Approximate solutions for the Bogoliubov–de Gennes equations: Superconductor–normal-metal–supercondcutor junctions and the vortex problem
William L. Clinton
DOI 10.1103/PhysRevB.46.5742 · Physical Review B
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Abstract
We present a method for generating wave functions for inhomogeneous superconductors. The method is based on the Andreev approximation to the Bogoliubov–de Gennes equations. Bound states for the superconductor–normal-metal–superconductor junction and the single vortex are discussed. The following simple expression for the bound-state energy as a function of the angular quantum number μ is derived: Eμ=Δ(rμ), where rμ=μ/k11≃μ/kF is the classical turning point. The agreement with recently reported exact numerical wave functions and energies is excellent.
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