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     

Josephson effect in superconducting hybrid S/F structures with parallel and antiparallel magnetizations of the ferromagnetic layers

The Josephson effect in S-MB-S, S/F-MB-S, and S/F-MB-F′/S superconducting hybrid structures with the parallel or antiparallel orientation of exchange fields in the layers of metal ferromagnets (F and F′) and in the magnetic barrier (MB) with arbitrary transparency has been investigated. It has been shown that the properties of the studied structures depend strongly on the orientation of the exchange fields: the exchange-field-induced stimulation of the critical current is possible for one orientation, whereas the critical current is suppressed at the opposite orientation of the exchange fields. A change in the orientation of the exchange fields can lead to the switching of the Josephson structures between 0 and π states. The effect of the pair-breaking mechanisms on the Josephson effect and on the spectrum of the Andreev levels in the S-MB-S structures has been analyzed. The results indicate the possibility of stimulating the critical current by the external magnetic field in the S-MB-S structures with thin-film superconducting banks.     

Zero-energy bound states in superconductor/ferromagnet superlattices

Andreev bound states in monoatomic superconductor–ferromagnet (S/F) superlattices are studied theoretically, assuming tunneling between S and F layers in perpendicular direction. Andreev reflection at S/F interfaces is strongly affected by the exchange interaction h in F layers. In the ground state, only for h≠0 zero-energy states (ZES) are formed on S and F layers. For h=0, corresponding to superconductor–normal metal (S/N) superlattices, ZES may appear in the nonequilibrium phase, =π. This is found both for s-wave and d-wave symmetry of the order parameter in S. The conditions for ZES are obtained as a function of h, of the transfer integral t for movement of quasiparticles (QPs) between S and F layers, and of the corresponding ground state phase difference _eq between two neighboring S layers.     

Andreev reflection in strong magnetic fields

We have studied the interplay of Andreev reflection and cyclotron motion of quasiparticles at a superconductor-normal-metal interface with a strong magnetic field applied parallel to the interface. Bound states are formed due to the confinement introduced by both the external magnetic field and the superconducting gap. These bound states are a coherent superposition of electron and hole edge excitations similar to those realized in finite quantum-Hall samples. We find the energy spectrum for these Andreev edge states and calculate transport properties.     

Effects of spin-orbit interaction on superconductor-ferromagnet heterostructures: Spontaneous electric and spin surface currents

We find proximity-induced spontaneous spin and electric surface currents at all temperatures below the super-conducting T _c in an isotropic s-wave superconductor deposited with a thin ferromagnetic metal layer with spin-orbit interaction. The currents are carried by Andreev surface states and generated as a joint effect of the spin-orbit interaction and the exchange field. The background spin current arises in the thin layer due to different local spin polarizations of electrons and holes, which have almost opposite velocities in each of the surface states. The spontaneous surface electric current in the superconductor originates in the asymmetry of Andreev states with respect to sign reversal of the momentum component parallel to the surface. The conditions for electric and spin currents to show up in the system significantly differ from each other.     

Effect of surface Andreev bound states on the Bean-Livingston barrier in d-wave superconductors

We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory, we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap.     

Fano effect and Andreev bound states in T-shape double quantum dots

In this Letter, we investigate the transport through a T-shaped double quantum dot coupled to two normal metal leads left and right and a superconducting lead. Analytical expressions of Andreev transmission and local density of states of the system at zero temperature have been obtained. We study the role of the superconducting lead in the quantum interferometric features of the double quantum dot. We report for first time the Fano effect produced by Andreev bound states in a side quantum dot. Our results show that as a consequence of quantum interference and proximity effect, the transmission from normal to normal lead exhibits Fano resonances due to Andreev bound states. We find that this interference effect allows us to study the Andreev bound states in the changes in the conductance between two normal leads.     

