Field theory approach to interacting topological insulators - Chan, Wei Jie (2019)
We aim to understand a range of conceptual and developmental topics in the fields of topological insulators. Starting from the non-trivial geometrical structure in the Brillouin zone, and eventually the first topological invariant. Consequently, we aim to show how this gives rise to the Quantum Hall effect. We will then apply these concepts to non-interacting TIs both ($2+1$)D and ($3+1$)D. Next, we will be constructing the framework in both the Matsubara field theory and the Topological Band theory approach, which will allow us to understand the effects of having interactions in Topological insulators. Finally, we will be constructing the framework of the ($4+1$)D time-reversal invariant Topological Insulator with the effective Topological Field Theory in terms of the Chern-Simons gauge theory. From there we will be successfully applying the dimensional reduction technique to get the Topological Field theory for both ($3+1$)D and ($2+1$)D time-reversal invariant Topological insulators. Lastly, we will end off by showing the correspondence between Topological Field theory invariants and the Topological Band theory invariants.