Structure of a Vortex in a Dirty Superconductor
In a vortex core at low temperature the order parameter ∆ varies from zero at the center to the Meissner state value ∆0 outside, in a distance of the order of the coherence length ξ. Under these conditions no form of generalized Ginzburg-Landau theory applies and it is necessary to solve the Gor’kov equations. In pure material this can be achieved by solving the Bogoliubov equations.1–3 In material with a finite mean free path Eilenberger4 has derived integrodifferential equations determining single-particle Green’s functions integrated with respect to the excitation energy. The integration has the effect of making the two points whose position vectors are arguments of the Green’s function coincide, but in an inhomogeneous situation the Green’s function depends on the initial direction of the particle motion. Eilen-berger and Buttner’ have started to solve the equations for the vortex case but their results only apply to the asymptotic region r ≫ max (λ,ξ), where r is the distance from the center and λ is the penetration depth.
KeywordsVortex Core Integrodifferential Equation Trial Form Meissner State Bogoliubov Equation
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