On the self-consistent theory of Josephson effect in ballistic superconducting microconstrictions

The microscopic theory of current-carrying states in the ballistic supercon ducting microchannel is presented. The effects of the contact length L on t he Josephson current are investigated. For the temperatures T close to the critical temperature T-c the problem is treated self-consistently, with all owance for the distribution of the order parameter Delta(r) inside the cont act. The closed integral equation for Delta in strongly inhomogeneous micro contact geometry (L less than or similar to xi(0), where xi(0) is the coher ence length at T=0) replaces the differential Ginzburg-Landau equation. The critical current I-c(L) is expressed in terms of the solution of this inte gral equation. The limiting cases of L much less than xi(0) and L much grea ter than xi(0) are considered. With increasing length L, the critical curre nt decreases, although the ballistic Sharvin resistance of the contact rema ins the same as at L=0. For ultrashort channels with L less than or similar to a(D) (a(D)similar to upsilon(F)/omega(D), where omega(D) is the Debye f requency) the corrections for the value of the critical current I-c (L=0) a re sensitive to the strong-coupling effects. (C) 1999 American Institute of Physics. [S1063-777X(99)00311-4].