Theory of novel properties of Josephson effect in anisotropic superconductors

Recent studies on high- T_csuperconductors aroused our new interest on the Josephson effects in anisotropic superconductors. In contrast to the conventional s-wave superconductors, there are two additional intrinsic effects originating from an internal phase of the pair potential. One is the sign change of the Josephson current depending on the direction of the motion of the Cooper pair. The other is the formation of localized states near the insulator. By taking account of these two effects, a general formula for the Josephson current is presented. Calculated results predict several anomalous properties including a strong enhancement of the Josephson current at low temperature. The influences of the spatial dependence of the pair potential on the Josephson current are also clarified.     

Josephson effect in ferromagnetic superconductors

The DC Josephson effect in ferromagnetic superconductors is theoretically studied in the presence of external magnetic fields. In addition to the usual term for the Josephson tunneling current, a new term expressing the pair tunneling current induced by the magnetization appears. The amplitude and period of the Fraunhofer pattern of the maximum Josephson current drastically diminish near the phase transition temperature for the magnetization bound around the junction.     

Supercurrent pumping in Josephson junctions with a half-metallic ferromagnet

A Josephson current through a half-metallic ferromagnet between two conventional superconductors is theoretically studied. The spin dynamics such as magnon excitation plays a crucial role not only for the conversion between spin-singlet and spin-triplet pairs but also for the formation of the composite state of a triplet Cooper pair and magnon, by which the Josephson current flows between the superconductors. We propose the supercurrent pumping driven by the coherent precession of the magnetization by tuning the microwave frequency to the ferromagnetic resonance frequency in a ferromagnetic Josephson junction.     

Quantum dissociation of a vortex-antivortex pair in a long josephson junction

The thermal and the quantum dissociation of a single vortex-antivortex (VAV) pair in an annular Josephson junction is experimentally observed and theoretically analyzed. In our experiments, the VAV pair is confined in a pinning potential controlled by external magnetic field and bias current. The dissociation of the pinned VAV pair manifests itself in a switching of the Josephson junction from the superconducting to the resistive state. The observed temperature and field dependence of the switching current distribution is in agreement with the analysis. The crossover from the thermal to the macroscopic quantum tunneling mechanism of dissociation occurs at a temperature of about 100 mK. We also predict the specific magnetic field dependence of the oscillatory energy levels of the pinned VAV state.     

Vortices in a Josephson junction sandwiched between two superconducting waveguides

For a Josephson junction magnetically coupled to the superconducting waveguides enclosing it, solutions to the equation for the difference of the Cooper pair phases over the Josephson junction are found and the corresponding magnetic field values are calculated. Two gaps imposing an upper limit for the vortex velocity are found for free vortices (moving without dissipation). Existence conditions are found for fast vortices in the two high-velocity allowed regions. The dependence of the transport current on vortex velocity is established in cases where the current flows through the Josephson junction only or through the entire structure. A reverse current phenomenon is discovered in which vortices inside allowed velocity regions move opposite to the usual direction.     

Mesoscopic Josephson effect

In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current–voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.     

ac Josephson effect and resonant Cooper pair tunneling emission of a single Cooper pair transistor

We measure the high-frequency emission of a single Cooper pair transistor (SCPT) in the regime where transport is only due to tunneling of Cooper pairs. This is achieved by coupling on chip the SCPT to a superconductor-insulator-superconductor junction and by measuring the photon assisted tunneling current of quasiparticles across the junction. This technique allows a direct detection of the ac Josephson effect of the SCPT and provides evidence of Landau-Zener transitions for proper gate voltage. The emission in the regime of resonant Cooper pair tunneling is also investigated. It is interpreted in terms of transitions between charge states coupled by the Josephson effect.     

On the Bosonic Phase Operator Realization for Josephson Hamiltonian Model

On the assumption that a Cooper pair acts as a Bose particle and based on the newly estabished (η|representation,which is the common eigenvector of two particles‘ relative position and total momentum,we introduce a mesoscopic Josephson junction Hamiltonian constituted by two-mode Bose phase operator and number-difference operator,The number-difference-phase uncertainty relation can then be set up,which implies the existence of Josephson current.     

Resonance tunneling of cooper pairs in a superconductor-polymer-superconductor josephson junction

It is shown that the superconducting current flowing though a polymer in a superconductor-polymer-superconductor Josephson structure is due to resonant tunneling of Cooper pairs. The critical current and the thickness of the polymer in which the superconducting current is observed depend on the coherence length of a Cooper pair in the superconductor contacting the polymer.     

Fast and accurate single-island charge pump: implementation of a cooper pair pump

We introduce a Cooper pair "sluice" for the implementation of a frequency-locked current source. The device consists of two mesoscopic SQUIDs and of a single superconducting island with a gate. We demonstrate theoretically that it is possible to obtain a current as high as 0.1 nA at better than ppm accuracy via periodically modulating both the gate charge and the effective Josephson coupling. We find that the device is tolerant against background charge noise and operates well even in a dissipative environment. The effect of the imperfect suppression of the Josephson coupling and the finite operating frequency are also investigated.     

