Dual order parameter for the nodal liquid

The guiding conception of vortex-condensation-driven Mott insulating behavi or is central to the theory of the nodal liquid. We amplify our earlier des cription of this idea and show how vortex condensation in two-dimensional ( 2D) electronic systems is a natural extension of ID Mom insulating and 2D b osonic Mott insulating behavior. For vortices in an underlying superconduct ing 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 confine; ment, exemplified by the band insulator and the charge-density wav e. In the latter case, spin and charge are liberated, leading directly to a 2D Mott insulator exhibiting spin-charge separation. Possible upshots incl ude not only the nodal liquid, but also an undoped antiferromagnetic insula ting phase with gapped excitations exhibiting spin-charge separation.