Peculiarities of the proximity effect in superconductor-multilayered ferromagnet structures with collinear magnetizations in ferromagnetic layers

The proximity effect is investigated theoretically in different superconducting structures including multilayered ferromagnet consisting of arbitrary number of metallic ferromagnet (F) layers. The in-plane exchange fields in the F-layers are supposed to be collinear. Different cases of the exchange fields ordering including the case of antiferromagnetic one. It is shown for the last case that the proximity effect (for the fixed thickness of the M-interlayer) increases with the growing number of the layers N and significantly depends on whether this number is odd or even. It is shown that under the condition of diffusive electron transport, the anomalous proximity effect is exhibited which is related with singlet component of the condensate Green’s function. Peculiarities of the proximity effect are analyzed for S-M, S-I-M-S, and S-M-S superconducting structures (S is a superconductor, I is an insulating layer). It is shown that when the M-structure consists of N seriously connected F₁-N-F₂-N links in which F layers are separated by normal metallic layers (N), for antiferro-magnetic ordering of the magnetization the exchange field induced enhancement of the critical current may occur.     

Density of states anomalies in hybrid superconductor-ferromagnet-normal metal structures

The results of calculations of the spatially-resolved density of states (DOS) in an S(F/N) bilayer are presented (S is a superconductor, F is a metallic ferromagnet, N is a normal metal) within quasiclassical theory in the dirty limit. Analytical solutions are obtained in the case of thin F, N layers which demonstrate the peculiar features of DOS in this system. The dependences of the minigap and the DOS peak positions on the exchange energy and parameters of the layers are studied numerically.     

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     

Modification of normal metal transport by the superconducting proximity effect

When a normal (N) metal makes intimate contact with a superconductor (S), the density of states in the normal metal is modified by the proximity effect. As a consequence, if a point contact is made with the normal metal the resulting tunnel conductance,G, is a function of the distance,x, from the N-S interface. We show that, for allx, G possesses a minimum at zero voltage and at finite voltage,G equals that of the structure without superconductivity present. The conductance is independent of the magnitude of the superconducting order parameter but depends upon the amount of normal scattering at the N-S interface.     

Proximity effect in normal metal/ferromagnet/d-wave superconductor structures

The superconducting proximity effect in normal metal/insulator/ferromagnet/d-wave superconductor (N/I/F/D) structures is studied based on an extended Blonder–Tinkham–Klapwijk (BTK) theory. The transition from the “0” to “π” state is found in the conductance spectra with increasing thickness of F or the ferromagnetic exchange energy. The superconducting proximity effect is drastically changed by the orientation angle α, as α increases the proximity effect is enhanced, being strongest for α/π = 0.25.     

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.     

Electron entanglement near a superconductor and bell inequalities

Near the interface between a normal metal and a superconductor, Cooper pairs penetrate into the normal side, giving rise to the proximity effect. The two electrons of these pairs have entangled spin and orbital degrees of freedom. Nonlocal features of quantum mechanics can be probed by separating these two electrons. This is achieved with a fork geometry with two normal leads containing either spin- or energy-selective filters. A signature of entanglement can be detected by measuring the positive noise cross-correlations in this fork. In the case of energy filters, Bell-inequality checks constitute a definite probe of entanglement. We formulate Bell-type inequalities in terms of current-current cross-correlations associated with contacts with varying magnetization orientations. We find maximal violation (as in photons) when a superconductor is the particle source.     

Charge transport in the normal metal/diffusive ferromagnet/s-wave superconductor junctions

Charge transport in the normal metal/insulator/diffusive ferromagnet/insulator/s-wave superconductor (N/I/DF/I/S) junctions is studied for various situations solving the Usadel equation under the Nazarov's generalized boundary condition. Conductance of the junction is calculated by changing the magnitude of the resistance in DF, Thouless energy in DF, the exchange field in DF, the transparencies of the insulating barriers. We have found a new broad peak around zero voltage as well as zero bias conductance peak splitting and dip splitting.     

Model calculations of the proximity effect in finite multilayers

The proximity-effect theory developed by Takahashi and Tachiki for infinite superconductor/normal (S/N) multilayers is applied to multilayer systems with a finite number of layers in the growth direction. The purpose is to investigate why previous applications to infinite multilayers fail to describe the measured data satisfactorily. It is shown that surface superconductivity may appear, depending on the thickness of the covering normal metallic layers, on both the top and the bottom. Most of the parameters used refer to the V/Ag system, but systems in which the N metal is also a superconductor are considered as well. The nucleation process is studied as a function of the system parameters, including the transparency of the S/N interface.     

Negative Differential Resistance and Other Features of Spin-Dependent Electron Transport in Double-Barrier Hybrid Superconductor–Ferromagnetic Metal–Normal Metal Structures

Spin-dependent electronic transport is theoretically investigated for double-barrier hybrid structures S–IF–F–IF–N and S–IF–N–IF–N, where S is a superconductor; F and N are ferromagnetic and normal metals, respectively; and IF is the spin-active barrier. It is shown that in the case of strong superconducting proximity effect and sufficiently thin F layers, the differential resistance of such structures can become negative at some voltages, and the voltage dependence of the current can have an N-shaped form. Characteristic feature of the differential resistance is its asymmetric dependence on voltage, which is most clearly manifested at strong polarization of at least one of the barriers. The influence of impurity spin–orbit scattering processes in the N-layer located between the barriers is investigated. The study was carried out for the case of diffusion electron transport.     

