Current-phase relation and phase-dependent conductance of superconducting point contacts from rf impedance measurements

The rf impedance of superconducting point contacts has been measured as a function of the quantum-mechanical phase difference φ across the point contact. By representing the point contact as a parallel combination of an inductor L(φ)=(2e)(∂Iₚ∂φ)^-1 and a resistor R≡1G(φ) the current-phase relation Iₚ(φ) and the phase-dependent conductance G(φ) have been determined from measurements at 30 MHz on phase-biased niobium point contacts. For point contacts with sufficiently small critical current Ic, the inductance was L(φ)=2eIccosφ yielding the expected negative inductance branch for π2≤φ≤π and a sinusoidal current-phase relation. For larger critical currents there were departures from the sinusoidal form for the measured Iₚ(φ). There was a phase-dependent conductance that is an increasing function of φ corresponding to a negative coefficient for the cosφ term in the Josephson current.