Critical current of a quasi-one-dimensional superconducting wire

Li-Fu Chang; Santanu Chaudhuri; Philip F. Bagwell

doi:10.1103/PhysRevB.54.9399

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Critical current of a quasi-one-dimensional superconducting wire

Li-Fu Chang, Santanu Chaudhuri, Philip F. Bagwell

DOI 10.1103/PhysRevB.54.9399 · Physical Review B

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Abstract

We solve the Bogoliubov–de Gennes equations self-consistently to obtain the critical current Ic versus Fermi energy μ for a ballistic quasi-one-dimensional superconducting wire. Instead of the ‘‘discretized’’ critical current Ic(μ)=NeΔbulk/ħ predicted for a superconducting point contact, we find Ic(μ)=[4eΔwire(μ)/h][n(μ)/n1(μ)] for the superconducting wire. The normalized electron density n(μ)/n1(μ)=∑i=1N(kFi/kF1)⩽ N is a slowly increasing function of μ. The superconducting order parameter Δwire(μ) must be obtained self-consistently for each value of the Fermi energy. We find Δwire(μ) follows the normal-metal quasi-one-dimensional density of states N(μ) of the wire, as does the critical current Ic(μ) . ©1996 The American Physical Society.