Topological defects in systems with two competing order parameters: Application to superconductors with charge- and spin-density waves
Physical Review B
On the basis of coupled Ginzburg--Landau equations we study nonhomogeneous states in systems with two order parameters (OP). Superconductors with superconducting OP Δ, and charge- or spin-density wave (CDW or SDW) with amplitude W are examples of such systems. When one of OP, say Δ, has a form of a topological defect, like, e.g., 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 temperature or doping level are close to some discrete values T_n and μ_n, the spacial dependence of the function W(x) is determined by the form of the eigenfunctions of the linearized Gross--Pitaevskii equation. The spacial dependence of W_0 corresponding to the ground state has the form of a soliton, while other possible solutions W_n(x) have nodes. 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 non-homogeneous states of OPs are discussed.