Switching a research topic is not so easy at first, but I'm taking great advantage from it now!! I can see how different branches of condensed matter physics are constructed in some parallel and similar way, also I can struggle to get some unifying understanding of the seemingly totally different branches!
During the undergraduate years I did multiferroics and now switched to topological insulators, and recently I found myself starting to get aware of their deep-lying connections!
1) Both are quite related to symmetry, no matter time-reversal symmetry or space inversion symmetry. Though seemingly both are broken in the former while preserved in the latter. But please take a look at the surface state of topological insulators, they are just residing on where the inversion symmetry of the system is most severely broken!
2) This point is also somehow related with the above. I just start to find symmetry analysis so important in constructing effective Hamiltonian to both. Group theory is actually a necessary tool (Well, maybe this is the best word for him) in condensed matter physics when tackling with the various fancy crystal structures!
3) Spin-orbital coupling is playing an essential role in both. In the former, it is determining the magnetic ground states by eliminating the degeneracy of d/f orbitals, also introducing spin-dependent hopping term (However, this energy scale is much smaller than the Hund rule effect?) While in the latter, SOC also determines which bands would be essential when accounting for the topological nature.
TO BE CONTINUED...
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