D-wave Superconducting Order Parameter Research Articles

Twisted van der Waals Josephson Junction Based on a High-Tc Superconductor.

Stacking two-dimensional van der Waals (vdW) materials rotated with respect to each other show versatility for studying exotic quantum phenomena. In particular, anisotropic layered materials have great potential for such twistronics applications, providing high tunability. Here, we report anisotropic superconducting order parameters in twisted Bi2Sr2CaCu2O8+x (Bi-2212) vdW junctions with an atomically clean vdW interface, achieved using the microcleave-and-stack technique. The vdW junctions with twist angles of 0° and 90° showed the maximum Josephson coupling, comparable to that of intrinsic Josephson junctions. As the twist angle approaches 45°, Josephson coupling is suppressed, and eventually disappears at 45°. The observed twist angle dependence of the Josephson coupling can be explained quantitatively by theoretical calculation with the d-wave superconducting order parameter of Bi-2212 and finite tunneling incoherence of the junction. Our results revealed the anisotropic nature of Bi-2212 and provided a novel fabrication technique for vdW-based twistronics platforms compatible with air-sensitive vdW materials.

Influence of pseudo-gap and interlayer coupling on isotope effect in bilayer cuprate superconductors

The present investigations deal with the study of the isotope effect in bilayer cuprate superconductors. We have considered the BCS-effective Hamiltonian that includes the intra and inter-layer kinetic energies and in plane attractive interaction responsible for pairing in these systems. In order to look for pseudo-gap having momentum dependence of the form of d-wave superconducting order parameter, a pseudo-gap order parameter is also introduced in the in-plane quasi-particle energy. Such a model calculation can be applicable for the high Tc cuprates like Bi2Sr2CaCu2O8+x having two CuO2 planes per unit cell and also for several other cuprate systems with a possibility to extend for the multi-layer cuprates. Employing Green's function formalism, we obtain the expressions for the superconducting order parameter and hence the isotope effect coefficient as a function of interlayer coupling, transition temperature and pseudo-gap order parameter. On the basis of numerical computation, we have pointed out that isotope effect increases due to coupling between the planes and decreases with the transition temperature. The presence of phenomenological pseudo-gap parameter in the quasi-particle spectrum enhances the isotope effect. These results are viewed in terms of recent experimental works on isotope effect in layered cuprate superconductors.

Nature of Cooper Instability of Spin Polarons in Cuprate High- $$T_\mathrm{c}$$ T c Superconductors

It is shown that the exchange interaction in the subsystem of localized moments of copper ions can trigger a Cooper instability in the ensemble of spin-polaron quasiparticles in cuprate high-temperature superconductors. It is important that, inherent to cuprates, strong coupling between Fermi and spin degrees of freedom leads on the one hand to formation of spin-polaron quasiparticles and, on the other hand, allows to transfer the interaction between Bose degrees of freedom onto the interaction between Fermi quasiparticles. The solution of the integral equation for the d-wave superconducting order parameter is well consistent with the available experimental data.

Hidden-order symmetry and superconductivity inURu2Si2investigated by quasiparticle interference

The hidden order (HO) in URu2Si2 has been determined as a high rank multipole formed by itinerant 5f-electrons with distinct orbital structure imposed by the crystalline electric field. Because this can lead to a considerable number of different multipoles it is of great importance to use microscopic techniques that are sensitive to their subtle physical differences. Here we investigate whether quasiparticle interference (QPI) method can distinguish between the two most frequently proposed HO parameter models: the even rank-4 hexadecapole and the odd-rank-5 dotriacontapole model. We obtain the quasiparticle dispersion and reconstructed Fermi surface in each HO phase adapting an effective two-orbital model of 5f bands that reproduces the main Fermi surface sheets of the para phase. We show that the resulting QPI spectrum reflects directly the effect of fourfold symmetry breaking in the rank-5 model which is absent in the rank-4 model. Therefore we suggest that QPI method should give a possibility of direct discrimination between the two most investigated models of HO in URu2Si2. Furthermore the signature of proposed chiral d-wave superconducting (SC) order parameter in QPI of the coexisting HO+SC phase is investigated.

