Pair Tunneling Research Articles

Quantum regime of Cooper pair tunneling in small-area Bi 2Sr 2CaCu 2O 8+ δ mesas in magnetic fields

We show that application of an c-axis magnetic field decreases the effective interlayer Josephson coupling in small-area Bi 2Sr 2CaCu 2O 8+ δ (Bi-2212) mesas at low temperatures. As magnetic field increases, the crossover from the classical regime of Cooper pair tunneling to the quantum regime leads to an additional drastic suppression of the Josephson coupling due to the Coulomb blockade. As result, the stack of many intrinsic junctions is nonsuperconducting at high fields. The quantum regime of superconducting tunneling may be reached in mesas with N junctions and area 0.3 μm 2 made of intercalated Bi-2212 crystals by applying c-axis magnetic fields B>4/ N 2 T at N≫1.

Interplay of single particle and Cooper pair tunnelings on the superconducting state of layered high- Tc cuprates

In the present paper we report the interplay of single particle tunneling and Cooper pair tunneling on the low temperature superconducting state of layered high- T c cuprate superconductors. For this a microscopic model Hamiltonian has been considered that incorporates the intra-planar interactions along with contributions corresponding to the coupling between the planes in the form of single particle tunneling as well as Josephson Cooper pair tunneling. The expressions of the superconducting order parameter and the out-of-plane correlation parameter which describes the hopping of a particle from one layer to another layer in the superconducting state, are obtained as a function of various parameters of the model Hamiltonian within the BCS formalism using the Green’s function technique for a bilayer cuprate. It is found that the superconducting order parameter at zero temperature is robust against single particle tunneling while the Cooper pair tunneling between the layers enhances superconducting order parameter and provides favorable conditions for the formation of Cooper pairs within the planes. We have also calculated the out-of-plane contributions to the superconducting condensation energy which is in agreement with the existing calculations on the condensation energy of bilayer cuprates from the specific heat and the c-axis penetration depth measurements.

Observability of quantum phase fluctuations in cuprate superconductors.

We study the order parameter phase fluctuation effects in cuprate superconductors near T = 0, using a quasi-two-dimensional d-wave BCS model. An effective phason theory is obtained which is used to estimate the strength of the fluctuations, the fluctuation correction to the in-plane penetration depth, and the pair-field susceptibility. We find that, while the phase fluctuation effects are difficult to observe in the renormalization of the superfluid phase stiffness, they may be observed in a pair tunneling experiment which measures the pair-field susceptibility.

Quantum phase transition in one-dimensional Josephson junction arrays

We describe experiments on one-dimensional arrays of small capacitance Josephson junctions which show how the Coulomb blockade of Cooper pair tunneling is influenced by changing the Josephson coupling energy in situ with an externally applied magnetic flux. We show how the zero bias resistance of the array is affected by the length of the array, and we use the length scaling of this resistance to infer that a quantum phase transition occurs as the Josephson coupling energy is changed. The data are qualitatively analyzed in terms of a theoretical model of the quantum phase transition which uses a mapping to the two-dimensional XY model.

Scaling of transition temperature and CuO 2 plane buckling in the cuprate superconductors

A universal feature of all high temperature superconductors is the existence of a chemical composition that gives maximum T c, separating so-called under- and over-doped region. Recently, it is seen by Chmaissem et al. [Nature 397 (1999) 45] that both T c and the buckling angle of the CuO 2 planes goes through a maximum at the same doping level. We show that only for optimal doping concentration the Fermi surface touches the M(0,π) point in the BZ, where the matrix element for interlayer pair tunneling amplitude is largest, so that the gain in delocalization energy by tunneling (in pairs) along the c-axis is largest. Buckling of the planes on the other hand modulates the separation between the planes and thereby modulates the interlayer pair tunneling amplitude. That is why both T c and buckling angle (oxygen atom displacement out of the plane) scales the same way with doping concentration. We have calculated T c and buckling angle for various doping concentration. The agreement with experiment is remarkably good. We also point out the possible reason for large (about 1%) change of the buckling mode phonon frequency, across the transition temperature for optimal doping concentration, observed in neutron scattering experiments by Pyka et al. [Phys. Rev. Lett. 70 (1993) 1457].

Spin polarized carrier injection into high-Tcsuperconductors: A test for the superconductivity mechanism

We point out in this short paper, that be it an s-wave or d-wave superconductor, in a nonequilibrium situation (i.e., in the presence of excess unpolarized and polarized quasiparticles maintained by an injection current) the superconducting gap suppression by the presence of the same amount of excess quasiparticles, can at best differ by a factor of 2, for a conventional BCS superconductor. For the high-${T}_{c}$ superconductors on the other hand, there is a huge difference in gap suppression between unpolarized and polarized quasiparticle injection, as observed in the experiments [V. A. Vasko et al., Phys. Rev. Lett. 78, 1134 (1997); T. A. Venkatesan et al., Appl. Phys. Lett. 71, 1718 (1997)]. We argue that this large anomaly has a natural explanation within the interlayer tunneling mechanism of Wheatley, Hsu, and Anderson [J. M. Wheatley, T. C. Hsu, and P. W. Anderson, Phys. Rev. B 37, 5897 (1988)], and is due to the excess polarized quasiparticles blocking the interlayer pair tunneling process. We also point out that spin polarized quasiparticle injection in a superconductor is a very easy way to distinguish between an s-wave or an anisotropic gap superconductor.

