Y2-wave Superconductors Research Articles

Probing Majorana flat bands in nodal [formula omitted] superconductors with Rashba spin–orbit coupling

We show that Majorana fermions associated with Majorana flat bands emerge as zero energy modes on the [110] edge of single layer or multilayer nodal superconductors with dx2−y2-wave pairing and Rashba spin–orbit coupling. Moreover, as long as the global inversion symmetry of the single layer or multilayer superconductor is broken, and in the presence of an in-plane magnetic field parallel to the [110] edge, the Majorana fermions together with usual fermionic Andreev bound states induce a triple-peak structure in tunnelling spectroscopy experiments. Importantly, we show that the zero bias conductance peak is induced by Majorana fermions. Therefore, tunnelling spectroscopy can be used to probe Majorana fermions in nodal dx2−y2-wave superconductors.

Dc Josephson current for d-wave superconductors with charge density waves

dc Josephson tunnel current Ic between a dx2−y2-wave superconductor and charge density waves (CDWs)—e.g. a high-Tc oxide and a conventional isotropic superconductor—was considered theoretically. Directionality of tunneling was taken into account. It was found that the dependence of Ic on the angle γ between the direction of the superconducting lobe and the plane normal to the junction is significantly altered by CDWs. For certain doping levels it may be nonmonotonic, as can be readily determined experimentally. For comparison, presented here are the corresponding results obtained for the tunnel junction between CDWs in an s-superconductor and a conventional isotropic superconductor.

Does a ferromagnet with spin-dependent masses produce a spin-filtering effect in aferromagnetic/insulator/superconductor junction?

We analyze charge transport through a ballistic ferromagnet/insulator/superconductorjunction by means of the Bogoliubov–de Gennes equations. We take into account thepossibility that ferromagnetism in the first electrode may be driven by a massrenormalization of oppositely polarized carriers, i.e. by a spin bandwidth asymmetry, ratherthan by a rigid splitting of up- and down-spin electron bands as in a standard Stonerferromagnet. By evaluating the averaged charge conductance for both an s- and adx2 − y2-wave order parameter for the S side, we show that the mass mismatch in the ferromagneticelectrode may mimic a spin active barrier. Indeed, in the s-wave case we show that undersuitable conditions the spin-dependent conductance of minority carriers below the energy gapΔ0 can be larger than for majority carriers, and lower aboveΔ0. On the otherhand, for a dx2 − y2-wave superconductor similar spin-dependent effects give rise to an asymmetric peaksplitting in the conductance. These results suggest that the junction may work as aspin-filtering device.

Tunneling Conductance in dx2 − y2 + idxy Mixed Wave Superconductor Graphene Junctions

Using the extended Blonder—Tinkham—Klapwijk formalism, we investigate the conductance spectra of normal metal/dx2 − y2 + idxy mixed wave superconductor graphene junctions. It is found that the conductance spectra vary strongly with the orientation of the gap and the amplitude ratio (Δ1/Δ0 of two components for dx2 − y2 + idxy mixed wave. The zero bias conductance is nearly 2 and the conductance peak vanishes in doped graphene for α = 0 and Δ1/Δ0 = 1. The conductance increases with increasing the amplitude ratio of two components for α = π/4 and Δ1/Δ0 = 1. The ZBCP becomes observable wide with 1 < EF/Δ0 < 100 for α = π/4 and Δ1/Δ0 = 1. This property is different from that in normal metal/dx2 − y2 wave superconductor graphene junctions.

Differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent

This paper applies the Bogoliubov–de Gennes equation and the Blonder–Tinkham–Klapwijk approach to study the oscillatory behaviour of differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent Is. We find that (i) a three-humped structure appears at a nearly critical supercurrent Is and z ≈ 0.5 for the normal metal/insulator/metal/dx2+y2-wave superconductor junction; (ii) the zero-bias conductance peak splits into two peaks with sufficiently large applied current for the normal metal/insulator/metal/dxy-wave superconductor junction; (iii) the conductance spectrum exhibits oscillating behaviour with the bias voltage and the peaks of the resonances are suppressed by increasing supercurrent Is.

