Andreev scattering and cotunneling between two superconductor-normal metal interfaces: the dirty limit

Crossed Andreev reflections and cotunneling occur between two neighbouring superconductor- normal metal or superconducting-ferromagnet interfaces. Previous works assumed a clean BCS superconductor. Here the calculation of the corresponding crossed conductance terms is generalized to a dirty superconductor. The range of the effect is shown to be the coherence length , instead of the BCS coherence length . Moreover, in three dimensions, the algebraic prefactor scales as 1/r instead of 1/r ². The calculation involves the virtual diffusion probability of quasiparticles below the superconducting gap, in the normal and the anomalous channel.Received: 10 October 2003, Published online: 23 December 2003PACS: 74.45. + c Proximity effects; Andreev effect; SN and SNS junctions - 73.63.Rt Nanoscale contacts - 74.78.-w Superconducting films and low-dimensional structures     

Fractional ac Josephson effect in p- and d-wave superconductors

For certain orientations of Josephson junctions between two p_x-wave or two d-wave superconductors, the subgap Andreev bound states produce a -periodic relation between the Josephson current I and the phase difference : . Consequently, the ac Josephson current has the fractional frequency , where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current between unconventional superconductors is carried by single electrons, rather than by Cooper pairs. The fractional ac Josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction. We also study junctions between singlet s-wave and triplet p_x-wave, as well as between chiral -wave superconductors.Received: 24 September 2003, Published online: 2 April 2004PACS: 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects - 74.70.Kn Organic superconductors - 74.72.-h Cuprate superconductors (high-T_c and insulating parent compounds) - 74.70.Pq Ruthenates     

Effective field theory approach to structure functions at small $x_{\mathrm{Bj}}$

We relate the structure functions of deep inelastic lepton-nucleon scattering to current-current correlation functions in a Euclidean field theory depending on a parameter r. The r-dependent Hamiltonian of the theory is P ⁰ -(1-r)P ³ , with P⁰ the usual Hamiltonian and P³ the third component of the momentum operator. We show that a small in the structure functions corresponds to the small r limit of the effective theory. We argue that for there is a critical regime of the theory where simple scaling relations should hold. We show that in this framework Regge behaviour of the structure functions obtained with the hard pomeron ansatz corresponds to a scaling behaviour of the matrix elements in the effective theory where the intercept of the hard pomeron appears as a critical index. Explicit expressions for various analytic continuations of the structure functions and matrix elements are given as well as path integral representations for the matrix elements in the effective theory. Our aim is to provide a framework for truly non-perturbative calculations of the structure functions at small for arbitrary Q². Received: 16 July 2002 / Published online: 9 December 2002 RID="a" ID="a" e-mail: O.Nachtmann@thphys.uni-heidelberg.de     

Spin polarization of charge carriers and Andreev reflection in (LaCa)MnO/superconductor point contacts

Spin polarization of charge carriers in La_0.65Ca_0.35MnO₃ (LCMO) is studied using point-contact Andreev spectroscopy. Pb and MgB₂ are used to make superconducting electrodes. In all cases, the transport spin polarization obtained from the conductivity of LCMO/superconductor point contacts does not exceed 80–85%. Different models of the current flow through the superconductor-ferromagnetic metal contact and possible reasons for noncomplete spin polarization of a current in manganites are explored. The level of spin polarization observed in Sharvin contacts (contact area ～10⁴ Ų) is most naturally explained in terms of a model that suggests separation of the crystal into nanosized magnetic phases, only one of which is a ferromagnetic metal with full spin polarization of charge carriers.     

Spin density of states of proximity effect superconducting sandwiches in high fields

We use a tunneling Hamiltonian model to study the behavior of a thin film superconducting-normal metal sandwich in a parallel magnetic field including the effects of Pauli spin paramagnetism. The field acts to spin-split the density of states of the superconductor and the normal metal. With increasing magnetic field the sandwich displays zero temperature electron spin paramagnetism and a first-order transition to the normal state. We present a calculation of the field dependence of the density of states and order parameter.     