Two-square-well model for layered superconductors: Effect of intralayer and interlayer Coulomb interactions on thed-wave gap

On the basis of Fermi liquid theory, we study the effect of intralayer and interlayer Coulomb interactions on the energy gap of layered superconductors assuming the BCS d-wave pairing model. The gap equation is derived for the two-square-well model, assuming a boson-mediated attraction and a long-range Coulomb repulsion that leads to intralayer and interlayer Coulomb scattering of Cooper pairs. The d-wave gap amplitude ${\ensuremath{\Delta}}_{1}$ at $T=0\mathrm{K}$ is evaluated as a function of the attractive pairing strength and of the screened Coulomb interactions. For optimally doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ we find that intralyer Coulomb scattering reduces ${\ensuremath{\Delta}}_{1}$ by a factor between 1.5 and 2. The additional effect of interlayer Coulomb scattering depends in a crucial manner on the relative phases of the gap functions in adjacent layers. If Josephson and boson-assisted interlayer pair tunneling (ILT) are responsible, the three-dimensional phase coherence, that is, the phase difference between adjacent layers $\ensuremath{\Delta}\ensuremath{\varphi}=0,$ interlayer Coulomb scattering leads to a further reduction of the gap that can be comparable with or larger than the effect of intralyer scattering. If, however, the phase of the gap function alternates, that is $\ensuremath{\Delta}\ensuremath{\varphi}=\ensuremath{\pi},$ because the interlayer Coulomb scattering dominates the ILT effect, the interlayer Coulomb scattering of Cooper pairs enhances ${\ensuremath{\Delta}}_{1}.$ This effect is studied as a function of the strength of the Coulomb interaction and it is shown that, with increasing strength, the pseudo-Coulomb parameter ${\mathrm{\ensuremath{\mu}}}^{\mathrm{*}}$ decreases and may change sign when the Coulomb interaction is sufficiently strong. The possible role of the interlayer Coulomb effect is discussed in relation to scanning tunneling microscopy experiments.

Tunneling dynamics of Bose-Einstein condensates with Feshbach resonances

We study tunneling dynamics of atomic pairs in Bose-Einstein condensates with Feshbach resonances. It is shown that the tunneling of the atomic pairs depends on not only the tunneling coupling between the atomic condensate and the molecular condensate, but also the inter-atomic nonlinear interactions and the initial number of atoms in these condensates. It is found that in addition to oscillating tunneling current between the atomic condensate and the molecular condensate, the nonlinear atomic-pair tunneling dynamics sustains a self-locked population imbalance: macroscopic quantum self-trapping effect. Influence of decoherence induced by non-condensate atoms on tunneling dynamics is investigated. It is shown that decoherence suppresses atomic-pair tunneling.

The correlation of the number and the phase uncertainties in the loop-type single-electron tunneling device

The electric and the magnetic transport properties of the loop-type Al/Al 2O 3/Al single-electron tunneling device were studied. Even for the sample with charging energy about one order of magnitude greater than the Josephson coupling energy, the magnetoresistance showed h/2 e-oscillation at low bias voltage, attributed to the phase-coherent pair tunneling. The behavior of the magnetoresistance depends on the gate voltage, showing large and noiseless oscillations with the even number of excess charges but small and noisy oscillations with the odd number of excess charges in the metal islands.

Tunneling characteristics of I- and HgI 2-intercalated Bi 2Sr 2CaCu 2O 8+ x single crystals

We compared c-axis tunneling characteristics of small stacked intrinsic Josephson junctions prepared on the surface of pristine, I-, and HgI 2-intercalated Bi 2Sr 2CaCu 2O y (Bi2212) single crystals. Relation between the interlayer coupling and the in-plane gap, estimated from I– V characteristics, seems to contradict to the interlayer pair tunneling mechanism of high- T c superconductivity.

Arrays of Josephson junctions in an environment with vanishing impedance

The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunneling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalization of the Hamiltonian operator is used in order to reliably parametrize the effects due to inhomogeneity in the array and nonideal gating sequences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.

