Charge transport through ferromagnet/two-dimensional electron gas/d-wave superconductor junctions with Rashba spin-orbit coupling

Along the lines of Blonder, Tinkham and Klapwijk, we investigate the charge transport through ferromagnet/two-dimensional electronic gas/d-wave superconductor (F/2DEG/S) junctions in the presence of Rashba spin-orbit (SO) coupling and focus our attention on the interplay between spin polarization and spin precession. At zero spin polarization, the spin-mixing scattering resulted from Rashba SO coupling decreases the zero-bias conductance peak. Under spin polarization, spin precession introduces novel Andreev reflection, which competes with the effect of spin-mixing scattering. If the F layer is a half metal, the later effect is overwhelmed by that of novel Andreev reflection. As a result, the zero-bias conductance dip caused by spin polarization is enhanced, and at strong Rashba SO coupling, a split zero-bias peak is found in the gap. In an intermediate region where the two effects are comparable with each other, the zero-bias conductance shows a reentrant behavior as a function of Rashba SO coupling.     

Josephson current through a ferromagnetic semiconductor/semiconductor/ferromagnetic semiconductor structure

We theoretically calculate the Josephson current for two superconductor/ferromagnetic semiconductor (SC/FS) bilayers separated by a semiconductor (SM) layer. It is found that the critical Josephson current I_C in the junction is strongly determined by not only the relative orientations of the effective exchange field of the two bilayers and scattering potential strengths at the interfaces but also the kinds of holes (the heavy or light) in the two FS layers. Furthermore, a robust approach to measuring the spin polarization P for the heavy and light holes is presented.     

Coexistence of superconductivity and ferromagnetism in ferromagnet/superconductor proximity structures

The Nambu spinor Green's function approach is applied to calculating the density of states (DOS) and superconducting order parameter in normal-metal/insulator/ferromagnet/superconductor (NM/I/FM/SC) junctions. It is found that the s-wave superconductivity and ferromagnetism can coexist near the FM/SC interface, which is induced by proximity effect. On the SC side, the spin-dependent DOS appears both within and without the energy gap. On the FM side, the superconducting order parameter displays a damped oscillation and the DOS exhibits some superconducting behavior. The calculated result for the DOS in FM for “0 state” and “π state” can reproduce recent tunneling spectra in Al/Al₂O₃/PdNi/Nb tunnel junctions. Received 1st July 2002 Published online 19 November 2002     

Coherent quantum transport in two-dimensional electron gas/superconductor double junctions with Rashba spin-orbit coupling

Based on the extended Blonder-Tinkham-Klapwijk (BTK) approach, we have investigated the coherent quantum transport in two-dimensional electron gas/superconductor (2DEG/SC) double tunneling junctions in the presence of the Rashba spin-orbit coupling (RSOC). It is found that all the reflection coefficients in BTK theory as well as conductance spectra oscillate with the external voltage and energy. The oscillation feature of conductance can be tuned largely by the RSOC for low insulating barriers, while for high insulating barriers it is almost independent of the RSOC. These phenomena are essentially different from those found in ferromagnet/superconductor double tunneling junctions.     

Smearing origin of zero-bias conductance peak in Ag-SiO-Bi2Sr2CaCu2O8+δ planar tunnel junctions: influence of diffusive normal metal verified with the circuit theory

We propose a new approach of smearing origins of a zero-bias conductance peak (ZBCP) in high-T_c superconductor tunnel junctions through the analysis based on the circuit theory for a d-wave pairing symmetry. The circuit theory has been recently developed from conventional superconductors to unconventional superconductors. The ZBCP frequently appears in line shapes for this theory, in which the total resistance was constructed by taking account of the effects between a d-wave superconductor and a diffusive normal metal (DN) at a junction interface, including the midgap Andreev resonant states (MARS), the coherent Andreev reflection (CAR) and the proximity effect. Therefore, we have analyzed experimental spectra with the ZBCP of Ag-SiO-Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) planar tunnel junctions for the {110}-oriented direction by using a simplified formula of the circuit theory for d-wave superconductors. The fitting results reveal that the spectral features of the ZBCP are well explained by the circuit theory not only excluding the Dynes's broadening factor but also considering only the MARS and the DN resistance. Thus, the ZBCP behaviors are understood to be consistent with those of recent studies on the circuit theory extended to the systems containing d-wave superconductor tunnel junctions.     

