Charge Transport in Voltage-Biased Superconducting Single-Electron Transistors

Charge is transported through superconducting SSS single-electron transistors at finite bias voltages by a combination of coherent Cooper-pair tunneling and quasiparticle tunneling. At low transport voltages the effect of an ``odd'' quasiparticle in the island leads to a $2e$-periodic dependence of the current on the gate charge. We evaluate the $I-V$ characteristic in the framework of a model which accounts for these effects as well as for the influence of the electromagnetic environment. The good agreement between our model calculation and experimental results demonstrates the importance of coherent Cooper-pair tunneling and parity effects.Comment: RevTeX, 12 pages, 4 figure

Connecting Berry's phase and the pumped charge in a Cooper pair pump

The properties of the tunnelling-charging Hamiltonian of a Cooper pair pump are well understood in the regime of weak and intermediate Josephson coupling, i.e. when $E_{\mathrm{J}}\lesssim E_{\mathrm{C}}$. It is also known that Berry's phase is related to the pumped charge induced by the adiabatical variation of the eigenstates. We show explicitly that pumped charge in Cooper pair pump can be understood as a partial derivative of Berry's phase with respect to the phase difference $\phi$ across the array. The phase fluctuations always present in real experiments can also be taken into account, although only approximately. Thus the measurement of the pumped current gives reliable, yet indirect, information on Berry's phase. As closing remarks, we give the differential relation between Berry's phase and the pumped charge, and state that the mathematical results are valid for any observable expressible as a partial derivative of the Hamiltonian.Comment: 5 pages, 5 figures, RevTeX, Presentation has been clarifie

Proximity Induced Josephson-Quasiparticle Process in a Single Electron Transistor

We have performed the first experiments in a superconductor - normal metal - superconductor single electron transistor in which there is an extra superconducting strip partially overlapping the normal metal island in good metal-to-metal contact. Superconducting proximity effect gives rise to current peaks at voltages below the quasiparticle threshold. We interpret these peaks in terms of the Josephson-quasiparticle process and discuss their connection with the proximity induced energy gap in the normal metal island.Comment: 4 pages + 4 figure

Electronic Transport in Hybrid Mesoscopic Structures: A Nonequilibrium Green Function Approach

We present a unified transport theory of hybrid structures, in which a confined normal state ($N$) sample is sandwiched between two leads each of which can be either a ferromagnet ($F$) or a superconductor ($S$) via tunnel barriers. By introducing a four-dimensional Nambu-spinor space, a general current formula is derived within the Keldysh nonequilibrium Green function formalism, which can be applied to various kinds of hybrid mesoscopic systems with strong correlations even in the nonequilibrium situation. Such a formula is gauge invariant. We also demonstrate analytically for some quantities, such as the difference between chemical potentials, superconductor order parameter phases and ferromagnetic magnetization orientations, that only their relative value appears explicitly in the current expression. When applied to specific structures, the formula becomes of the Meir-Wingreen-type favoring strong correlation effects, and reduces to the Landauer-B\"uttiker-type in noninteracting systems such as the double-barrier resonant structures, which we study in detail beyond the wide-band approximation.Comment: 24 pages, 12 eps figures, Revtex

Coulomb Blockade of Andreev Reflection in the NSN Single-Electron Transistor

URL: http://www-drecam.cea.fr/spec/articles/s93/001/ in: Proceedings of the 20th International Conference on Low Temperature Physics (LT-20), Eugene, Oregon, USA, August 4-11, 1993; Org.: Donnelly R.J.We have measured at low temperatures the current through a submicrometer superconducting island connected to normal metal leads by ultrasmall tunnel junctions. At low bias voltages, the current changes from being $e$-periodic in the applied gate charge to $2e$-periodic. We interpret this $2e$-periodic current as a manifestation of a sequence of Andreev reflection events which transports two electrons at a time across the island. This behavior is clear evidence that there is a difference in total energy between ground states of differing electron number parity

Magnetic-field-induced tunneling and minigap transport in double quantum wells

We review recent theoretical and experimental results on low- temperature tunneling and in-plane transport properties in double quantum wells (DQWs) in an in-plane magnetic field B{parallel}. These properties arise from combined effect of B{parallel}-induced relative displacement of the wave vectors in the two QWs and the interwell tunneling. In weakly coupled DQWs, the tunneling conductance has two sharp maxima as a function of B{parallel}. In strongly coupled DQWs, a partial minigap is formed due to anticrossing of the two QW dispersion curves, yielding sharp B{parallel}-dependent structures in the density of states and in- plane transport properties. Excellent agreement is obtained between theory and data from GaAs/AlGaAs DQWs

Tuning a double quantum well Fermi surface with in-plane magnetic fields

A double quantum well (QW) subject to in-plane magnetic fields B{sub {parallel}} has the dispersion curves of its two QWs shifted in k-space. When the QWs are strongly coupled, an anticrossing and partial energy gap occur, yielding a tunable multi-component Fermi surface. We report measurements of the resultant features in the conductance, capacitive density of states, and giant deviations in cyclotron effective masses