‘Metallic’ phase in a system of spin-orbit coupled bosons

We study a system of interacting bosons in the presence of isotropic spin-orbit coupling in two space dimensions. An isotropic spin-orbit coupling leads to a highly degenerate band-minima that lie along a ring in momentum space. Further, the density of states of the non-interacting system diverges as the ring is approached in analogy to one dimensional bosonic systems and fermionic systems at van Hove filling. A large number of low energy states enhances the effects of interaction which is expected to strongly dress the non-interacting system. Indeed, many candidate ground states have been proposed that differ from conventional Bose-Einstein condensate or superfluid state. Here we show that it is possible to stabilize a critical phase that does not break any symmetries of the non-interacting system, and resembles a Tomonaga-Luttinger liquid. We also identify the leading instability, and obtain a phase diagram.