Single particle tunneling and photoemission spectra in anisotropic layered high-temperature superconductors

We explore the effects of an anisotropic order parameter on the single particle tunneling conductance and on angular integrated and angular resolved photoemission spectra. Adopting a tight-binding model band structure, extendeds-wave pairing and the BCS strategy, we calculate the tunneling conductance for specular and diffuse transmission and the coherent part of the photoemission spectrum. Recent evidence for gap anisotropy, resulting from tunneling perpendicular and parallel to the layers, is traced back tox,y-anisotropy mediated by nearestneighbor intralayer pairing. This anisotropy is also found to be consistent with angular integrated photoemission measurements. It is shown that angular resolved photoemission experiments with high resolution would allow a more detailed identification of this anisotropic superconducting state.     

Triplet pairing states with equal spins in ferromagnet/superconductor heterojunctions for noncollinear magnetizations

Four-component Bogoliubov-de Gennes equations are applied to study tunneling conductance spectra of ferromagnet/ferromagnet/d-wave superconductor (F₁/F₂/d-wave S) tunnel junctions and to find out signs of spin-triplet pairing correlations induced in the proximity structure. The pairing correlations with equal spins arises from the novel Andreev reflection (AR), which requires at least three factors: the usual AR at the F₂/S interface, spin flip in the F₂ layer, and superconducting coherence kept up in the F₂ layer. Effects of angle α between magnetizations of the two F layers, polarizations of the F₁ and F₂ layers, the thickness of the F₂ layer, and the orientation of the d-wave S crystal on the tunneling conductance are investigated. A conversion from a zero-bias conductance dip at α = 0 to a zero-bias conductance peak at a certain value of α can be seen as a sign of generated spin-triplet correlations.     

Coexistence of superconducting and spiral spin orders: Models of ruthenate

The effect of a spiral spin structure on superconducting (SC) pairing in a three-band Hubbard model related to Sr₂RuO₄ is analyzed in the mean-field approximation. Such a structure with incommensurate vector Q=2π (1/3, 1/3) is the simplest one that removes the nesting instability of α and β bands. It is assumed that there is an intralayer pairing interaction between two types of neighbor sites, those with attraction in a singlet channel and with attraction in both two-singlet and triplet channels. In both cases, a mixed singlet-triplet SC order is observed in the γ band: a d-wave singlet order is accompanied by the formation of p-wave triplet pairs (k,-k-Q)? and (k,?k+Q)? with large total momenta ?Q and the spin projections ±1 onto an axis perpendicular to the spin rotation plane of the spiral spin structure. Both the SC and normal states are states with broken time-reversal symmetry. In contradiction to the experiment, the models give different scales of T _c for the γ band and for α and β bands. This fact shows that the models with intralayer interactions or with the spin structure assumed are insufficient.     

A microscopic model for the intrinsic Josephson tunneling in high- superconductors

A quantitative analysis of a microscopic model for the intrinsic Josephson effect in high-temperature superconductors based on interlayer tunneling is presented both within a mean-field BCS evaluation and a numerically essentially exact Quantum Monte-Carlo study. The pairing correlations in the CuO₂-planes are modelled by a 2D Hubbard model with attractive interaction, a model which accounts well for some of the observed features such as the short planar coherence length. The stack of Hubbard planes is arranged on a torus, which is threaded by a magnetic flux. The current perpendicular to the planes is calculated as a function of applied flux (i.e. the phase), and - after careful elimination of finite-size effects due to single-particle tunneling - found to display a sinusoidal field dependence in accordance with interlayer Josephson tunneling. Studies of the temperature dependence of the supercurrent reveal at best a mild elevation of the Josephson transition temperature compared to the planar Kosterlitz-Thouless temperature. These and other results on the dependence of the model parameters are compared with a standard BCS evaluation. Received: 24 February 1998 / Revised: 28 April 1998 / Accepted: 23 June 1998     

Theoretical calculations and Raman spectrum of intercalation modes in LixInSe

By using an extended linear-chain model which includes the interlayer forces, we have calculated the new vibrational modes, of Li intercalated InSe. The dispersion curves along thek _z wavevector perpendicular to the layers for the -polytype are determined in the first Brillouin zone. Assuming that the interlayer interaction is not modified upon intercalation and the interaction between lithium atom and adjacent layers in the van der Waals plane has the same value than the interlayer one, the new modes are determined with the force constant given by the rigid layer mode of the, -polytype at 18 cm^–1. This model gives the variation of the acoustic branches and the appearance of two optical intercalation modes at higher frequencies. The Brillouin zone boundary modes of the acoustic branches at 18 and 41 cm^–1 in the pure material are calculated to be 22 and 50 cm^–1 respectively forx=1/2. The dispersion of the new optical branches is flat along thez-direction and frequencies are obtained at 96 cm^–1 for the Li mode perpendicular tok _z and at 218 cm^–1 for the Li mode parallel tok _z. We compare also our results with the Li mode frequencies obtained in a total energy calculation. Raman scattering experiments have been performed in intercalated sample in order to verify the proposed model.     

