Quantuminterference phenomena in point contacts between two superconductors
Abstract
A point contact, weakly connecting two superconductors, can be represented by an ideal Josephson junction ( i_{s} = i_{1} sin ϕ) and an effective resistance ( R _{n} = V/i _{n}; V = = ( h̵/2e)(∂ϕ/∂t )) shunted in parallel to it. By solving the equation i = i _{s} + i _{n} = = i _{1}sin ϕ(t)  (1/R _{n})( h̵/2e)(∂ϕ(t)/∂t ) = constant, the d.c. current ( t̄)  d.c. voltage ( V̄) characteristic for a single point contact is found to be overlineV(t) = R _{n}√(i ^{2}  i ^{2}_{1}), independent of the magnetic field B⊥. The relationship between d.c. current (ī), d.c. voltage (V̄) and magnetic field ( B⊥) is also derived for a double junction, taking the selfinductance ( L) of the area ( O) embraced by the contacts into account. If πLi_{1} ≪ h/2 e then the selfinduced flux is ignored and the current i=2i _{1}sinφt cos{e}/{h̵} B⊥O  {1}/{R _{n}}{h̵}/{2e}{∂ϕ}/{∂t} = constant and ovbar V( t) = R_{n}√( i^{2}  i^{2}_{c}( B_{⊥})) for i _{c} = 2i _{1  cos(e/ h̵}) B _{⊥ O}. This result explains the observed voltage oscillations in the resistivesuperconductive region as a function of the external magnetic field B_{⊥} when the applied current is constant and exceeds the critical value. If the selfinduced flux is taken into account it is impossible to give a simple analytical solution and numerical methods are used. The total magnetic flux enclosed appears to be approximately quantized: B_{⊥}O + Li_{circ} ≈ nh/2 e, giving rise to a circulating current ( i_{circ}) which adds to the applied current in one of the contacts and subtracts in the other. The modulation in the critical current is approximately given by i_{c} ≈ 2 i_{1}  (2/ L)  nh/2 e  B_{⊥}O, when πLi_{1} ≪ h/2 e. The relationship between ī, V̄ and B_{⊥} is in agreement with experiment and can be represented by a corrugated surface periodic in B_{⊥}.
 Publication:

Physica
 Pub Date:
 February 1969
 DOI:
 10.1016/00318914(69)901165
 Bibcode:
 1969Phy....41..225D