format | application/pdf |
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