Zeeman effects on d-wave superconductor and tunneling spectrum in normal-metal/d-wave superconductor tunnel junction

We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman magnetic field may make the zero-bias conductance peak split into two peaks, and the energy difference between the two splitting peaks in the conductance spectrum is equal to 2h ₀ (h ₀ is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks, however, neither of them can influence the Zeeman effect.     

Conductance spectroscopy of spin-triplet superconductors

We propose a novel experiment to identify the symmetry of superconductivity on the basis of theoretical results for differential conductance of a normal metal connected to a superconductor. The proximity effect from the superconductor modifies the conductance of the remote current depending remarkably on the pairing symmetry: spin singlet or spin triplet. The clear-cut difference in the conductance is explained by symmetry of Cooper pairs in a normal metal with respect to frequency. In the spin-triplet case, the anomalous transport is realized due to an odd-frequency symmetry of Cooper pairs.     

Peculiarities of the amplitude of elastic subbarrier impurity scattering

A formula for the amplitude of electron elastic subbarrier (in the domain of imaginary momenta) scattering by an impurity modeled as a spherical potential well is derived. An equation is obtained to find the features (poles) of this amplitude in a complex energy plane in the close vicinity of which the energy spectrum of quantum resonant percolation trajectories in M-I-M contacts (M = N (normal metal) or S (superconductor) and I is an insulator) with weak (low impurity concentration) structural disorder in the I layer is concentrated [1–4].     

Anomalous density of states in hybrid normal metal-superconductor bilayers

In contact with a superconductor, the Andreev reflection of the electrons locally modifies the N metal electronic properties, including the local density of states (LDOS). We investigated the LDOS in superconductor-normal metal (Nb-Au) bilayers using a very low temperature (60 mK) STM on the normal metal side. High resolution tunneling spectra measured on the Au surface show a clear proximity effect with an energy gap of reduced amplitude compared to the bulk Nb gap. The dependence of this mini-gap width with the normal metal thickness is discussed in terms of the Thouless energy. Within the mini-gap, the density of states does not reach zero and shows clear sub-gap features. We compare the experimental spectra with the well-established quasi-classical theory.     

The current–voltage characteristic in an ultrasmall junction

The current–voltage characteristics of ultrasmall superconductor–insulator–normal metal (S–I–N), and a superconductor–insulator–superconductor (S–I–S) junctions are computed in the presence of a dissipative transmission line. The amplitude of the discontinuous jump at the energy gap of a single-particle current is greatly influenced by the size of the capacitance and the impedance of the external transmission line in the small junction. The results agree with Ambegaokar–Baratoff in the limit of vanishing impedance of a transmission line or large junction capacitance.     

Electronic transport in mesoscopic superconductor/2D electron gas junctions in strong magnetic field

The hybrid superconductor/2D electron gas (S/2DEG) structures based on InGaAs-InP hetero-junctions with a high-mobility 2D electron gas and superconducting NbN electrodes have been investigated. The electronic transport and current-voltage characteristics of S/2DEG/normal metal (S/2DEG/N) structures in strong perpendicular magnetic fields have been studied. Oscillations in the magnetoresistance of S/2DEG/N structures have been found in strong magnetic fields. It is shown that at bias voltages lower than the superconducting gap the amplitude of oscillations in S/2DEG/N structures significantly exceeds the oscillation amplitude in the reference N/2DEG/N samples. The experimental results can be explained within the quasiclassical theory of magnetotransport in S/2DEG structures developed by N.M. Chtchelkatchev and I.S. Burmistrov (Phys. Rev. B, 2007, vol. 75, 214 510).     

Supercooling in a system of two superconductors

Supercooling in the transition of a type I superconductor to the superconducting state in contact with another superconductor whose critical temperature is higher has been measured. Using aluminum as a test material, it has been demonstrated that at temperatures below the critical temperature T _c and magnetic fields below the critical field H _c(T), aluminum remains in a metastable normal state, in spite of its contact with another superconductor. This means that it is not possible to generate a thermodynamic instability in a superconductor’s electronic system through the “proximity effect” with another superconductor whose critical temperature is higher. This experimental observation demonstrates a radical difference between surface superconductivity, which certainly generates instability in normal electronic states, and superconductivity induced by the proximity effect near a junction with another superconductor. Zh. éksp. Teor. Fiz. 112, 1119–1131 (September 1997)     

Boron/nitrogen pairs Co-doping in metallic carbon nanotubes: a first-principle study

By using the first-principles calculations, the electronic structure and quantum transport properties of metallic carbon nanotubes with B/N pairs co-doping have been investigated. It is shown that the total energies of metallic carbon nanotubes are sensitive to the doping sites of the B/N pairs. The energy gaps of the doped metallic carbon nanotubes decrease with decreasing the concentration of the B/N pair not only along the tube axis but also around the tube. Moreover, the I--V characteristics and transmissions of the doped tubes are studied. Our results reveal that the conducting ability of the doped tube decreases with increasing the concentrations of the B/N pairs due to symmetry breaking of the system. This fact opens a new way to modulate band structures of metallic carbon nanotubes by doping B/N pair with suitable concentration and the novel characteristics are potentially useful in future applications.     

Unconventional surface impedance of a normal-metal film covering a spin-triplet superconductor due to odd-frequency cooper pairs

We discuss the dynamic response of odd-frequency Cooper pairs to an electromagnetic field. By using the quasiclassical Green function method, we calculate the impedance (Z=R-iX) of a normal-metal thin film which covers a superconductor. In contrast with the standard relation (i.e., R?X), the impedance in spin-triplet proximity structures shows anomalous behavior (i.e., R>X) in the low frequency limit. This unusual relation is a result of the penetration of odd-frequency pairs into the normal metal and reflects the negative Cooper pair density.