Pair Tunneling Research Articles

Radio-frequency-induced transport of Cooper pairs in superconducting single electron transistors in a dissipative environment

We investigate low-temperature and low-voltage-bias charge transport in a superconducting Al single electron transistor in a dissipating environment, realized as on-chip high-ohmic Cr microstrips. In samples with relatively large charging energy Ec>EJ, where EJ is the Josephson coupling energy, two transport mechanisms were found to be dominant, both based on discrete tunneling of individual Cooper pairs: Depending on the gate voltage Vg, either sequential tunneling of pairs via the transistor island [in the conducting state of the transistor around the points Qg≡CgVg=e mod (2e), where Cg is the gate capacitance] or their cotunneling through the transistor (for Qg away of these points) was found to prevail in the net current. As the conducting state of our transistors had been found to be subject to quasiparticle poisoning, high-frequency gate cycling (at f∼1 MHz) was applied to study the sequential tunneling mechanism. A simple model based on the master equation was found to be in a good agreement with the experimental data.

Josephson effect between superconducting nanograins with discrete energy levels

We investigate the Josephson effect between two coupled superconductors, coupled by the tunneling of pairs of electrons, in the regime that their energy level spacing is comparable to the bulk superconducting gap, but neglecting any charging effects. In this regime, BCS theory is not valid, and the notion of a superconducting order parameter with a well-defined phase is inapplicable. Using the density matrix renormalization group, we calculate the ground state of the two coupled superconductors and extract the Josephson energy. The Josephson energy is found to display a reentrant behavior (decrease followed by increase) as a function of increasing level spacing. For weak Josephson coupling, a tight-binding approximation is introduced, which illustrates the physical mechanism underlying this reentrance in a transparent way. The DMRG method is also applied to two strongly coupled superconductors and allows a detailed examination of the limits of validity of the tight-binding model.

Transport Dynamics and Superconductivity with Mesoscopic Jahn–Teller Pairs

The inhomogeneous-state transport properties in the superconducting and normal state are discussed in the context of the mesoscopic Jahn–Teller pair model. Bose condensation of preformed pairs and phase coherence percolation models with pair tunneling are compared and the predictions examined. The normal-state resistivity in the a–b plane as a function of doping and temperature is found to be described very well by a simple two-component model of the inhomogeneous state with coexisting Bosons and Fermions.

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

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.

Josephson Transport through a Hubbard Impurity Center

We investigate the Josephson transport through a thin semiconductor barrier containing impurity centers with the on-site Hubbard interaction u of an arbitrary sign and strength. We find that in the case of the repulsive interaction the Josephson current changes sign with the temperature increase if the energy of the impurity level epsilon (measured from the Fermi energy of superconductors) falls in the interval (-u,0). We predict strong temporal fluctuations of the current if only a few centers are present within the junction. In the case of the attractive impurity potential (u<0) and at low temperatures, the model is reduced to the effective two level Hamiltonian allowing thus a simple description of the nonstationary Josephson effect in terms of pair tunneling processes.

Influence of charging energy on cooper pair tunneling in Bi-2212 small intrinsic Josephson junctions

We have investigated the properties of submicron intrinsic Josephson junctions (IJJs) fabricated on Bi/sub 2/Sr/sub 2/CaCu/sub 2/O/sub 8+/spl delta// liquid phase epitaxy film. The IJJs with junction area S<2 /spl mu/m/sup 2/ showed individual current-voltage curves, which have suppressed 1st branch and unsuppressed other branches. This suppression was observed systematically as an increase the ratio of charging energy and Josephson coupling energy. It is expected that such suppressions are due to charging effect in IJJs.

Effect of the Coulomb blockade of Cooper pairs on the dynamic properties of small-size Josephson junctions

The dynamics of Cooper pair tunneling under Coulomb blockade in small-size Josephson junctions is studied in terms of the resistive model. A relationship between the delay time and temperature fluctuations of the Coulomb blockade edge and the rate of rise of the voltage across the junction is derived.

Escape from a zero-current state in a one-dimensional array of Josephson junctions

A long one dimensional array of small Josephson junctions exhibits Coulomb blockade of Cooper pair tunneling. This zero current state exists up to a switching voltage, Vsw, where there is a sudden onset of current. In this paper we present histograms showing how Vsw changes with temperature for a long array and calculations of the corresponding escape rates. Our analysis of the problem is based on the existence of a voltage dependent energy barrier and we do not make any assumptions about its shape. The data divides up into two temperature regimes, the higher of which can be explained with Kramers thermal escape model. At low temperatures the escape becomes independent of temperature.