Midgap Andreev resonant state affected by superconducting proximity effect of high-Tc cuprate attached to diffusive normal metal

We report how a midgap Andreev resonant state (MARS) is affected by the superconducting proximity effect at an interface of diffusive normal metal/insulator/dx.2_y2-wave superconductor (DN/I/DS) junctions. A zero-bias conductance peak (ZBCP) was observed for the (110)-oriented interface in Ag/SiO/Bi2Sr2CaCu2O8+δ (Bi-2212) planar junctions. The experimental ZBCP was analyzed by the extended circuit theory, which was improved by the introduction of spatial variations of the pair potential in a DS electrode near the junction interface. Our experimental results are well explained by the extended circuit theory for DN/I/DS junctions.

Interacting molecules on the surface of adx2−y2-wave superconductor

We study interacting molecules on the surface of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductor. We show that the interplay between the molecules' excitation spectrum and quantum interference of the scattered host electrons leads to a series of characteristic signatures and intriguing quantum effects in the superconductor's local density of states. We demonstrate that these effects give insight into both the nature of the superconducting pairing correlations and the intermolecular interactions.

The BCS–BE crossover phase diagram atT = 0 K for a d-wave superconductor: the importance of the Debye frequency and the tightbinding band structure

We consider the phase diagram of the BCS (Bardeen–Cooper–Schrieffer)–BE (Bose–Einstein) crossover in theground state (T = 0 K) of a dx2−y2-wave superconductor, with a nearest neighbour tight binding structure, when wetake into account the Debye (phononic) frequency around the chemical potential,μ. This approach is a continuation of the work of den Hertog (1999 Phys. Rev. B60 559) and that of Soares et al (2002 Phys. Rev. B 65 174506). The latterauthors considered the influence of the second-nearest neighbours, butneither set of authors took into account the effect of the Debye frequency,ωD, or the influence of the next nearest neighbour matrix hopping element. We have found thefollowing results: (1) there is not a metallic phase—that is, when , , , and , where n is the carrierdensity per site, V is theattractive interaction, t is the nearest neighbour hopping integral, and is the next nearest neighbour hopping ratio; (2) the BCS–BE crossover line is strongly affected by thepresence of ωD/4t and that of —actually, the values of V/4t needed to achieve the Bose–Einstein regime become extremely large for small values ofωD/4t; and(3) both Δ/4t andμ/4t strongly dependon the values of ωD/4t and . The results (1) are in agreement with the ones found by Perali et al (2003 Phys. Rev. B 68066501 (Preprint cond-mat/0211132)) and Rodríguez-Núñez et al (2003 Phys. Rev. B 68066502), and in disagreement with those of den Hertog and Soares et al.

Reply to “Comment on‘c-axis Josephson tunneling indx2−y2-wave superconductors’ ”

This reply responds to criticisms raised in the preceding Comment by G. B. Arnold, R. A. Klemm, W. K\orner, and K. Scharnberg [Phys. Rev. B 68, 226501 (2003)].

Multiple components of the order parameter induced around the dx2−y2-wave vortex core

On the basis of the Bogoliubov–de Gennes theory for the two-dimensional extended Hubbard model, the vortex structure of dx2−y2-wave superconductors is analyzed. Multiple components of the order parameter are induced around the dx2−y2-wave vortex core. We study the spatial structure of the induced px±ipy and extended s-wave components. We also study the case when the antiferromagnetism (checkerboard or stripe) is induced at the vortex core. There, spin-triplet dx2−y2-wave component is also induced.

Zero-bias conductance peak in disordered ferromagnetic metal/dx2−y2-wave superconductor junction

We investigate numerically the spin-polarized tunneling effect in ferromagnetic metal/insulator/dx2−y2-wave superconductor junctions. It is shown that the height of the zero-bias conductance peak owing to the zero energy states is depending on the magnitude of the exchange potential and the randomness near the junction interface.

Relation between vortex excitation and thermal conductivity in superconductors

Thermal conductivity κ xx(T) under a field is investigated in d x2 - y2-wave superconductors and isotropic s-wave superconductors by the linear response theory, using a microscopic wave function of the vortex lattice states. To study the origin of the different field dependence of κxx(T) between higher and lower temperature regions, we analyze the spatially-resolved thermal conductivity around a vortex at each temperature, which is related to the spectrum of the local density of states. We also discuss the electric conductivity in the same formulation for a comparison.

Quasiparticle transport in the vortex state of nodal superconductors

The symmetry of the superconductivity is the central issue in nodal superconductors. The angular-dependent thermal conductivity in the vortex state provides a new window to study this symmetry. We find the intriguing angular-dependent thermal conductivity found in single crystals of YBCO is described semi-quantitatively in terms of a dx2−y2-wave superconductor. Also the phononic thermal conductivity in general depends both on H and the angle. Further, we can identify Δ(k) in Sr2RuO4, CeCoIn5 and more recently in κ-(ET)2Cu(NCS)2 from the angular-dependent thermal conductivity data.

