  A phase diagram for a 2D metal with variable carrier density has been studied
using the modulus-phase representation for the order parameter in a fully
microscopic treatment. This amounts to splitting the degrees of freedom into
neutral fermion and charged boson degrees of freedom. Although true long range
order is forbidden in two dimensions, long range order for the neutral fermions
is possible since this does not violate any continuous symmetry. The phase
fluctuations associated with the charged degrees of freedom destroy long range
order in the full system as expected. The presence of the neutral order
parameter gives rise to new features in the superconducting condensate
formation in low dimensional systems. The resulting phase diagram contains a
new phase which lies above the superconducting (here
Berezinskii-Kosterlitz-Thouless) phase and below the normal (Fermi-liquid)
phase. We identify this phase with the pseudogap phase observed in underdoped
high-$T_{c}$ superconducting compounds above their critical temperature. We
also find that the phase diagram persists even in the presence of weak
3-dimensionalisation.