Single electron transistors with Nb/AlOx/Nb junctions

Deep submicron Nb/AlOx/Nb tunnel junctions and single electron transistors were fabricated by electron beam gun shadow evaporation, using stencil masks consisting of the thermostable polymer polyethersulfone and germanium. The I(U) characteristics of the single electron transistors show special features due to the tunneling of single Cooper pairs and quasiparticles. Significant e-periodic gate modulation is observed in both the superconducting and the normal state and a gap energy Δeff of up to ≈1 meV has been achieved. The special features of using the refractory metal Nb in combination with the shadow evaporation technique are discussed.

EXACT SOLUTION AT INTEGRABLE COUPLING OF A MODEL FOR THE JOSEPHSON EFFECT BETWEEN SMALL METALLIC GRAINS

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Stripes, electron fractionalization, and ARPES

Although structurally the high temperature superconductors are quasi-two-dimensional, there is both theoretical and experimental evidence of a substantial range of temperatures in which ‘stripe’ correlations make the electronic structure locally quasi-one-dimensional. We consider an array of Josephson coupled, spin gapped one dimensional electron gases as a model of the high temperature superconductors. For temperatures above T c, this system exhibits electron fractionalization, yielding a single particle spectral response which is sharp as a function of momentum, but broad as a function of energy. For temperatures below the spin gap but above T c, there are enhanced one-dimensional superconducting fluctuations and pseudogap phenomena. Pair tunneling induces a crossover to three-dimensional physics as T c is approached. Below T c, solitons are confined in multiplets with quantum numbers which are simply related to the electron, and a coherent piece of the single particle spectral function appears. The weight of this coherent piece vanishes in the neighborhood of T c in proportion to a positive power of the interchain superfluid density. This behavior is highly reminiscent of recent ARPES measurements on the high temperature superconductors.

Single electron transistors with high-quality superconducting niobium islands

Deep submicron Al/AlOx/Nb tunnel junctions and single electron transistors with niobium islands were fabricated by electron beam gun shadow evaporation. Using stencil masks consisting of the thermostable polymer polyethersulfone and germanium, high quality niobium structures with good superconducting properties and a gap energy of up to 2ΔNb=2.5 meV were achieved. The I(U) characteristics of the transistors show special features due to tunneling of single Cooper pairs and significant gate modulation in both the superconducting and the normal state.

Creation of nonlocal spin-entangled electrons via Andreev tunneling, Coulomb blockade, and resonant transport

We discuss several scenarios for the creation of nonlocal spin-entangled electrons which provide a source of electronic Einstein–Podolsky–Rosen (EPR) pairs. Such EPR pairs can be used to test nonlocality of electrons in solid state systems, and they form the basic resources for quantum information processing. The central idea is to exploit the spin correlations naturally present in superconductors in form of Cooper pairs possessing spin-singlet wavefunctions. We show that nonlocal spin-entanglement in form of an effective Heisenberg spin interaction is induced between electron spins residing on two quantum dots with no direct coupling between them, but each of them being tunnel-coupled to the same superconductor. We then discuss a nonequilibrium setup with an applied bias where mobile and nonlocal spin-entanglement can be created by coherent injection of two electrons, in a pair (Andreev) tunneling process, into two spatially separated quantum dots and subsequently into two Fermi liquid leads. The current for injecting two spin-entangled electrons into different leads shows a resonance and allows the injection of electrons at the same orbital energy, which is a crucial requirement for the detection of spin-entanglement via the current noise. On the other hand, tunneling via the same dot into the same lead is suppressed by the Coulomb blockade effect of the quantum dots. We discuss Aharonov–Bohm oscillations in the current and show that they contain h/e and h/2e periods, which provides an experimental means to test the nonlocality of the entangled pair. Finally, we discuss a structure consisting of a superconductor weakly coupled to two separate one-dimensional leads with Luttinger liquid properties. We show that strong correlations again suppress the coherent subsequent tunneling of two electrons into the same lead, thus generating again nonlocal spin-entangled electrons in the Luttinger liquid leads.

Quantum Complementarity for the Superconducting Condensate and the Resulting Electrodynamic Duality

Experiments with small capacitance Josephson junction arrays are described that demonstrate the quantum behavior of the phase of the superconducting condensate. This quantum behavior is based on the complementarity of phase and number for a condensate state of many bosons. A key factor to observation of this quantum behavior is the coupling of the superconducting condensate state to dissipation in the electrodynamic environment of the Josephson junction. It is shown how one-dimensional Josephson junction arrays can be used to design an environment with very weak coupling to dissipation, allowing for measurement of condensate with well defined number. The well defined number is manifest in the Coulomb blockade of Cooper pair tunneling.