Inelastic relaxation and noise temperature in S/N/S junctions

We studied electronic relaxation in long diffusive superconductor/normal metal/superconductor (S/N/S) junctions by means of current noise and transport measurements down to very low temperature (100mK). Samples with normal metal lengths of 4, 10 and 60μm have been investigated. In all samples the shot noise increases very rapidly with the voltage. This is interpreted in terms of enhanced heating of the electron gas confined between the two S/N interfaces. Experimental results are analyzed quantitatively taking into account electron-phonon interaction and heat transfer through the S/N interfaces. Transport measurements reveal that in all samples the two S/N interfaces are connected incoherently, as shown by the reentrance of the resistance at low temperature. The complementarity of noise and transport measurements allows us to show that the energy dependence of the reentrance at low voltage is essentially due to the increasing effective temperature of the quasiparticles in the normal metal. Received 5 February 2002 / Received in final form 6 September 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: hoffmann@drfmc.ceng.cea.fr     

Investigations on phase locking in a two-dimensional Josephson junction array within the Werthamer and the RCSJ model

The synchronization properties of a simple two-dimensional Josephson array consisting of two coupled SQUID cells are studied within the Werthamer as well as the RCSJ model. Special emphasis is placed on the role of inductances arranged perpendicular and parallel to the current bias direction for the phase locking behavior. The general behavior within the Werthamer model is found to be similar to that within the RCSJ model. However, there are quantitative differences, e.g. an enhanced phase shift between the voltage oscillations within one cell and a shift of the parameter range for the in-phase regime between different cells towards lower values of the McCumber parameter in the Werthamer model. Received: 23 March 1998 / Revised: 3 June 1998 / Accepted: 9 June 1998     

Critical temperature and interface transparency of N/S/N triple layers: theory and experiment

The influence of the finite transparency, , of superconductor/normal metal (S/N) interface on the critical temperature of proximity coupled layered structures is investigated in the dirty limit on the basis of the microscopic equations solved exactly by a matrix method. The calculated theoretical curves satisfactory reproduce the experimental dependencies of the critical temperature on the thickness of the superconducting layers in N/S/N trilayers. The relation between the transparency coefficient and the normal metal coherence length is also discussed.     

Electronic entanglement in the vicinity of a superconductor

A weakly biased normal-metal-superconductor junction is considered as a potential device injecting entangled pairs of quasi-particles into a normal-metal lead. The two-particle states arise from Cooper pairs decaying into the normal lead and are characterized by entangled spin- and orbital degrees of freedom. The separation of the entangled quasi-particles is achieved with a fork geometry and normal leads containing spin- or energy-selective filters. This solid state entangler is characterized by noise cross-correlations which are identical to the noise in one lead, a signature consistent with entanglement. A connection to Bell-type experiments is envisioned (cond-mat/0009193). Received 20 September 2001     

Josephson and Andreev transport through quantum dots

In this article, we review the state of the art on the transport properties of quantum dot systems connected to superconducting and normal electrodes. The review is mainly focused on the theoretical achievements, although a summary of the most relevant experimental results is also given. A large part of the discussion is devoted to the single-level Anderson-type models generalized to include superconductivity in the leads, which already contains most of the interesting physical phenomena. Particular attention is paid to the competition between pairing and Kondo correlations, the emergence of π-junction behavior, the interplay of Andreev and resonant tunneling, and the important role of Andreev bound states that characterized the spectral properties of most of these systems. We give technical details on the several different analytical and numerical methods which have been developed for describing these properties. We further discuss the recent theoretical efforts devoted to extend this analysis to more complex situations like multidot, multilevel or multiterminal configurations in which novel phenomena is expected to emerge. These include control of the localized spin states by a Josephson current and also the possibility of creating entangled electron pairs by means of non-local Andreev processes.     

Resonant effects in ballistic Josephson junctions

We study the Josephson effect in ballistic double-barrier SINIS planar junctions, consisting of bulk superconductors (S), a clean normal metal or semiconductor (N), and insulating interfaces (I) modeled as a δ-function potential-energy barriers. We solve the scattering problem based on the Bogoliubov-de Gennes equations and derive a general expression for the dc Josephson current, valid for arbitrary interfacial transparency, the Fermi wave vectors mismatch, and for different effective band masses. The effect of transmission resonances on the Josephson current and on the normal conductance is analyzed for short junctions. Curvature of the temperature dependence of the critical Josephson current is related to the presence of resonances at the Fermi level and to the interfacial transparency. For thin semiconductor layers with negative effective masses of the carriers, finite interfacial transparency and large Fermi wave vectors mismatch we find that an unusual and significant enhancement of both the normal conductance and the critical Josephson current occurs at low temperatures due to the presence of an evanescent mode localized at interfaces.     

