Note added 5/28/2020: I just learnt that there’s a tool called UIUC Fellowship Finder. While completing excellent research work is the most important thing for a Ph.D. student, selling yourself is also critical to your career. Getting a fellowship from big tech companies like Google, IBM and Microsoft in the early stage of your Ph.D. study would definitely boost your future career significantly. It’s really a pit that I only get to know this when I’m about to graduating.

In one of my recent paper entitled Topological phases in spin-1 Fermi gases with two-dimensional spin-orbit coupling, we study the topological phases of Rashba spin-orbit (SO) coupled three-component Fermi gases. In fact, I also investigated the stability of the band crossings under repulsive $SU(3)$-invariant interactions, which is not included in the paper. In the following, I share my note on this matter.