Pair and quasiparticle tunneling characteristics of small-sized intrinsic Josephson junctions in Bi 2Sr 2CaCu 2O y

Tunneling properties of small-sized intrinsic Josephson junctions in Bi 2Sr 2CaCu 2O y single crystals have been investigated in order to understand their inherent properties. We have successfully fabricated mesas with lateral dimensions ranging from sub-μm 2 to several tens μm 2 on the same crystal. As a result, a clear gap structure and the normal resistance region could be observed without significant overheating together with typical multiple branches. The gap value, 2 Δ, was about 60 meV at 4.2 K, while the I c R n product was about 2.4 mV. Additionally, we observed that the temperature dependence of I c slightly deviates from the Ambegaoker–Baratoff relation for the s-wave superconductor. This is interpreted as evidence of the d-wave symmetry of the order parameter and coherent interlayer tunneling. We also found that from the simultaneous observation of the superconducting gap and the pseudogap, the pseudogap may be different from the precursor of superconductivity.

Two-dimensional behavior of the naturally layered superconductor (LaSe) 1.14(NbSe 2)

The three-dimensional to two-dimensional (2D) crossover of the superconducting state is presented for the naturally layered single crystal of (LaSe) 1.14(NbSe 2) with the critical temperature T c of 1.23 K. Namely, the temperature dependence of the upper critical magnetic field B c2 parallel to the layers reveals an upturn at the crossover temperature T * due to the vortex confinement between the superconducting layers. Below this temperature in the 2D regime the angular dependence of B c2 displays a cusp at the field parallel to the layers. In the superconducting state the interlayer transport is accomplished in this system by the tunneling of quasiparticles and Cooper pairs.

Resonant Cooper pair tunneling through a double-island qubit.

We have measured transport in the Coulomb blockade regime through a quantum system consisting of two superconducting islands coupled by a Josephson junction. The double island is weakly connected to leads by small superconducting tunnel junctions. At low bias voltages, a new resonant transport process for Cooper pairs is observed. The results show that Cooper pair transport can be used as a probe of the macroscopic energy levels of the double island.

( Sr / Ca ) 14 Cu 24 O 41 spin ladders studied by NMR under pressure

(63)Cu-NMR measurements have been performed on two-leg hole-doped spin ladders Sr_{14-x}Ca_{x}Cu_{24}O_{41} single crystals (0-x-12) at several pressures up to the pressure domain where the stabilization of a superconducting ground state can be achieved. The data reveal marked decrease of the spin gap derived from Knight shift measurements upon Ca substitution and also under pressure and confirm the onset of low lying spin excitations around P_{c} as previously reported. The spin gap in Sr_{2}Ca_{12}Cu_{24}O_{41} is strongly reduced above 20 kbar. However, the data of an experiment performed at P=36 kbar where superconductivity has been detected at 6.7K by an inductive technique have shown that a significant amount of spin excitations remains gapped at 80K when superconductivity sets in. The standard relaxation model with two and three-magnon modes explains fairly well the activated relaxation data in the intermediate temperature regime corresponding to gapped spin excitations using the spin gap data derived from Knight shift experiments.The data of Gaussian relaxation rates of heavily doped samples support the limitation of the coherence lenght at low temperature by the average distance between doped holes. We discuss the interplay between superconductivity and the spin gap and suggest that these new results support the exciting prospect of superconductivity induced by the interladder tunnelling of preformed pairs as long as the pressure remains lower than the pressure corresponding to the maximum of the superconducting critical temperature.

Superconducting single-charge transistor in a tunable dissipative environment.

We study a superconducting single-charge transistor, where the coherence of Cooper pair tunneling is destroyed by the coupling to a tunable dissipative environment. Sequential tunneling and cotunneling processes are analyzed to construct the shape of the conductance peaks and their dependence on the dissipation and temperature. Unexpected features are found due to a crossover between two distinct regimes, one "environment assisted" the other "environment dominated." Several of the predictions have been confirmed by recent experiments. The model and results apply also to the dynamics of Josephson junction quantum bits on a conducting ground plane, thus explaining the influence of dissipation on the coherence.

Interlayer tunneling of quasiparticles and Cooper pairs in Bi-2212 from experiments on small stacks

The interlayer tunneling has been studied on high quality Bi-2212 stacks of micron to the submicron lateral size. We found that low temperature and low voltage tunneling I– V characteristics can be self-consistently described by Fermi-liquid model for a d-wave superconductor with a significant contribution from coherent interlayer tunneling. For micron-sized stacks we found very clear Fraunhofer type dependence of critical current across the stack on parallel magnetic field with periodicity corresponding to one flux quantum per elementary junction. The gap and pseudogap interplay with variation of temperature and magnetic field has been extracted from the I– V characteristics. We consider also the role of charging effects for submicron stacks.