Contribution of Andreev reflection to the increase in the resistance of the normal metal in a bimetallic N-S structure

We study the resistive properties of 3D normal-metal-superconductor systems in the pure mean-free-path limit l _N,S ≫ξ(T) (l _N,S are the mean free paths in the metals, and ξ is the coherence length) at liquid helium temperatures. In contrast to the situation where l≪ξ, which is common in experiments involving either sandwiches or mesoscopic samples, here the N-S system exhibits unusual temperature behavior that cannot be described by existing theories of boundary resistance. What is most remarkable is a rise in normal resistance in regions that do not incorporate the N-S boundary as the temperature decreases, with asymptotic behavior resembling that of the temperature curve of the gap of a superconductor in contact with a normal metal. We show that this effect, not observed earlier in 3D systems, is due to the nonequivalence of the cross sections of scattering by normal-metal impurities of electron and hole excitations in conditions of Andreev reflection. We also show that in standard measurements of the contribution of the N-S boundary lying between the test contacts, this effect is masked by accompanying effects, the proximity effect and the boundary resistance, whose estimate requires taking into account the presence on the N-S boundary of an electrostatic barrier of the Schottky type, a barrier that redistributes the probabilities of ordinary and Andreev reflections of quasiparticles in the nonequilibrium conditions due to current flow. Zh. éksp. Teor. Fiz. 113, 1064–1070 (March 1998)     

Andreev reflection between a normal metal and the FFLO superconductor

We consider a process of the Andreev reflection between a normal metal and the s-wave superconductor in the FFLO state. It is shown that the process takes place if the energy of the incoming electron is bound within the finite interval called the Andreev window. The position of the window determines the value of the non-zero total momentum of Cooper pairs and the value of the gap.     

Thermal effect in the phase-periodic conductance of disordered mesoscopic N/S structures

We report measurements of the temperature dependence of the amplitude of phase-periodic conductance oscillations in disordered (diffusive) normal metal (Ag) structures attached to a superconducting (Pb) wire at two points. The oscillation amplitude exceeds the value of e ²/h by orders of magnitude and reaches its maximum at a temperature corresponding to the Thouless energy. The results support the recent theory of Nazarov and Stoof, [Phys. Rev. Lett. 76, 823 (1996)], which takes into account the characteristic energy dependence of the change in the diffusion coefficient of quasiparticles in a normal conductor due to Andreev reflections. The line shape of the oscillations as a function of the superconducting phase difference is found to be extremely sensitive to the quality of N/S interfaces and shows hysteretic behavior in interferometers with specially prepared clean interfaces. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 789–793 (10 December 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Proximity-induced transport in hybrid mesoscopic normal–superconducting metal structures

Using an approach based on quasiclassical Green’s functions we present a theoretical study of transport in mesoscopic SN structures in the diffusive limit. The subgap conductance in SN structures with barriers (zero bias and finite bias anomalies) are discussed. We also analyse the temperature dependence of the conductance variationδS (T) for a Andreev interferometer. We show that besides the well know low temperature maximum a second maximum near T_cmay appear. We present the results of studies on the Josephson effect in 4-terminal SNS contacts and on the possible sign reversal of the Josephson critical current.     

d(x2-y2)+idxy混合波正常金属/绝缘层/超导体结中的隧道谱

考虑界面粗糙散射,在Blonder-Tinkham-Klapwijk(BTK)理论框架下,通过求解Bogoliubov-de-Gennes(BdG)方程,分别计算T=0K和有限温度下,d_(x²-y²)+id_xy混合波正常金属绝缘层超导体结中的准粒子输运系数和隧道谱.研究表明:隧道谱中的电导峰的劈裂程度强烈地依赖于d_xy波分量的强度、超导体的晶轴方位和界面粗糙强度,而温度的升高能压低电导峰. 关键词： NIS结 (x²-y²)+id_xy混合波超导体')" href="#">d_(x²-y²)+id_xy混合波超导体 隧道谱     

Inelastic resonant tunneling

A general expression for the resonant contribution to a tunneling current has been obtained and analyzed in the tunneling Hamiltonian approximation. Two types of resonant tunneling structures are considered: structures with a random impurity distribution and double-barrier structures, where the resonant level results from size quantization. The effect of temperature on the current-voltage curves of tunneling structures is discussed. The study of the effect of potential barrier profile on the d ² I/dV ² line shape is of interest for experiments in inelastic tunneling spectroscopy. Various experimental situations where the inelastic component of the tunneling current can become comparable to the elastic one are discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 1151–1155 (June 1998)     

Nonlinear operation of a finite-size tunnel junction between 2D electron systems

A nonlinear regime of electron tunneling into double quantum wells with independent contacts to each well is investigated theoretically. The nonlinear current–voltage response in these systems takes place when the voltageV applied to the contacts exceeds the tunneling resonance width. It is found that such a nonlinearity acquires essentially new features when the length of the tunneling area is comparable with the square root of the ratio of the averaged in-plane conductivity of the electrons to the resonance tunneling conductance. Under these conditions, the local interlayer voltagev does not coincide with V and depends on the in-plane coordinate x. The local tunneling conductance also depends on x in the nonlinear regime. This dependence creates a positive feedback, which leads to a bistable behavior of the system (two stable patterns of the local voltage at a fixed V). The bistability is reflected by Z -like regions of the current–voltage characteristics.     

