Abstract
We describe the effects of spin–orbit (SO) coupling on the collective properties of a two-dimensional (2D) ultracold Fermi gas with Rashba and Dresselhaus SO couplings of equal strength. We first analyse the thermodynamics of the Fermi gas in the absence of repulsive interaction between the atoms (non-interacting system) showing that SO coupling determines one or more second-order phase transitions in the equation of state of the system; we subsequently suggest an experimental strategy that can make these transitions visible. We then study the interacting system using Feynman’s path integral formulation. The aim of this analysis is to describe the collective properties of the system in the paramagnetic phase and in weak non-equilibrium conditions. Particular emphasis is given to the numerical analysis of the collective modes of the system, in particular to the zero sound mode and to the spin modes.
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