Josephson effect in ballistic graphene

M. Titov; C. W. J. Beenakker

doi:10.1103/PhysRevB.74.041401

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Josephson effect in ballistic graphene

M. Titov, C. W. J. Beenakker

DOI 10.1103/PhysRevB.74.041401 · Physical Review B

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Abstract

We solve the Dirac–Bogoliubov–de Gennes equation in an impurity-free superconductor–normal-metal–superconductor junction, to determine the maximal supercurrent Ic that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result Ic≃(W∕L)eΔ0∕ℏ is determined by the superconducting gap Δ0 and by the aspect ratio of the junction (length L small relative to the width W and to the superconducting coherence length). Moving away from the Dirac point of zero doping, we recover the usual ballistic result Ic≃(W∕λF)eΔ0∕ℏ, in which the Fermi wavelength λF takes over from L. The product IcRN≃Δ0∕e of the critical current and normal-state resistance retains its universal value (up to a numerical prefactor) on approaching the Dirac point.