Topological defects in systems with two competing order parameters: Application to superconductors with charge- and spin-density waves

Abstract

On the basis of coupled Ginzburg-Landau equations we study nonhomogeneous states in systems with two order parameters (OPs). Superconductors with a superconducting OP $\ensuremath{\Delta}$ and a charge- or spin-density wave with amplitude $W$ are examples of such systems. When one OP, say $\ensuremath{\Delta}$, has a form of a topological defect, like, e.g., a vortex or domain wall between the domains with the phases 0 and $\ensuremath{\pi}$, the other OP $W$ is determined by the Gross-Pitaevskii equation and is localized at the center of the defect. We consider in detail the domain-wall defect for $\ensuremath{\Delta}$ and show that the shape of the associated solution for $W$ depends on temperature and doping (or on the curvature of the Fermi surface) $\ensuremath{\mu}$. It turns out that, provided the temperature or doping level is close to some discrete values ${T}_{n}$ and ${\ensuremath{\mu}}_{n}$, the spatial dependence of the function $W(x)$ is determined by the form of the eigenfunctions of the linearized Gross-Pitaevskii equation. The spatial dependence of ${W}_{0}$ corresponding to the ground state has the form of a soliton, while other possible solutions ${W}_{n}(x)$ have nodes. The inverse situation when $W(x)$ has the form of a topological defect and $\ensuremath{\Delta}(x)$ is localized at the center of this defect is also possible. In particular, we predict a surface or interfacial superconductivity in a system where a superconductor is in contact with a material that suppresses $W$. This superconductivity should have rather unusual temperature dependence existing only in certain intervals of temperature. Possible experimental realizations of such nonhomogeneous states of OPs are discussed.