Layered superconductors with anisotropic energy gap: specific heat and infrared absorption

New oxide superconductors with layered structure are expected to have anisotropic energy gap in the generalized BCS pairing theory. The gap parameter can be quite different for perpendicular to the plane of the layers as compared tok parallel to layer planes. Because of short coherence lengths ξ, quite small compared to the normal state carrier meanfree pathl, the effect of these anisotropies do not average out, as in many of the conventional superconductors. For a proper comparison of experimental results with the correct predictions of the pairing theory, a formulation is developed to obtain important physical quantities like specific heat and infrared absorption in the superconducting state of such anisotropic systems. This includes a brief account of the pairing theory generalized to layered crystals with arbitrary number of layers per unit cell, not necessarily equidistant. In an explicit model for the anisotropy of the gap parameter ink-space, with a simple form for the nonspherical Fermi-surface, it is shown that the low-temperature specific heat can have even a linear or a power-law temperature-dependence in the superconducting state. Even if the gap parameter does not vanish anywhere, its smeared-out exponential temperature-dependence may be difficult to be distinguished experimentally from a power-law behaviour. Similarly, it is shown that in the case of appreciable anisotropy, infrared absorption can take place much below the in-plane gap parameter , wherek _t is the wavevector in the plane of the layers.     

A comparison of the magnetic anisotropy of [001] and [111] oriented Co/Pd Multilayers

Superlattices of [001]_fcc Co/Pd with varying Co thicknesses from one to eight atomic layers per modulation period were epitaxially grown on NaCl by vapour deposition in UHV. Transmission electron diffraction indicates lattice coherence between the Co and the Pd layers for Co thicknesses up to six atomic layers. If deposited at a substrate temperatureT _s=50°C, only the superlattices containing Ci-monolayers show perpendicular magnetization. By raisingT _s to 200°C, the perpendicular anisotropy for Co monolayers is increased, and is also observed for Co bilayers. We suggest that this is due tolayer smoothening, which increases Néel's interface anisotropy. For more than 6 atomic layers of Co a loss of coherence is observed atT _s=50°C, accompanied by a structure transformation to hcp Co with a (0001)_Co(111)_Pd orientation.Non-epitaxial polycrystalline [111]-multilayers have a different anisotropy versus thickness behaviour. For such multilayers the range of Co thicknesses giving perpendicular magnetization is extended from 8 Å up to 12 Å atT _s=200°C. The different behaviour of the single crystal [001] films is caused by a strong volume contribution to the anisotropy, which favours in-plane magnetization, opposing the perpendicular interface anisotropy. This easy-plane term is attributed to magneto-elastic anisotropy due to stretching of the Co layers, via a positive magnetostriction.     

The effect of the superconducting–normal proximity on the Josephson tunneling of high-Tc superconductors

The Josephson coupling between two identical high-temperature superconductors was studied theoretically based on a superconducting–normal (SN) bilayer model with s+id-wave pairing in the S layer. It is indicated that due to the proximity effect between S and N layers as the interlayer hopping t_⊥ decreases, the product of the tunneling current through the junction and the normal-state resistance of the junction can be substantially reduced from the value described by the Ambegaokar–Baratoff (AB) theory. Our theoretical result is in good agreement with the experiments.     

The analysis of tunneling characteristics measured on Bi2Sr2CaCu2O8 surface

Cleaved in air a-b surface of Bi₂Sr₂CaCu₂O₈ (BSCCO-2212) was measured by means of STM and STS at 4.2 K in liquid hellium bath. From fitting experimental conductivity curves by Dynes' function two superconductivity parameters (gap value) and (smearing parameter) were obtained. The shape of gap structure superimposed on dI/dV characteristics depends on tip-sample distance, what is expressed by the increase of and decrease of with shortening of s. The phenomenon of becoming gap structure more distinct when approaching the tunneling tip to the surface is explained by us as the non-vacuum tunneling, where the surface contamination layer on non-metallic BiO top-surface layer strongly influences the tunneling process. Only for s short enough tunneling electrons penetrate to deeper situated CuO layers and reflect their superconducting behaviour. Non-vacuum STM images are therefore sensitive to the tip-sample distance adjustment. The dependence of gap parameters on lateral position of the tip above the sample can also occur. In such cases STS enables to state which elements of the image belong to the topography of the surface and which to its electron density of states.     