Intrinsic Josephson effect and single Cooper pair tunneling

We proposed a new, small and fast switching gate based on the intrinsic Josephson effect of single crystals of a cuprate superconductor. The switching time is of subpicosecond order, and the operating frequency is up to several terahertz. We used the focused-ion-beam (FIB) method for the fabrication of small Bi 2Sr 2CaCu 2O 8 (Bi-2212) stacked intrinsic Josephson junctions (IJJ) with in-plane size down to the submicron level without the degradation of their T c. We observed clear Fraunhofer patterns in I c– B curves and flux-flow velocity of up to 10 6 m/s for the stack junctions with the size of several micrometer scale. For the submicron junction, the low-temperature behavior is governed by the Coulomb-charging effects. This is the first observation of the Coulomb-charging effects in layered high- T c materials.

Effect of electromagnetic environment effect on coherent and incoherent Cooper pair tunneling in superconducting C-SET

Cooper pair tunneling in voltage-biased superconducting C-SET structure is discussed with emphasis on the electromagnetic environment effect based on the self-consistent microscopic theory of Coulomb blockade in C-SET. It is shown that coherent Cooper pair tunneling survives only in the low impedance limit where charge fluctuation is large, while incoherent Cooper pair tunneling survives in both low- and high-impedance limits.

Josephson junction quantum logic gates

Low-capacitance Josephson junctions, where Cooper pairs tunnel coherently while Coulomb blockade effects allow the control of the total charge, provide physical realizations of quantum bits (qubits), with logical states differing by one Cooper-pair charge on an island. The single- and two-bit operations required for quantum computation can be performed by applying a sequence of gate voltages (Shnirman et al., 1997). The phase coherence time is sufficiently long to allow a series of operations. A new design (Makhlin et al., 1999), close to ideal, where the Josephson junctions are replaced by controllable SQUIDs relaxes the requirements on the time control and system parameters substantially, and the two-bit coupling can be switched exactly between zero and a non-zero value for arbitrary pairs.

Hysteretic current–voltage characteristics and Coulomb blockade in 1D-arrays of Josephson junctions

The IV characteristics (IVC) of 1D-arrays of small capacitance Josephson junctions with E C∼ E J have been measured. The IVC show Coulomb blockade of Cooper pair tunneling and exhibit a pronounced hysteresis which appears to be dual to the well-known resistively shunted junction behavior of ordinary Josephson junctions. A dual serially resistive junction model is used to qualitatively explain the measured data.

Enhancement of Josephson Quasiparticle Current in Coupled Superconducting Single-electron Transistors

The Josephson quasiparticle (JQP) cycle in a voltage-biasedsuperconducting single-electron transistor (SSET) combinescoherent Cooper pair tunneling with incoherent quasiparticledecay. We have measured a striking modification of the JQPprocess in a system of two SSET's having a large mutualcapacitance. We find, among other effects, that the JQPcurrent in one SSET may be enhanced by the presence of aquasiparticle current through the other SSET. A simplified model of the coupled-SSET system is presented which reproducesthe enhancement effect.

The penetration depth in the interlayer tunnelling model for high-temperature superconductors

We investigate numerically the temperature dependence of the London penetration depth within the mean-field treatment of the interlayer pair tunnelling model for the copper oxide superconductors. It is found that the assumption that the pair tunnelling is the dominant pairing mechanism in YBCO (yttrium-barium-copper oxide) is not consistent with the experimental results on this material. We also consider the Knight shift and the dynamic spin susceptibility at a low temperature within the model. We find that the experimental results for these quantities are consistent with a relatively small contribution of the interlayer pair tunnelling to the pairing channel provided that, at least in the case of the dynamic susceptibility, the in-plane pairing produces a gap of d(x2-y2)-wave symmetry which is non-zero within at most a few tens of meV off the Fermi line.

Single cooper pair electronics

Abstract Single electron devices are based on small normal metal electrodes called ‘islands’ separated by tunnel junctions. In such circuits, electrons can be transfered one by one when the energy of thermal fluctuations is less than the electrostatic energy necessary to add an extra electron to an island. We present here experimental results in single electron devices for which all normal-metal electrodes are replaced by superconducting ones. In such devices coherent Cooper pair tunneling (i.e. the DC-Josephson effect) combines with Coulomb blockade. These effects can be tuned in such a way that signatures of the macroscopic quantum coherence between two well-defined charge states become observable.

Temperature Dependence of the Josephson Current

A fundamental error in the derivation of the Josephson critical current has been detected. The corrected temperature dependence differs from the standard result, e.g., that of Ambegaokar and Baratoff. Spurious contributions to the coherent tunneling of pairs are identified; they arise when Gor'kov factorization is imposed on the ensemble average of the tunneling operator.

Incoherent Pair Tunneling as a Probe of the Cuprate Pseudogap

We argue that incoherent pair tunneling in a cuprate superconductor junction with an optimally doped superconducting and an underdoped normal lead can be used to detect the presence of pairing correlations in the pseudogap phase of the underdoped lead. We estimate that the junction characteristics most suitable for studying the pair tunneling current are close to recently manufactured cuprate tunneling devices.