An array of strongly correlated electrons in the plane possibly representing the superconducting state in a cuprate. The equally directed center flux in adjacent vortex sections provides for an attractive force (Ampere’s law) at intermediate distances. For a given electron, out of six neighboring vortex sectors there are four sectors with attraction and two sectors with repulsion. At short distance, there is repulsion since an overlap of CVL sections, leading to new intersection points each of mass , is topologically forbidden. Thus there is a typical equilibrium configuration contributing to long-range order in the 2D system. If the externally provided resolution (temperature) falls below a critical value, then statistical fluctuations of the position of an intersection point relative to another one (the location of the electronic charge) will vanish. That is, electrons no longer can disperse energy provided by the heat bath (phonons; spin fluctuations) and thus provide a 2D material free of electric resistivity.
