# Why is the symmetric phase in a Bose gas not superfluid?

In the theory of superfluidity in weakly interacting Bose gases, one finds that in the symmetric phase the exctitations have the dispersion relation

$\omega = \frac{k^2}{2m}-\mu$

with gap $\Delta=-\mu>0$.

In the symmetry-broken phase the low energy excitations have energy

$\omega = c|\mathbf{k}|$

As far as I understood, according to Landau's criterion for superfluidity ($v_c=min_k \frac{\omega_k}{k}$), in order for a critical velocity $>0$ to exist, the spectrum must either be gapped (as in the case of superconductivity) or linear.

So why is the symmetric phase not superfluid? Where am I going wrong?