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

Abstract

The rf impedance of superconducting point contacts has been measured as a function of the quantum-mechanical phase difference $\ensuremath{\varphi}$ across the point contact. By representing the point contact as a parallel combination of an inductor $\mathfrak{L}(\ensuremath{\varphi})=(\frac{\ensuremath{\hbar}}{2e}){(\frac{\ensuremath{\partial}{I}_{p}}{\ensuremath{\partial}\ensuremath{\varphi}})}^{\ensuremath{-}1}$ and a resistor $R\ensuremath{\equiv}\frac{1}{G(\ensuremath{\varphi})}$ the current-phase relation ${I}_{p}(\ensuremath{\varphi})$ and the phase-dependent conductance $G(\ensuremath{\varphi})$ have been determined from measurements at 30 MHz on phase-biased niobium point contacts. For point contacts with sufficiently small critical current ${I}_{c}$, the inductance was $\mathfrak{L}(\ensuremath{\varphi})=\frac{\ensuremath{\hbar}}{2e{I}_{c}cos\ensuremath{\varphi}}$ yielding the expected negative inductance branch for $\frac{\ensuremath{\pi}}{2}\ensuremath{\le}\ensuremath{\varphi}\ensuremath{\le}\ensuremath{\pi}$ and a sinusoidal current-phase relation. For larger critical currents there were departures from the sinusoidal form for the measured ${I}_{p}(\ensuremath{\varphi})$. There was a phase-dependent conductance that is an increasing function of $\ensuremath{\varphi}$ corresponding to a negative coefficient for the $cos\ensuremath{\varphi}$ term in the Josephson current.