Andreev bound states in high temperature superconductors

Andreev bound states at the surface of superconductors are expected for any pair potential showing a sign change in different k-directions with their spectral weight depending on the relative orientation of the surface and the pair potential. We report on the observation of Andreev bound states in high temperature superconductors (HTS) employing tunneling spectroscopy on bicrystal grain boundary Josephson junctions (GBJs). The tunneling spectra were studied as a function of temperature and applied magnetic field. The tunneling spectra of GBJ formed by YBa₂Cu₃O (YBCO), Bi₂Sr₂CaCu₂O(BSCCO), and La_1.85Sr_0.15CuO₄ (LSCO) show a pronounced zero bias conductance peak that can be interpreted in terms of Andreev bound states at zero energy that are expected at the surface of HTS having a d-wave symmetry of the order parameter. In contrast, for the most likely s-wave HTS Nd_1.85Ce_0.15CuO_4-y (NCCO) no zero bias conductance peak was observed. Applying a magnetic field results in a shift of spectral weight from zero to finite energy. This shift is found to depend nonlinearly on the applied magnetic field. Further consequences of the Andreev bound states are discussed and experimental evidence for anomalous Meissner currents is presented. Received: 17 February 1998 / Revised: 27 April 1998 / Accepted: 23 June 1998     

超导体/铁磁体绝缘层-超导体隧道结的直流Josephson效应

在超导体铁磁体绝缘层超导体结(SFIS)中,运用BogoliubovdeGennes(BdG)方程和FurusakiTsukada(FT)电流公式,计算铁磁超导共存态的自洽方程和SFIS结中的直流Josephson电流.研究表明,铁磁超导态的磁交换能h对准粒子的Andreev反射有抑制作用,使得SFIS结中的直流Josephson电流随铁磁超导共存态的磁交换能h增大而减弱 关键词： S/F-I-S结 铁磁超导态 直流Josephson电流     

Spectrum of Andreev bound states in a molecule embedded inside a microwave-excited superconducting junction

Nondissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, the so-called Andreev states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a superconducting-phase-dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift can be used for Andreev bound state spectroscopy.     

Phase diagram of the electron-doped La2-xCexCuO4 cuprate superconductor from Andreev bound states at grain boundary junctions

We use quasiparticle tunneling across La2-xCexCuO4 grain boundary junctions to probe the superconducting state and its disappearance with increasing temperature and magnetic field. A zero bias conductance peak due to zero energy surface Andreev bound states is a clear signature of the phase coherence of the superconducting state. Hence, such a peak must disappear at or below the upper critical field Bc2(T). For La2-xCexCuO4 this approach sets a lower bound for Bc2(0) approximately 25 T which is substantially higher than reported previously. The method of probing the superconducting state via Andreev bound states should also be applicable to other cuprate superconductors.     

Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0-<Emphasis Type="Italic">π</Emphasis> transition

Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetricallyattached to superconducting leads is studied via the perturbation expansion in theinteraction strength. We find the exact asymptotic form of the spin-symmetric solution forthe Andreev states continuously approaching the Fermi level. We thereby derive a criticalinteraction at which the Andreev states at zero temperature merge at the Fermi energy,being the upper bound for the 0-π transition. We show that the spin-symmetricsolution becomes degenerate beyond this interaction, in the π phase, and the Andreevstates do not split unless the degeneracy is lifted. We further demonstrate that thedegeneracy of the spin-symmetric state extends also into the 0 phase in which the solutions with zero andnon-zero frequencies of the Andreev states may coexist.     

Signals for specular Andreev reflection

We report a theoretical investigation of the spin-dependent Andreev reflection at the interface of a graphene-based ferromagnet/superconductor junction. It is found that the ferromagnetic exchange interaction in the ferromagnet can suppress Andreev retroreflection but enhance the specular Andreev reflection. There is a transition between the specular Andreev reflection and Andreev retroreflection at which the shot noise vanishes and the Fano factor has a universal value. The present work provides a new method of detecting the specular Andreev reflection, which can be experimentally tested within the present-day technique.     

