Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

AIP conference proceedings

Current-Phase Relation of a Well-Characterized Superconducting Atomic Point Contact

Hisao Miyazaki, Takahide Yamaguchi, Akinobu Kanda, Youiti Ootuka

Published Jan 1, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.2354929

Related papers

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

Robert Rifkin, Bascom S. Deaver

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.

Physical review. B, Solid state•May 1, 1976•89 citations

ac Josephson effect in asymmetric superconducting quantum point contacts

Shin-Tza Wu, Sungkit Yip

We investigate ac Josephson effects between two superconductors connected by a single-mode quantum point contact, where the gap amplitudes in the two superconductors are unequal. In these systems, it was found in previous studies on the dc effects that, besides the Andreev bound states, the continuum states can also contribute to the current. Using the quasiclassical formulation, we calculate the current-voltage characteristics for general transmission $D$ of the point contact. To emphasize bound versus continuum states, we examine in detail the low bias, ballistic $(D=1)$ limit. It is shown that in this limit the current-voltage characteristics can be determined from the current-phase relation, if we pay particular attention to the different behaviors of these states under the bias voltage. For unequal gap configurations, the continuum states give rise to nonzero sine components. We also demonstrate that in this limit, the temperature dependence of the dc component follows $\mathrm{tanh}({\ensuremath{\Delta}}_{s}∕2T)$, where ${\ensuremath{\Delta}}_{s}$ is the smaller gap, with the contribution coming entirely from the bound state.

arXiv:cond-mat/0407163•Physical Review B•Sep 20, 2004•7 citations

Theory of Microwave-Assisted Supercurrent in Quantum Point Contacts

F. S. Bergeret, Pauli Virtanen, Tero Tapio Heikkilä +1 more

We present a microscopic theory of the effect of a microwave field on the supercurrent through a quantum point contact of arbitrary transmission. Our theory predicts that (i) for low temperatures and weak fields, the supercurrent is suppressed at certain values of the superconducting phase, (ii) at strong fields, the current-phase relation is strongly modified and the current can even reverse its sign, and (iii) at finite temperatures, the microwave field can enhance the critical current of the junction. Apart from their fundamental interest, our findings are also important for the description of experiments that aim at the manipulation of the quantum state of atomic point contacts.

arXiv:1006.3181•Physical Review Letters•Sep 8, 2010•42 citations

Effect of nonequilibrium phenomena in a superconducting point contact on the properties of a single-contact quantum interferometer

V. A. Khlus

The behavior of a superconducting ring incorporating a point contact, coupled inductively to an oscillatory circuit (hf SQUID), with the rate of change of the magnetic flux in the ring being comparable, to the inverse energy relaxation time of excitations in the superconductor τϵ−1, is examined. For T ∽ Tc the results of the microscopic theory of the nonstationary behavior of point contacts, in which the coupling between the phase difference and the current of the Josephson junction differs from the usual expression I = V/R + Icsinφ in the resistive model, are used. It is shown that the nonequilibrium behavior of a weak link for ω≳τϵ−1 significantly changes the amplitude–frequency and signal characteristics of the SQUID as compared with the case ωτϵ−1≪1, for which the results based on the resistive model are valid. The characteristics of the SQUID in the nonequilibrium situation are sensitive to the ratio between the size of the contact and the mean free path of electrons relative to scattering by impurities.

Soviet Journal of Low Temperature Physics•Jan 1, 1984•0 citations

Current-phase relation and Josephson inductance in a superconducting Cooper-pair transistor

Antti Paila, David Gunnarsson, Jayanta Sarkar +2 more

We have investigated the Josephson inductance ${L}_{J}$ of a superconducting Cooper pair transistor (SCPT). We traced the inductance using microwave reflection measurements on a tuned resonance circuit in which a SCPT was mounted in parallel to a $\ensuremath{\sim}200\text{ }\text{pH}$ strip line inductance. When the inverse of the Josephson inductance, determined on the charge-phase bias plane for a SCPT with a Josephson to Coulomb energy ratio of ${E}_{J}/{E}_{C}=1.75$, is integrated over the phase, we obtain a current-phase relation, which is strongly nonsinusoidal near the charge degeneracy point.

