On the self-consistent 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 T-c the problem is treated self-consistently, with allowance for the distribution of the order parameter Delta(r) inside the contact. The closed integral equation for Delta in strongly inhomogeneous microcontact geometry (L less than or similar to xi(0), where xi(0) is the coherence 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 integral equation. The limiting cases of L much less than xi(0) and L much greater than xi(0) 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 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 frequency) the corrections for the value of the critical current I-c (L=0) are sensitive to the strong-coupling effects. (C) 1999 American Institute of Physics. [S1063-777X(99)00311-4].