Evidence for spontaneous interlayer phase coherence in a bilayer quantum Hall exciton condensate

Recent experimental work on the quantized Hall state at total filling factor ν_T=1 in bilayer 2D electron systems has revealed a number of striking phenomena, including a giant and sharply resonant enhancement of the interlayer tunneling conductance at zero bias. The tunneling enhancement is a compelling indicator of spontaneous interlayer phase coherence among the electrons in the system. Such phase coherence is perhaps the single most important attribute of the excitonic Bose condensate which describes this remarkable quantum Hall state.     

Magnetic impurity effects inAgMn,AuFe, andCuCr studied by tunneling in superconducting proximity layers

Magnetic interactions were studied by superconducting tunneling into diluteAgMn,AuFe, andCuCr alloys in which superconductivity had been induced by a proximity effect. A detailed investigation ofAgMn, for concentrations up to 0.4 at.% Mn and at temperatures down to 0.05 K, revealed a weak impurity band within the energy gap of the density of excited states at about 0.68 of the half energy gap . The amplitude of the band, however, was twenty times smaller than expected from the theory by Müller-Hartmann and Zittartz. This makes the interpretation of the effect as being due to bulkAgMn doubtful. The localisation of the band would imply a Kondo temperature,T _K , of about 1 mK for an impurity spinS=5/2. No effect of spin-glass ordering was seen in the temperature dependence of the tunneling density of states inAgMn which contradicts a report by Schuller et al. The zero bias conductance could instead be reproduced from low temperature measurements if the temperature variation in was taken into account. InCuCr, the shape of the impurity band was found to be temperature dependent. The location of an impurity band at about 0.68 inAuFe indicates. together with previous observations, the presence of two impurity bands in this alloy. The one found here, might be due to long-range Fe pairs.     

Mesoscopic transport through toroidal carbon nanotubes threaded with a THz magnetic flux

We have investigated the quantum transport through mesoscopic systems with a toroidal carbon nanotube coupled with two metal leads (N-TCN-N) threaded with an ac magnetic flux. The energy shifting takes place by applying the magnetic flux, and this shifting arises from both the dc and ac components of magnetic flux. The dc magnetic flux induces the periodic variation of energy gap E _g of the TCN, and the ac magnetic flux component always increases the energy gap. As the photon energy is larger than the energy gap , the electrons in the valence band can jump to the conductance band at zero temperature, and the tunneling current appears for , ( ). The differential conductance and tunneling current display clear effect of ac flux by modifying the current oscillation structures. The photon-assisted tunneling current exhibits stair-like I-V characteristics, and it shows different behaviors for different TCN systems. The magnitude of the current is suppressed by the applied ac flux. We also present the time-dependent current evolution, which is contributed by the oscillating current components.Received: 31 May 2004, Published online: 3 August 2004PACS: 73.40.-c Electronic transport in interface structures - 73.63.Fg Nanotubes - 73.61.Wp Fullerenes and related materials - 73.22.-f Electronic structure of nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals     

Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains

We study the transport through the Kitaev chain with incommensurate potentials coupled to two normal leads by the numerical operator method. We find a quantized linear conductance of e ² / h, which is independent to the disorder strength and the gate voltage in a wide range, signaling the Majorana bound states. While the incommensurate potential suppresses the current at finite voltage bias, and then narrows the linear response regime of the I-V curve which exhibits two plateaus corresponding to the superconducting gap and the band edge, respectively. The linear conductance abruptly drops to zero as the disorder strength reaches the critical value 2g _s + 2Δ with Δ the p-wave pairing amplitude and g _s the hopping between neighbor sites, corresponding to the transition from the topological superconducting phase to the Anderson localized phase. Changing the gate voltage also causes an abrupt drop of the linear conductance by driving the chain into the topologically trivial superconducting phase, whose I-V curve exhibits an exponential shape.     

Tunneling conductance in ferromagnet/Sr2RuO4 junction: Detection of the d-vector direction

When a spin-triplet superconductor is attached to a ferromagnet, the tunneling conductance depends not only on the degree of the spin polarization but also sensitively on the relative angles between the magnetic moment in ferromagnet and the d-vector in spin-triplet superconductor. We study theoretically the tunneling conductance in ferromagnet/triplet superconductors assuming three nodal unitary gap functions, which are promising candidates for the pairing symmetry of Sr₂RuO₄. Our results suggest that the d-vector direction in Sr₂RuO₄ may be detected by performing angular dependent tunneling spectroscopy in this hybrid structure. We also show that these three gap functions can be distinguished by their distinctive conductance spectra.     

