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.Comment: 4 papges, 14 figure

Quantum critical phenomena of unconventional superconductors: U(1) gauge model of link Cooper pair

In this paper we shall study quantum critical behavior of lattice model of unconventional superconductors (SC) that was proposed in the previous papers. In this model, the Cooper-pair (CP) field is defined on lattice links in order to describe d-wave SC. The CP field can be regarded as a U(1) lattice gauge field, and the SC phase transition takes place as a result of the phase coherence of the CP field. Effects of the long-range Coulomb interactions between the CP's and fluctuations of the electromagnetic field are taken into account. We investigate the phase structure of the model and the critical behavior by means of the Monte Carlo simulations. We find that the parameter, which controls the fluxes (vortices) of the CP, strongly influences the phase structure. In three-dimensional case, the model has rich phase structure. In particular there is a "monopole proliferation" phase transition besides the SC phase transition. Depending on the parameters, this transition exists within the SC phase or takes place simultaneously with the SC transition. This new type of transition is relevant for unconventional SC's with strong spatial three-dimensionality and to be observed by experiments.Comment: 13pages,25figure

Quantum Phase Transition in Lattice Model of Unconventional Superconductors

In this paper we shall introduce a lattice model of unconventional superconductors (SC) like d-wave SC in order to study quantum phase transition at vanishing temperature ($T$). Finite-$T$ counterpart of the present model was proposed previously with which SC phase transition at finite $T$ was investigated. The present model is a noncompact U(1) lattice-gauge-Higgs model in which the Higgs boson, the Cooper-pair field, is put on lattice links in order to describe d-wave SC. We first derive the model from a microscopic Hamiltonian in the path-integral formalism and then study its phase structure by means of the Monte Carlo simulations. We calculate the specific heat, monopole densities and the magnetic penetration depth (the gauge-boson mass). We verified that the model exhibits a second-order phase transition from normal to SC phases. Behavior of the magnetic penetration depth is compared with that obtained in the previous analytical calculation using XY model in four dimensions. Besides the normal to SC phase transition, we also found that another second-order phase transition takes place within the SC phase in the present model. We discuss physical meaning of that phase transition.Comment: 12 pages, 10 figures, references added, some discussion on the results adde