On the self-consistent theory of Josephson effect in ballistic superconducting microconstrictions - Zareyan, M.; Kolesnichenko, Yu. A.; Omelyanchouk, A. N. (ФІЗИКА НИЗЬКИХ ТЕМПЕРАТУР, 1999)
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 self-consistently, with allowance for the distribution of the order parameter D(r) inside the contact. The closed integral equation for D in strongly inhomogeneous microcontact geometry (L&lt and ~x0 , where x0 is the coherence length at T=0) replaces the differential Ginzburg-Landau equation. The critical current Ic(L) is expressed in terms of the solution of this integral equation. The limiting cases of L&lt&ltx0 and L>>x0 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&lt and ~ aD (aD~nF/wD , where w D is the Debye frequency) the corrections for the value of the critical current Ic(L=0) are sensitive to the strong-coupling effects.