Lattice Ginzburg-Landau model of a ferromagneticp-wave pairing phase in superconducting materials and an inhomogeneous coexisting state

Abstract

We study the interplay of the ferromagnetic (FM) state and the p-wave superconducting (SC) state observed in several materials such as UCoGe and URhGe in a totally nonperturbative manner. To this end, we introduce a lattice Ginzburg-Landau model that is a genuine generalization of the phenomenological Ginzburg-Landau theory proposed previously in the continuum and also a counterpart of the lattice gauge-Higgs model for the s-wave SC transition, and study it numerically by Monte-Carlo simulations. The obtained phase diagram has qualitatively the same structure as that of UCoGe in the region where the two transition temperatrures satisfy TFM > TSC. For TFM/TSC < 0.7, we find that the coexisting region of FM and SC orders appears only near the surface of the lattice, which describes an inhomogeneous FMSC coexisting state.

Lattice gauge theory for condensed matter physics: ferromagnetic superconductivity as its example

“…In the present section, we introduce and discuss the results of numerical calculations 28,30 for the lattice GL model (3.11), which include the phase diagram and Meissner effect in the SC phase. …”

First-order superconducting phase transition in a chiralp+ipsystem

“…(1) in the London limit are investigated using Monte Carlo simulations. This is achieved by discretizing the model on a numerical cubic lattice, where the matter fields live on lattice points and the gauge field is discretized through renormalized noncompact link variables [57]. Periodic boundary conditions are used because we are interested in bulk properties of the model.…”

“…for μ ∈ {x, y, z}. These are noncompact in the sense that they do not have a 2π periodicity [57] and this means that the discretization of the pure gauge term in Eq. (1b) will have the form…”

Thermal fluctuations and vortex lattice structures in chiral p -wave superconductors: Robustness of double-quanta vortices

“…(1d) and represents a soft constraint on the fluctuations of the amplitude ρ h r . Finally, the gauge field energy is given a noncompact discretization [53]…”

“…This amounts to calculating the lattice curl of the gauge-invariant phase difference q θ h r − A r,q around a fundamental plaquette of the numerical lattice. By adding the constant magnetic flux density f , we obtain a quantity which we will call the local vorticity of each component [53]…”