The resonance states around an impurity in d x2− y2-wave superconductors

We investigate the local density of states (LDOS) around a nonmagnetic impurity in the superconducting state of the two-dimensional t– t′– J model away from half-filling. The order parameters are determined self-consistently within the Gutzwiller approximation and the Bogoliubov-de Gennes theory. Similar to our previous results of the t– J model near half-filling, the zero-energy peak in the LDOS is also found when the electron–hole symmetry is broken.

Spontaneous time reversal and parity breaking in a d x2– y2-WAVE superconductor with magnetic impurities

It is argued that the d x 2– y 2 superconductor exhibits a transition into the d x 2– y 2 +id xy state in the presence of magnetic impurities in certain conditions. Linear coupling between impurity magnetization and the d xy component drives this transition. Violation of time-reversal symmetry and parity occurs spontaneously via the second order transition. In the ordered phase both impurity magnetization and d xy component of the order parameter develop and are proportional to each other.

Zero bias conductance peaks in high- Tc superconductors: clues and ambiguities of two mutually excluding models

The origin of the zero bias conductance peak (ZBCP) observed in the tunneling characteristics of different high- T c based junctions, is analyzed in the framework of the Anderson–Applebaum theory for Kondo type scattering from magnetic impurities at the barrier or in terms of midgap states induced by proximity effect at the surface of a d x2− y2 wave superconductor. The two models mutually exclude each other since they describe a normal state or a superconducting state effect, respectively. We show that the appearance of the anomaly above or below the junction T c, is the main indication that enable us to distinguish between the two cases. In addition to this, in the most controversial situations, the simultaneous presence at low temperatures of dips on both sides of the central structure as well as of conductance maxima at the expected values of the main high- T c superconductor (HTS) energy gap, can be considered as indications of d-wave superconductivity. The case of ZBCP's that for decreasing temperatures merge in conductance minima, is also discussed.

Evidence of d-wave pairing in the thermal conductivity of YBa2Cu3O7−d and Bi2Sr2CaCu2O8 single crystals

The electronic contribution to the thermal conductivity of a d x 2−y 2-wave superconductor is calculated within a variational method. By considering the scattering of electrons by point defects and acoustic phonons, the behavior of the thermal conductivity of YBa2Cu3O7−δ and Bi2Sr2CaCu2O8 single crystals can be well described with realistic values of the physical parameters. Besides, the values obtained for the transport electron-phonon coupling constant λ tr lie in the same range of magnitude than those derived from electrical resistivity measurements. b]References

Effects of atomic-scale roughness at the surface of dx2− y2-wave superconductor

The quasiparticle properties of d x 2− y 2 -wave superconductor near the rough surfaces is calculated using extended Hubbard model. Here, we calculate the local density of states (LDOS) near the surface with atomic-scale roughness, and investigate the correlation between the appearance of the zero energy states (ZES) and the surface roughness. In order to obtain the energy spectrum of quasiparticles, or LDOS, a numerical method is developed which is suitable to treat the disorder in the atomic-scale order length.

Exotic phase properties of d x2− y2-wave superconductors

Phase-sensitive test experiments for pairing symmetry of the high-temperature superconductors are reviewed. These experiments are discussed under the assumption of d x 2− y 2 -wave pairing. The influence of the superconducting state on the c-axis Josephson effect is analyzed. Special grain boundaries between the YBCO films can be described as Josephson junctions with alternating segments with 0- and π-phase shifts. The occurrence of spontaneous flux pattern on these grain boundaries is discussed.

Josephson effect in dx2 − y2-wave superconductors

Basic properties of the Jospephson effect in an s-wave superconductor/ Insulator/ d x 2 − y 2 -wave superconductor ( s/I/d) junction and a d x 2 − y 2 -wave superconductor/Insulator/ d x 2 − y 2 -wave superconductor ( d/I/d) junction are clarified for various crystal orientations. In both junctions, the phase difference ϑ dependence of the supercurrent does not always exhibit the usual sinusoidal behaviour. In general the minimum Free energy occurs neither at ϑ = 0 or ϑ = π. Zero-energy bound states of quasiparticles which are formed at zero energy can induce anomalous temperature dependence of maximum supercurrent in some d/I/d junctions.