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Physica C Superconductivity

Current-phase relation of a superconducting quantum point contact

Hisao Miyazaki, Akinobu Kanda, Youiti Ootuka

Published Feb 4, 2006• 8 citations
Publisher
DOI
10.1016/j.physc.2005.12.051

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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 Ic{I}_{c}Ic​, 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.
According to theories of a superconducting quantum point contact (QPC), Cooper pairs are transferred via a few channels which are fully characterized by a set of transmission coefficients {τi}. Indeed, the I–V characteristics and the current‐phase relation I(φ, τ) of a single‐channel QPC have been calculated as a function of the coefficient τ. However, the experimental quantitative verification has not been done yet. In this paper, we propose an experiment in which both the transmission coefficients {τi} and I(φ, {τi}) relation can be determined independently.