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

TL;DR

This paper investigates the quantum critical behavior of a lattice model for unconventional superconductors, focusing on phase transitions influenced by gauge fields and vortex fluxes, using Monte Carlo simulations to reveal complex phase structures.

Contribution

It introduces a U(1) gauge model with link-based Cooper pairs for d-wave superconductivity and analyzes its phase structure and critical phenomena including a novel monopole proliferation transition.

Findings

Rich phase structure in 3D model

Existence of monopole proliferation phase transition

Transition can occur within or alongside superconducting phase

Abstract

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.