arXiv:0910.1337•Physical Review B•Oct 21, 2009•11 citations

Direct measurements of current-phase relations for several types of superconducting weak links. Technical report

L. D. Jackel, John M. Warlaumont, Jessica Brown +2 more

While recent theoretical and experimental evidence have indicated that many commonly used superconducting weak links might have distinctly nonsinusoiual current-phase relations, precise measurement of these relations has been difficult to realize. Now a high resolution technique has been developed for the measurement of current-phase relations of weak links. This technique was used to determine the current-phase relations of various weak link structures including point contacts, thin film microbridges and proximity effect bridges. (GRA)

•Aug 1, 1975•0 citations
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.
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.
We investigate ac Josephson effects between two superconductors connected by a single-mode quantum point contact, where the gap amplitudes in the two superconductors are unequal. In these systems, it was found in previous studies on the dc effects that, besides the Andreev bound states, the continuum states can also contribute to the current. Using the quasiclassical formulation, we calculate the current-voltage characteristics for general transmission DDD of the point contact. To emphasize bound versus continuum states, we examine in detail the low bias, ballistic (D=1)(D=1)(D=1) limit. It is shown that in this limit the current-voltage characteristics can be determined from the current-phase relation, if we pay particular attention to the different behaviors of these states under the bias voltage. For unequal gap configurations, the continuum states give rise to nonzero sine components. We also demonstrate that in this limit, the temperature dependence of the dc component follows $\mathrm{tanh}({\ensuremath{\Delta}}_{s}∕2T)$, where ${\ensuremath{\Delta}}_{s}$ is the smaller gap, with the contribution coming entirely from the bound state.
We present a microscopic theory of the effect of a microwave field on the supercurrent through a quantum point contact of arbitrary transmission. Our theory predicts that (i) for low temperatures and weak fields, the supercurrent is suppressed at certain values of the superconducting phase, (ii) at strong fields, the current-phase relation is strongly modified and the current can even reverse its sign, and (iii) at finite temperatures, the microwave field can enhance the critical current of the junction. Apart from their fundamental interest, our findings are also important for the description of experiments that aim at the manipulation of the quantum state of atomic point contacts.
The behavior of a superconducting ring incorporating a point contact, coupled inductively to an oscillatory circuit (hf SQUID), with the rate of change of the magnetic flux in the ring being comparable, to the inverse energy relaxation time of excitations in the superconductor τϵ−1, is examined. For T ∽ Tc the results of the microscopic theory of the nonstationary behavior of point contacts, in which the coupling between the phase difference and the current of the Josephson junction differs from the usual expression I = V/R + Icsinφ in the resistive model, are used. It is shown that the nonequilibrium behavior of a weak link for ω≳τϵ−1 significantly changes the amplitude–frequency and signal characteristics of the SQUID as compared with the case ωτϵ−1≪1, for which the results based on the resistive model are valid. The characteristics of the SQUID in the nonequilibrium situation are sensitive to the ratio between the size of the contact and the mean free path of electrons relative to scattering by impurities.
We have investigated the Josephson inductance LJ{L}_{J}LJ​ of a superconducting Cooper pair transistor (SCPT). We traced the inductance using microwave reflection measurements on a tuned resonance circuit in which a SCPT was mounted in parallel to a $\ensuremath{\sim}200\text{ }\text{pH}$ strip line inductance. When the inverse of the Josephson inductance, determined on the charge-phase bias plane for a SCPT with a Josephson to Coulomb energy ratio of EJ/EC=1.75{E}_{J}/{E}_{C}=1.75EJ​/EC​=1.75, is integrated over the phase, we obtain a current-phase relation, which is strongly nonsinusoidal near the charge degeneracy point.
While recent theoretical and experimental evidence have indicated that many commonly used superconducting weak links might have distinctly nonsinusoiual current-phase relations, precise measurement of these relations has been difficult to realize. Now a high resolution technique has been developed for the measurement of current-phase relations of weak links. This technique was used to determine the current-phase relations of various weak link structures including point contacts, thin film microbridges and proximity effect bridges. (GRA)