Quantum-interference phenomena in point contacts between two superconductors
Abstract
A point contact, weakly connecting two superconductors, can be represented by an ideal Josephson junction ( is = i1 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 1sin ϕ(t) - (1/R n)( h̵/2e)(∂ϕ(t)/∂t ) = constant, the d.c. current ( t¯) - d.c. voltage ( V¯) characteristic for a single point contact is found to be overlineV(t) = R n√(i 2 - i 21), independent of the magnetic field B⊥. The relationship between d.c. current (ī), d.c. voltage (V¯) and magnetic field ( B⊥) is also derived for a double junction, taking the self-inductance ( L) of the area ( O) embraced by the contacts into account. If πLi1 ≪ h/2 e then the self-induced flux is ignored and the current i=2i 1sinφt cos{e}/{h̵} B⊥O - {1}/{R n}{h̵}/{2e}{∂ϕ}/{∂t} = constant and ovbar| V( t) = Rn√( i2 - i2c( B⊥)) for i c = 2i 1 | cos(e/ h̵) B ⊥ O|. This result explains the observed voltage oscillations in the resistive-superconductive region as a function of the external magnetic field B⊥ when the applied current is constant and exceeds the critical value. If the self-induced 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 + Licirc ≈ nh/2 e, giving rise to a circulating current ( icirc) 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 ic ≈ 2 i1 - (2/ L) | nh/2 e - B⊥O|, when πLi1 ≪ h/2 e. The relationship between ī, V¯ 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:
- 10.1016/0031-8914(69)90116-5
- Bibcode:
- 1969Phy....41..225D