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 Δ and a charge- or spin-density wave with amplitude W are examples of such systems. When one OP, say Δ, has a form of a topological defect, like, e.g., a vortex or domain wall between the domains with the phases 0 and π, 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 Δ and show that the shape of the associated solution for W depends on temperature and doping (or on the curvature of the Fermi surface) μ. It turns out that, provided the temperature or doping level is close to some discrete values Tn and μn, 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 W0 corresponding to the ground state has the form of a soliton, while other possible solutions Wn(x) have nodes. The inverse situation when W(x) has the form of a topological defect and Δ(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.

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