Dependence of the critical temperature of high-temperature cuprate superconductors on hoppings and spin correlations between CuO<Subscript>2</Subscript> planes

The influence of interlayer hoppings on the superconducting transition temperature (T _c) in bilayer cuprates has been studied. The parameter of hopping between layers is expressed as t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))² and treated as a small perturbation for the states of two CuO₂ planes described by the t-t′-t″-J* model. In the generalized mean field approximation for d_{x² - y²}{d_{{x^2} - {y^2}}} symmetry of the superconducting gap, neither the interlayer hopping or exchange interaction, nor the pair hopping between CuO₂ layers provides an additional mechanism of Cooper pair formation or an increase in T _c. In the concentration dependence of T _c, the bilayer splitting of the upper Hubbard band of quasi-holes is manifested as two peaks with temperatures slightly lower than the maximum T _c for a single-layer cuprate. Interlayer antiferromagnetic spin correlations suppress bilayer splitting.     

Twofold spin-triplet pairing states and tunneling conductance in ferromagnet/ferromagnet/iron pnictide superconductor heterojunctions

By applying an extended eight-component Bogoliubov–de Gennes equation, we study theoretically the tunneling conductance in clean ferromagnet/ferromagnet/iron pnictide superconductor (FM/FM/iron-based SC) heterojunctions. Under the condition of noncollinear magnetizations, twofold novel Andreev reflections exist due to the existence of two bands in the SC, in which the incident electron and the two Andreev-reflected holes, belonging to the same spin subband, form twofold spin-triplet pairing states near the FM/iron-based SC interface. It is shown that the conversions of the conductance not only between the zero-bias peak and valley at zero energy but also between the peaks and dips at two gap energies are strongly dependent on both the interband coupling strength in the SC and the spin polarization in the FM. The qualitative differences from tunneling into a conventional s$s$-wave SC are also presented, which may help with experimentally probing and identifying the antiphase s$s$-wave pairing symmetry in the iron-based SC.     

Effective Hamiltonian and properties of the normal and superconducting phases of <Emphasis Type="Italic">n</Emphasis>-type cuprates

An effective low-energy Hamiltonian is derived from a microscopic multiband p-d model in the regime of strong electron correlations. The parameters of the p-d model are determined by comparison with the ARPES data for undoped Nd₂CuO₄. The Hamiltonian is the t-J* model in which hopping and exchange slowly decay with distance and are taken into account up to the fifth coordination sphere. The quasiparticle band structure is calculated as a function of the doping concentration with regard to short-range magnetic order, and the superconductivity theory with the spin-fluctuation pairing mechanism is constructed. Assuming that the parameters of the model do not depend on the doping level, we obtained quantitative agreement with the properties observed experimentally for the normal and superconducting phases without introducing fitting parameters.     

Asymmetric d-wave superconducting topological insulator in proximity with a magnetic order

In the framework of the Dirac–Bogoliubov–de Gennes formalism, we investigate the transport properties in the surface of a 3-dimensional topological insulator-based hybrid structure, where the ferromagnetic and superconducting orders are simultaneously induced to the surface states via the proximity effect. The superconductor gap is taken to be spin-singlet d-wave symmetry. The asymmetric role of this gap respect to the electron–hole exchange, in one hand, affects the topological insulator superconducting binding excitations and, on the other hand, gives rise to forming distinct Majorana bound states at the ferromagnet/superconductor interface. We propose a topological insulator N/F/FS junction and proceed to clarify the role of d-wave asymmetry pairing in the resulting subgap and overgap tunneling conductance. The perpendicular component of magnetizations in F and FS regions can be at the parallel and antiparallel configurations leading to capture the experimentally important magnetoresistance (MR) of junction. It is found that the zero-bias conductance is strongly sensitive to the magnitude of magnetization in FS region $m_{zfs}$ and orbital rotated angle α of superconductor gap. The negative MR only occurs in zero orbital rotated angle. This result can pave the way to distinguish the unconventional superconducting state in the relating topological insulator hybrid structures.     

Microscopic description of superconductor-normal-metal superlattices

We study a model for superconductor-normal-metal superlattices in which adjacent layers are coupled via single-particle hopping. Examples include the high-T _c superconductor Bi₂Sr₂CaCu₂O_8+δ, where the BiO sheets seem to have normal metallic character. Using a BCS treatment, we investigate the influence of the interlayer hopping between the superconducting and the normal-metal slabs on the superconducting density of states, the tunneling characteristics for tunneling into both superconducting and normal-metal slabs as well as the temperature dependence of the London penetration depth.     

Temperature scaling of quantum Hall plateau transition in bilayer systems

We have investigated the scaling behavior of the quantum Hall plateau transition in double quantum well systems with different interlayer tunneling strengths. The scaling behavior of the localization property is found to be similar between the case when the relevant Landau level (LL) is non-degenerate and the case when two LLs associated with the two layers are accidentally degenerate. In both cases, the scaling exponent κ0.4 close to the canonical value is obtained, and it is unaffected by the in-plane magnetic field which changes the interlayer tunneling strength.