On the Selfconsistent Theory of Josephson Effect in Ballistic Superconducting Microconstrictions

The microscopic theory of current carrying states in the ballistic superconducting microchannel is presented. The effects of the contact length L on the Josephson current are investigated. For the temperatures T close to the critical temperature Tc the problem is treated selfconsistently, with taking into account the distribution of the order parameter ∆ (r) inside the contact. The closed integral equation for ∆ in strongly inhomogeneous microcontact geometry (L< ∼ξ0, ξ0 is the coherence length at T = 0 ) replaces the differential Ginzburg-Landau equation. The critical current Ic(L) is expressed in terms of solution of this integral equation. The limiting cases of L ≪ ξ0 and L ≫ ξ0 are considered. With increasing length L the critical current decreases, although the ballistic Sharvin resistance of the contact remains the same as at L = 0. For ultra short channels with L< ∼aD (aD ∼ vF /ωD , ωD is the Debye frequency) the corrections to the value of critical current Ic(L = 0) are sensitive to the strong coupling effects.