Spin-dependent barrier effects on the transport properties of graphene-based normal metal/ferromagnetic barrier/d-wave superconductor junction

Using the extended Blonder–Tinkham–Klapwijk formalism, the spin-dependent transport properties in a graphene-based normal metal/ferromagnetic barrier/d-wave superconductor (NFBd-wave) junction have been studied theoretically. Here, we have mainly studied the influences of spin-dependent barrier and rotation angle of d-wave superconducting order parameter (α) on the charge and spin conductance. It is found that the rotation angle has a strong effect on the amplitude and phase of the charge conductance oscillations. As a remarkable result, we obtained that because of the spin-dependent barrier (FB), the rotation angle cannot suppress the zero-bias charge conductance and for the maximum rotation angle α=π/4, the charge conductance shows oscillatory behavior which is different from similar non-spin-dependent barrier junctions. We have also shown that the spin filtering application of this junction is drastically changed by the rotation angle α. As α increases, the spin filtering application enhances, being strongest for α=π/4. At last, we propose an experimental setup to detect our predicted effects.

A model and calculation of evolving tunneling spectra for the gap and pseudogap in Bi2Sr2CaCu2O8+δ

By the intrinsic tunneling spectroscopy in Bi2Sr2CaCu2O8+δ (Bi2212), it is found that the superconducting coherence peak becomes greater and sharper and the pseudogap peak diminishes with the increase in doping. It is also found that these changes are accompanied by a significant almost exponential increase in the maximum Josephson current density Jc. In order to explain the experimental results, we propose a model, in which mobile carriers reside only in limited areas in the k-space, and are closely correlated with the d-wave superconducting order parameter. The range of the area in which mobile carriers reside depends on the doping level. Outside these areas the density of states is absent at the chemical potential and a semiconducting gap is assumed. Based on this model, the tunneling spectra are calculated at various doping levels to obtain the result that the superconducting peak increases from a cusp at the shoulder of the pseudogap to a dominantly strong peak as the doping increases. The results are in qualitatively good agreement with the experimental tunneling spectra observed.

Universal scaling of length, time, and energy for cuprate superconductors based on photoemission measurements of Bi2Sr2CaCu2O8+δ

A microscopic scaling relation linking the normal and superconducting states of the cuprates in the presence of a pseudogap is presented using angle-resolved photoemission spectroscopy. This scaling relation, complementary to the bulk universal scaling relation embodied by Homes' law, explicitly connects the momentum-dependent amplitude of the d-wave superconducting order parameter at T\sim0 to quasiparticle scattering mechanisms operative at T\gtrsimTc. The form of the scaling is proposed to be a consequence of the marginal Fermi-liquid phenomenology and the inherently strong dissipation of the normal pseudogap state of the cuprates.

Importance of local correlations for the order parameter of high-Tcsuperconductors

It is shown that local temporal correlations in addition to non-local spatial correlations are important to understand the size and the doping dependence of the d-wave superconducting order parameter of high-temperature superconductors. To this end, the hole- and electron-doped two-dimensional Hubbard model at zero temperature is considered and treated by an extension of the variational cluster approximation. Within this approach, the effects of temporal correlations can be studied systematically and in a thermodynamically consistent way by comparing results obtained from different reference clusters. Contact can be made with previous cellular (plaquette) dynamical mean-field calculations. This shows that temporal correlations considerably decrease the order parameter and provide a substantial gain of binding energy. Besides, a few methodical insights regarding real-space quantum-cluster approaches are obtained in addition.

