Collective excitations, emergent Galilean invariance, and boson-boson interactions across the BCS-BEC crossover induced by a synthetic Rashba spin-orbit coupling

Abstract

Upon increasing the strength of Rashba spin-orbit coupling λ, induced by a synthetic non-Abelian gauge field, a system of fermions at a finite density ρ≈k³_F evolves to a BEC-like state [J. P. Vyasanakere, S. Zhang, and V. B. Shenoy, Phys. Rev. B 84, 014512 (2011)], even in the presence of a weak attractive interaction described by a scattering length a_s. The BEC obtained at large spin-orbit coupling (λ≫k_F) is a condensate of novel bosonic bound pairs of fermions (called “rashbons”) whose properties are determined solely by the gauge field. Here we investigate the collective excitations of such superfluids by constructing a Gaussian theory using functional integral methods. We show that there is an emergent Galilean invariance at large λ, and the phase stiffness is determined by the rashbon density and mass, consistent with Leggett's theorem. We further demonstrate that the rashbon BEC (RBEC) is a superfluid of anisotropic rashbons interacting via a contact interaction characterized by a rashbon-rashbon scattering length a_R. We show that a_R goes as λ^-1 and is essentially independent of the interaction between the fermions as long as it is nonzero. Analytical results are reported for high-symmetry gauge fields.