Interacting Fermi gases with Rashba coupling, from Majorana zero-modes to non-Fermi liquids

In this talk I will discuss two non-trivial phases that may emerge in interacting Fermi gases with Rashba spin-orbit coupling:

In the first part of my talk I will consider one-dimensional Fermi gases, similar to those where Majorana zero-modes have recently been observed. However, I will consider replacing the proximity coupling to an external superconductor by intrinsic attractive interactions. I will show that despite particle number conservation and the absence of a single particle gap the interactions give rise to a novel topological state.

In the second part of my talk I will switch to two-dimensions, where I will consider repulsive interactions. I will show that despite strong renormalization of the interactions and regardless of how weak their bare value is, they give rise to a verity of liquid crystal phases, including a nematic-ferromagnet, nematic and spin-density wave states.  I will also argue that all of the above phases are expected to show strong deviations from Fermi liquid theory with a special emphasis on the nematic-ferromagnetic phase which is stable against a paring instability.