  Using $\varepsilon$ expansion technique proposed in \cite{Nishida:2006br} we
derive an effective Lagrangian (Ginzburg-Landau-like functional) of the
degenerate unitary Fermi gas to the next-to-leading (NLO) order in
$\varepsilon.$ It is demonstrated that for many realistic situations it is
sufficient to retain leading order (LO) terms in the derivative expansion. The
functional is used to study vortex structure in the symmetric gas, and
interface between normal and superfluid phases in the polarized gas. The
resulting surface free energy is about four times larger than the value
previously quoted in the literature.