Spin-dependent quasiparticle reflection and bound States at interfaces with itinerant antiferromagnets

We find a novel channel of quasiparticle reflection from the simplest two-sublattice antiferromagnet (AF) on a bipartite lattice. Low-energy quasiparticles in a normal metal (N) experience spin-dependent retroreflection at AF/N interfaces. As a combined effect of antiferromagnetic and Andreev reflections, subgap Andreev states arise at an AF/superconductor (SC) interface. When the antiferromagnetic reflection dominates the specular one, Andreev bound states have almost zero energy on AF/s-wave superconductor (sSC) interfaces, whereas there are no low-energy subgap states on AF/d-wave superconductor (dSC) boundaries. For an sSC/AF/sSC junction, the bound states are found to split, due to the finite width of the AF interlayer, and carry the supercurrent. The theory developed in the present Letter is based on a novel quasiclassical approach, which applies to interfaces involving itinerant antiferromagnets.     

Chirality sensitive effect on surface states in chiral p-wave superconductors

We study the local density of states at the surface of a chiral p-wave superconductor in the presence of a weak magnetic field. As a result, the formation of low-energy Andreev bound states is either suppressed or enhanced by an applied magnetic field, depending on its orientation with respect to the chirality of the p-wave superconductor. Similarly, an Abrikosov vortex, which is situated not too far from the surface, leads to a zero-energy peak of the density of states, if its chirality is the same as that of the superconductor, and to a gap structure for the opposite case. We explain the underlying principle of this effect and propose a chirality sensitive test on unconventional superconductors.     

Origin of excess low-energy states in a disordered superconductor in a Zeeman field

Tunneling density of states measurements of disordered superconducting Al films in high Zeeman fields reveal a significant population of subgap states which cannot be explained by standard BCS theory. We provide a natural explanation of these excess states in terms of a novel disordered Larkin-Ovchinnikov phase that occurs near the spin-paramagnetic transition at the Chandrasekhar-Clogston critical field. The disordered Larkin-Ovchinnikov superconductor is characterized by a pairing amplitude that changes sign at domain walls. These domain walls carry magnetization and support Andreev bound states that lead to distinct spectral signatures at low energy.     

Superconducting atomic contacts under microwave irradiation

We have measured the effect of microwave irradiation on the dc current-voltage characteristics of superconducting atomic contacts. The interaction of the external field with the ac supercurrents leads to replicas of the supercurrent peak, the well-known Shapiro resonances. The observation of supplementary fractional resonances for contacts containing highly transmitting conduction channels reveals their nonsinusoidal current-phase relation. The resonances sit on a background current which is itself deeply modified, as a result of photon-assisted multiple Andreev reflections. The results provide firm support for the full quantum theory of transport between two superconductors based on the concept of Andreev bound states.     

Novel 0–π transitions in Josephson junctions between noncentrosymmetric superconductors

We study the Josephson effect between two noncentrosymmetric superconductors(NCSs) with opposite polarization vectors of Rashba spin–orbit coupling(RSOC).We find a 0–π transition driven by the triplet–singlet ratio of NCSs.Different from conventional 0–π transitions,the Andreev bound states change their energy range instead of phase shift in the 0–π transition found here.This novel property results in a feature that the critical current becomes almost zero at the transition point,not only a minimum.Furthermore,when the directions of RSOC polarization vectors are the same in two NCSs,the similar effect can also be found in the presence of a perpendicular exchange field or a Dresselhause spin–orbit coupling in the interlayer.We find novel oscillations of critical current without 0–π transition.These novel 0–π transitions or oscillations of critical current present new understanding of the Josephson effect and can also serve as a tool to determine the unknown triplet–singlet ratio of NCSs.     

Spin polarized current in the ground state of superconductor-ferromagnet-insulator trilayers

We study the ground state properties of a superconductor-ferromagnet-insulator trilayer on the basis of a Hubbard Model featuring exchange splitting in the ferromagnet and electron-electron attraction in the superconductor. We solve the spin-polarized Hartree-Fock-Gorkov equations together with the Maxwell's equation (Ampere's law) fully self-consistently with respect to the order parameter and the current. For certain values of the exchange splitting we find that a spontaneous spin polarized current is generated in the ground state and is intimately related to Andreev bound states at the Fermi level. Moreover, the polarization of the current strongly depends on the band filling. Received 23 September 2002 / Received in final form 13 December 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: m.a.krawiec@bristol.ac.uk