Semiclassical theory of integrable and rough Andreev billiards

We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding light onto the origin of the differences between the semiclassical theory and the corresponding result derived from random matrix models. Applications to a square billiard geometry and billiards with boundary roughness are discussed. The saturation of the quasiparticle excitation spectrum is related to the classical dynamics of the billiard. The influence of weak magnetic fields on the proximity effect in rough Andreev billiards is discussed and an analytical formula is derived. The semiclassical theory provides an interpretation for the suppression of the proximity effect in the presence of magnetic fields as a coherence effect of time reversed trajectories. It is shown to be in good agreement with quantum mechanical calculations. Received 21 August 1999 and Received in final form 21 March 2001     

Electron transport in interacting hybrid mesoscopic systems

A unified theory for the current through a mesoscopic region of interacting electrons connected to two leads which can be either ferromagnet or superconductor is presented, yielding Meir-Wingreen-type formulas when applied to specific circumstances. In such a formulation, the requirement of gauge invariance is satisfied automatically. Moreover, one can judge unambiguously what quantities can be measured in the transport experiment. Received 22 August 2002 / Received in final form 14 February 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: phyzengz@nus.edu.sg     

Controllable π junction in a Josephson quantum-dot device with molecular spin

We consider a model for a single molecule with a large frozen spin sandwiched in between two BCS superconductors at equilibrium, and show that this system has a π junction behavior at low temperature. The π shift can be reversed by varying the other parameters of the system, e.g., temperature or the position of the quantum dot level, implying a controllable π junction with novel application as a Josephson current switch. We show that the mechanism leading to the π shift can be explained simply in terms of the contributions of the Andreev bound states and of the continuum of states above the superconducting gap. The free energy for certain configuration of parameters shows a bistable nature, which is a necessary pre-condition for achievement of a qubit.     

c-axis tunneling on YBCO films

We have measured I(V) characteristics of c-axis planar tunnel junctions on Y₁Ba₂Cu₃O _{7 - δ} films. Our results and their analysis provide experimental support for the importance of the two-dimensional character of the YBCO band structure, and a method to measure the ratio between the Fermi energy of YBCO and the barrier height. The analysis is based on the relation between the linear conductance background, related to the inelastic tunneling component, and the zero bias conductance, related to the elastic one. Received 24 September 2000 and Received in final form 15 November 2000     

Pertubation analysis of the dynamical behavior of two-junction interferometers

The dynamical properties of symmetric quantum interferometers with equal junctions of negligible capacitance have been studied by means of perturbation analysis in the limit of small values of the parameter β. In this limit, two characteristic time constants arise. These quantities may be linked to two different dynamical processes in the system: the first is related to the time evolution of the average superconducting phase difference across the two junctions; the second defines the time scale for flux motion. The response of the system to constant and time-dependent externally applied magnetic fields is considered and a general perturbed solution for the average superconducting phase difference and the fluxon number variable is derived to first order in β.     

Low-field magnetic response of multi-junction superconducting quantum interference devices

The magnetic states of multi-junction superconducting quantum interference device containing 2N identical conventional Josephson junctions are studied by means of a perturbation analysis of the non-linear first-order ordinary differential equations governing the dynamics of the Josephson junctions in these devices. In the zero-voltage state, persistent currents are calculated in terms of the externally applied magnetic flux Φ_ex . The resulting d.c. susceptibility curves show that paramagnetic and diamagnetic states are present, depending on the value of Φ_ex . The stability of these states is qualitatively studied by means of the effective potential notion for the system.     

Tunable supercurrent in a parallel double quantum dot system

The supercurrent through an Aharonov-Bohm interferometer containing two parallel quantum dots connected with two superconductor leads is investigated theoretically. The possibility of controlling the supercurrent is explored by tuning the quantum dot energy levels and the total magnetic flux. By tuning the energy levels, both quantum dots can be in the on-resonance or off-resonance states, and thus the optimal modulation of the supercurrent can be achieved. The supercurrent sign does not change by simply varying the quantum dot energy levels. However, by tuning the magnetic flux, the supercurrent can oscillate from positive to negative, which results in the π-junction transition.     

0-π oscillations in nanostructured Nb/Fe/Nb Josephson junctions

The physics of the π phase shift in ferromagnetic Josephson junctions may enable a range of applications for spin-electronic devices and quantum computing. We investigate transitions from “0” to “π” states in Nb/Fe/Nb Josephson junctions by varying the Fe barrier thickness from 0.5 nm to 5.5 nm. From magnetic measurements we estimate for Fe a magnetic dead layer of about 1.1 nm. By fitting the characteristic voltage oscillations with existing theoretical models we extrapolate an exchange energy of 256 meV, a Fermi velocity of 1.98 ×10⁵ m/s and an electron mean free path of 6.2 nm, in agreement with other reported values. From the temperature dependence of the I_CR_N product we show that its decay rate exhibits a nonmonotonic oscillatory behavior with the Fe barrier thickness.     

Dephasing of Andreev pairs entering a charge density wave

A Cooper pair from a s-wave superconductor (S) entering a conventional charge density wave (CDW) below the Peierls gap dephases on the Fermi wavelength while one particle states are localized on the CDW coherence length ξ_CDW. It is thus practically impossible to observe a Josephson current through a CDW. The paths following different sequences of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon: (i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and (ii) the Hamiltonian approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin density wave (SDW) is limited by the coherence length ξ_SDW, not by the Fermi wave-length. A Josephson current through a SDW might be observed in a structure with contacts on a SDW separated by a distance ξ_SDW.