Ginzburg-Landau Theory for Unconventional Superconductors: Noncompact   U(1) Lattice Gauge Model Coupled with Link Higgs Field
  In this paper, we introduce a Ginzburg-Landau (GL) theory for the extended-$s$ and d-wave superconductors (SC) in granular systems that is defined on a lattice. In contrast to the ordinary Abelian Higgs model (AHM) that is a GL theory for the s-wave SC, Cooper-pair field (Higgs field) is put on links of the lattice in the present model. By means of Monte-Carlo (MC) simulations, we study phase structure, gauge-boson mass (the inverse magnetic penetration depth) and density of instantons. In the ordinary {\em noncomapct} U(1) AHM, there exists a second-order phase transition from the normal to SC states and the gauge-boson mass develops continuously from the phase transition point. In the present gauge system with link Higgs field, on the other hand, phase transition to the SC state is of first order at moderate coupling constants. The gauge-boson mass changes from vanishing to finite values discontinuously at the phase transition points. 
Tomoyoshi Ono and Ikuo Ichinose