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 ID Mom 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 confine; ment, 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.