Properties of superconductor–Luttinger-liquid hybrid systems

In this paper, we review some recent results concerning the physics of superconductor–Luttinger-liquid proximity systems. We discuss both equilibrium (the pair amplitude, Josephson current, and the local density of states) and nonequilibrium (the subgap current) properties.     

Josephson current versus potential strength of the interface in ferromagnetic superconductors

Based on the scattering theory, we calculate the Josephson current in a junction between two ferromagnetic superconductors as a function of the interface potential z. We consider the ferromagnetic superconductor(FS) in three different Cooper pairing states: spin singlet s-wave pairing(SWP) state, spin triplet opposite spin pairing(OSP) state, and spin triplet equal spin pairing(ESP) state. We find that the critical Josephson current as a function of z shows clear differences among the SWP, OSP, and ESP states. The obtained results can be used as a useful tool for determining the pair symmetry of the ferromagnetic superconductors.     

Cooper-Pair Number-Phase Quantization for a Mesoscopic LC Circuit Including a Josephson Junction

By introducing the entangled state representation and Feynman assumption that ＇electron pairs are bosons, ..., a bound pair acts as a Bose particle ＇, we construct an operator Hamiltonian for a mesoscopic inductance-capacitance （LC） circuit including a Josephson junction, then we use the Heisenberg equation of motion to derive the current equation and the voltage equation across the inductance as well as across the Josephson junction. The result manifestly shows how the junction voltage is affected by the capacitance coupling. In this way the Cooper-pair number-phase quantization for this system is completed.     

Rectification by an imprinted phase in a Josephson junction

A Josephson phase shift can be induced in a Josephson junction by a strategically nearby pinned Abrikosov vortex (AV). For an asymmetric distribution of an imprinted phase along the junction (controlled by the position of the AV) such a simple system is capable of rectification of ac current in a broad and tunable frequency range. The resulting rectified voltage is a consequence of the directed motion of a Josephson antivortex which forms a pair with the AV when at local equilibrium. The proposed realization of the ratchet potential by an imprinted phase is more efficient than the asymmetric geometry of the junction itself, is easily realizable experimentally, and provides rectification even in the absence of an applied magnetic field.     

Cooper pair cotunneling in single charge transistors with dissipative electromagnetic environment

We observed current-voltage characteristics of superconducting single charge transistors with on-chip resistors of R approximately R(Q)=h/4e(2) approximately 6.45 kOmega, which are explained in terms of Cooper pair cotunneling. Both the effective strength of Josephson coupling and the cotunneling current are modulated by the gate-induced charge on the transistor island. For increasing values of the resistance R we found the Cooper pair current at small transport voltages to be dramatically suppressed.     

Current to frequency conversion in a Josephson circuit

The voltage oscillations which occur in an ideally current-biased Josephson junction were proposed to make a current standard for metrology. We demonstrate similar oscillations in a more complex Josephson circuit derived from the Cooper pair box: the quantronium. When a constant current I is injected in the gate capacitor of this device, oscillations develop at the frequency f(B)=I/2e, with e the electron charge. We detect these oscillations through the sidebands induced at multiples of f(B) in the spectrum of a microwave signal reflected on the circuit, up to currents I exceeding 100 pA. We discuss the potential interest of this current-to-frequency conversion experiment for metrology.     

Proximity effect, Andreev reflections, and charge transport in mesoscopic superconducting/semiconducting heterostructures

In the quasi-two-dimensional (Q2D) electron gas of an InAs channel between an AlSb substrate and superconducting niobium layers, the proximity effect induces a pair potential so that a Q2D mesoscopic superconducting/normal/superconducting (SNS) junction forms in the channel. The pair potential is calculated with quasiclassical Green’s functions in the clean limit. For such a junction, alternating Josephson currents and current–voltage characteristics (CVCs) are computed, using the nonequilibrium quasiparticle wavefunctions which solve the time-dependent Bogoliubov–de Gennes equations. The CVCs exhibit features found experimentally by the Kroemer group: a steep rise of the current at small voltages (‘foot’) changes at a ‘corner current’ to a much slower increase of current with higher voltages, and the zero-bias differential resistance increases with temperature. Phase-coherent multiple Andreev reflections and the associated Cooper pair transfers are the physical mechanisms responsible for the oscillating Josephson currents and the CVCs. Additional experimental findings not reproduced by the theory require model improvements, especially a consideration of the external current leads which should give rise to hybrid quasiparticle/collective-mode excitations.     

Dynamics of semifluxons in Nb long Josephson 0-pi junctions

We propose, implement, and test experimentally long Josephson 0-pi junctions fabricated using conventional Nb-AlOx-Nb technology. We show that by using a pair of current injectors one can create an arbitrary discontinuity of the Josephson phase and, in particular, a pi discontinuity, just as in d-wave/s-wave or in d-wave/d-wave junctions, and study fractional Josephson vortices which spontaneously appear. Moreover, using such junctions, we can investigate the dynamics of the fractional vortices-a domain which is not yet available for natural 0-pi junctions due to their inherently high damping. We observe half-integer zero-field steps which appear on the current-voltage characteristics due to the hopping of semifluxons.