Long-range coherence and mesoscopic transport in N–S metallic structures

We review the mesoscopic transport in a diffusive proximity superconductor made of a normal metal (N) in metallic contact with a superconductor (S). The Andreev reflection of electrons on the N–S interface is responsible for the diffusion of electron pairs in N. Superconducting-like properties are induced in the normal metal. In particular, the conductivity of the N metal is locally enhanced by the proximity effect. A re-entrance of the metallic conductance occurs when all the energies involved (e.g. temperature and voltage) are small. The relevant characteristic energy is the Thouless energy which is divided by the diffusion time for an electron travelling throughout the sample. In loop-shaped devices, a 1 / T temperature-dependent oscillation of the magnetoresistance arises with a large amplitude from the long-range coherence of low-energy pairs.     

Tunneling conductance of the graphene SNS junction with a single localized defect

Using the Dirac-Bogoliubov-de Gennes equation, we study the electron transport in a graphene-based superconductor-normal(graphene)-superconductor (SNS) junction. We consider the properties of tunneling conductance through an undoped strip of graphene with heavily doped superconducting electrodes in the dirty limit l _def ≪ L ≪ ξ. We find that the spectrum of Andreev bound states is modified in the presence of a single localized defect in the bulk. The minimum tunneling conductance remains the same, and this result is independent of the actual location of the imperfection.     

Andreev tunneling in strongly interacting quantum dots

We review recent work on resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We derive a general expression for the current flowing in the structure and discuss the linear and nonlinear transport in the nonperturbative regime. New effects associated with the Kondo resonance combined with the two-particle tunneling arise. The Kondo anomaly in the I–V characteristics depends on the relative size of the gap energy and the Kondo temperature.     

Surface-field induced interband tunneling in InAs

Metal/insulator/semiconductor junctions are prepared on degeneratep-type InAs substrates with hole concentrations ranging from 2.3×10¹⁷ cm^–3 to 2.7×10¹⁸ cm^–3. The low work function of the top metal Yb, Al, or Au and charged interface states influence a two-dimensional (2D) electron inversion layer at the InAs surface. The insulator barrier that is formed by thermal oxidation is designed sufficiently thin, so that the bias voltage applied at the metal electrode mainly drops across the depletion layer separating the electron channel from the bulk. The current-voltage (I–V) characteristics exhibit strong negative differential conductance due to interband, tunneling from the 2D subband into the 3D valence band with peak-to-valley current ratios up to 3.1, 18, and 32 at 300 K, 77 K, and 4.2 K, respectively. In agreement with a theoretical model based on coherentelastic tunneling, the form of the I–V curves resembles those of double-barrier resonant tunnel devices rather than those of 3D Esaki diodes. The series resistance is obtained from the saturation of the differential conductance dI/dV at high forward bias and from the shift of structures in d² I/dV ² arising from phonon assisted tunneling.Dedicated to G. Lautz on the occasion of his 65th birthday     

Conductance of SIN and SIS junctions with chiral superconductors

Low-temperature conductance peaks due to the surface Andreev bound states in SIN and SIS junctions with chiral superconductors are considered. It is shown that, in SIN junctions, the conductance as a function of voltage, G(V), is highly sensitive to the dependence of the barrier transparency on the direction of the quasiparticle momentum. A weak magnetic field applied to the junction shifts the conductance peaks. In symmetric SIS junctions, the presence of chiral levels of Andreev bound states on both sides of the barrier gives rise to a conductance peak at V=0.     

Microscopic theory of equilibrium properties of F/S/F trilayers with weak ferromagnets

The aim of this paper is to explain the non monotonic temperature dependence of the self-consistent superconducting gap of ferromagnet/superconductor/ferromagnet (F/S/F) trilayers with weak ferromagnets in the parallel alignment (equivalent to F/S bilayers). We show that this is due to Andreev bound states that compete with the formation of a minigap. Using a recursive algorithm we discuss in detail the roles of various parameters (thicknesses of the superconductor and ferromagnets, relative spin orientation of the ferromagnets, exchange field, temperature, disorder, interface transparencies).Received: 23 January 2004, Published online: 29 June 2004PACS: 74.78.Na Mesoscopic and nanoscale systems - 74.45. + c Proximity effects; Andreev effect; SN and SNS junctions - 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects