Dual order parameter for the nodal liquid

The guiding conception of vortex-condensation-driven Mott insulating behavior is central to the theory of the nodal liquid. We amplify our earlier description of this idea and show how vortex condensation in two-dimensional (2D) electronic systems is a natural extension of 1D Mott insulating and 2D bosonic Mott insulating behavior. For vortices in an underlying superconducting pair field, there is an important distinction between the condensation of flux $hc/2e$ and flux $hc/e$ vortices. The former case leads to spin-charge confinement, exemplified by the band insulator and the charge-density wave. In the latter case, spin and charge are liberated, leading directly to a 2D Mott insulator exhibiting spin-charge separation. Possible upshots include not only the nodal liquid, but also an undoped antiferromagnetic insulating phase with gapped excitations exhibiting spin-charge separation.