Abstract As charge carrier of the macroscopic superconductivity, the Cooper pair is a composite particle of two paired electrons, which has both center-of-mass and inner-pair degrees of freedom. In most cases, these two different degrees of freedom can be well described by the macroscopic Ginzburg-Landau theory and the microscopic Bardeen-Cooper-Schrieffer (BCS) theory, respectively. Near the superconducting phase transition where the Cooper pair is fragile and unstable because of the small binding energy, there are non-trivial couplings between these two different degrees of freedom due to such as finite energy and/or momentum transfer. The non-trivial couplings make the original derivation of the Ginzburg-Landau theory from the BCS theory fail in principle as where these two different degrees of freedom should not be decoupled. In this article, we will present a renormalization formalism for an extended Ginzburg-Landau action for the superconducting phase transition where there is finite energy transfer between the center-of-mass and the inner-pair degrees of freedom of Cooper pairs. This renormalization formalism will provide a theoretical tool to study the unusual dynamical effects of the inner-pair time-retarded physics on the superconducting phase transition.Abstract As charge carrier of the macroscopic superconductivity, the Cooper pair is a composite particle of two paired electrons, which has both center-of-mass and inner-pair degrees of freedom. In most cases, these two different degrees of freedom can be well described by the macroscopic Ginzburg-Landau theory and the microscopic Bardeen-Cooper-Schrieffer (BCS) theory, respectively. Near the superconducting phase transition where the Cooper pair is fragile and unstable because of the small binding energy, there are non-trivial couplings between these two different degrees of freedom due to such as finite energy and/or momentum transfer. The non-trivial couplings make the original derivation of the Ginzburg-Landau theory from the BCS theory fail in principle as where these two different degrees of freedom should not be decoupled. In this article, we will present a renormalization formalism for an extended Ginzburg-Landau action for the superconducting phase transition where there is finite energy transfer between the center-of-mass and the inner-pair degrees of freedom of Cooper pairs. This renormalization formalism will provide a theoretical tool to study the unusual dynamical effects of the inner-pair time-retarded physics on the superconducting phase transition.

arXiv:2210.03889Physica ScriptaJul 5, 20230 citations

Magnetoresistance in a Superconducting Single-Electron Transistor with a Multiply Connected Coulomb Island

Hideki Sato, Mitsuru Kimura, Shingo Katsumoto

The influence of phase fluctuation on fluxoid quantization in a small superconducting ring has been evaluated. In an isolated mesoscopic-sized superconductor, the number of Cooper pairs is fixed and the phase of the order parameter largely fluctuates due to Heisenberg's uncertainty principle. Under such conditions, it is not trivial whether the single-valuedness of the order parameter is kept and the fluxoid is quantized in the superconductor. We examined the problem experimentally using a superconducting single-electron transistor with a ring-shaped Coulomb island. We found that even when the fluctuation in the number of Cooper pairs is very small and a clear Coulomb oscillation is observed, the magnetic flux which goes through the ring is quantized.The influence of phase fluctuation on fluxoid quantization in a small superconducting ring has been evaluated. In an isolated mesoscopic-sized superconductor, the number of Cooper pairs is fixed and the phase of the order parameter largely fluctuates due to Heisenberg's uncertainty principle. Under such conditions, it is not trivial whether the single-valuedness of the order parameter is kept and the fluxoid is quantized in the superconductor. We examined the problem experimentally using a superconducting single-electron transistor with a ring-shaped Coulomb island. We found that even when the fluctuation in the number of Cooper pairs is very small and a clear Coulomb oscillation is observed, the magnetic flux which goes through the ring is quantized.

Japanese Journal of Applied PhysicsJun 1, 19970 citations

Quantum behaviour of superconducting rings

Timothy P. Spiller, Terrence D. Clark

NatureMay 1, 19862 citations

Measurement of coherent charge transfer in an adiabatic Cooper-pair pump

Rosario Fazio, F. W. J. Hekking, Jukka P Pekola

We study adiabatic charge transfer in a superconducting Cooper-pair pump, focusing on the influence of current measurement on coherence. We investigate the limit where the Josephson coupling energy ${E}_{J}$ between the various parts of the system is small compared to the Coulomb charging energy ${E}_{C}.$ In this case, the charge transferred in a pumping cycle ${Q}_{P}\ensuremath{\sim}2e,$ the charge of one Cooper pair: The main contribution is due to incoherent Cooper-pair tunneling. We are particularly interested in the quantum correction to ${Q}_{P},$ which is due to coherent tunneling of pairs across the pump and which depends on the superconducting phase difference ${\ensuremath{\varphi}}_{0}$ between the electrodes; $1\ensuremath{-}{Q}_{P}/(2e)\ensuremath{\sim}{(E}_{J}{/E}_{C})\mathrm{cos}{\ensuremath{\varphi}}_{0}.$ A measurement of ${Q}_{P}$ tends to destroy the phase coherence. We first study an arbitrary measuring circuit and then specific examples and show that coherent Cooper-pair transfer can, in principle, be detected using an inductively shunted ammeter.We study adiabatic charge transfer in a superconducting Cooper-pair pump, focusing on the influence of current measurement on coherence. We investigate the limit where the Josephson coupling energy ${E}_{J}$ between the various parts of the system is small compared to the Coulomb charging energy ${E}_{C}.$ In this case, the charge transferred in a pumping cycle ${Q}_{P}\ensuremath{\sim}2e,$ the charge of one Cooper pair: The main contribution is due to incoherent Cooper-pair tunneling. We are particularly interested in the quantum correction to ${Q}_{P},$ which is due to coherent tunneling of pairs across the pump and which depends on the superconducting phase difference ${\ensuremath{\varphi}}_{0}$ between the electrodes; $1\ensuremath{-}{Q}_{P}/(2e)\ensuremath{\sim}{(E}_{J}{/E}_{C})\mathrm{cos}{\ensuremath{\varphi}}_{0}.$ A measurement of ${Q}_{P}$ tends to destroy the phase coherence. We first study an arbitrary measuring circuit and then specific examples and show that coherent Cooper-pair transfer can, in principle, be detected using an inductively shunted ammeter.

arXiv:cond-mat/0302383Physical review. B, Condensed matterAug 7, 200324 citations

We study adiabatic charge transfer in a superconducting Cooper-pair pump, focusing on the influence of current measurement on coherence. We investigate the limit where the Josephson coupling energy

{E}_{J}

between the various parts of the system is small compared to the Coulomb charging energy

{E}_{C}.

In this case, the charge transferred in a pumping cycle ${Q}_{P}\ensuremath{\sim}2e,$ the charge of one Cooper pair: The main contribution is due to incoherent Cooper-pair tunneling. We are particularly interested in the quantum correction to

{Q}_{P},

which is due to coherent tunneling of pairs across the pump and which depends on the superconducting phase difference ${\ensuremath{\varphi}}_{0}$ between the electrodes; $1\ensuremath{-}{Q}_{P}/(2e)\ensuremath{\sim}{(E}_{J}{/E}_{C})\mathrm{cos}{\ensuremath{\varphi}}_{0}.$ A measurement of

{Q}_{P}

tends to destroy the phase coherence. We first study an arbitrary measuring circuit and then specific examples and show that coherent Cooper-pair transfer can, in principle, be detected using an inductively shunted ammeter.