Strong Correlations and Magnetic Frustration in the HighTcIron Pnictides

We consider the iron pnictides in terms of a proximity to a Mott insulator. The superexchange interactions contain competing nearest-neighbor and next-nearest-neighbor components. In the undoped parent compound, these frustrated interactions lead to a two-sublattice collinear antiferromagnet (each sublattice forming a Néel ordering), with a reduced magnitude for the ordered moment. Electron or hole doping, together with the frustration effect, suppresses the magnetic ordering and allows a superconducting state. The exchange interactions favor a d-wave superconducting order parameter; in the notation appropriate for the Fe square lattice, its orbital symmetry is dxy. A number of existing and future experiments are discussed in light of the theoretical considerations.

Field-induced nodal order parameter in the tunneling spectrum ofYBa2Cu3O7−xsuperconductor

We report planar tunneling measurements on thin films of YBa$_2$Cu$_3$O$_{7-x}$ at various doping levels under magnetic fields. By choosing a special setup configuration, we have probed a field induced energy scale that dominates in the vicinity of a node of the d-wave superconducting order parameter. We found a high doping sensitivity for this energy scale. At Optimum doping this energy scale is in agreement with an induced $id_{xy}$ order parameter. We found that it can be followed down to low fields at optimum doping, but not away from it.

Effective action for phase fluctuations in d-wave superconductors near a Mott transition

Phase fluctuations of a d-wave superconducting order parameter are theoretically studied in the context of high-T$_c$ cuprates. We consider the $t-J$ model describing layered compounds, where the Heisenberg interaction is decoupled by a d-wave order parameter in the particle-particle channel. Assuming first that the equilibirum state has long-range phase order, the effective action $\mathcal{S}_{eff}$ is derived perturbatively for small fluctuations within a path integral formalism, in the presence of the Coulomb and Hubbard interaction terms. In a second step, a more general derivation of $\mathcal{S}_{eff}$ is performed in terms of a gradient expansion which only assumes that the gradients of the order parameter are small whereas the value of the phase may be large. We show that in the phase-only approximation the resulting $\mathcal{S}_{eff}$ reduces in leading order in the field gradients to the perturbative one which thus allows to treat also the case without long-range phase order or vortices. Our result generalizes previous expressions for $\mathcal{S}_{eff}$ to the case of interacting electrons, is explicitly gauge invariant, and avoids problematic singular gauge transformations.

Systematic Study ofd-Wave Superconductivity in the 2D Repulsive Hubbard Model

The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the dynamical cluster approximation and quantum Monte Carlo simulations as a cluster solver. Because of the nonlocality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster size and display a finite temperature instability to d-wave superconductivity.

Andreev reflection at the normal-metal/heavy-fermion superconductorCeCoIn5interface

The dynamic conductance of the heavy-fermion superconductor CeCoIn$_5$ is measured by point-contact spectroscopy as a function of temperature from 60 K down to 400 mK. The contact between the gold tip and the single-crystal is shown to be in the Sharvin limit with the enhanced sub-gap conductance arising from Andreev reflection. The zero-bias conductance data are best fit using the extended Blonder-Tinkham-Klapwijk model with a d-wave superconducting order parameter. A fit to the full conductance curve at 400 mK indicates strong coupling ($2\Delta(0)/k_\textrm{B}T_\textrm{c} = 4.6$) and quantifies the suppressed Andreev reflection signal, which is a signature of normal-metal/heavy-fermion superconductor junctions. Possibilites for theoretical modeling to account for the suppressed Andreev conductance are suggested.

Irradiation-induced suppression of the critical temperature in high-T c superconductors: Pair breaking versus phase fluctuations

Experiments on the irradiation-induced suppression of the critical temperature in high-T c superconductors are analyzed within the mean-field Abrikosov-Gor’kov-like approach. It is shown that the experimental data for YBa2Cu3O7-δ single crystals can be quantitatively explained by the pair-breaking effects under the assumption of the combined effect of potential and spin-flip scattering on the critical temperature and with an accounting for a nonpure d-wave superconducting order parameter.

New insights into high temperature superconductivity from a computational solution of the two-dimensional Hubbard model

The Cray X1 in the Center for Computational Sciences at Oak Ridge National Laboratory as well as algorithmic improvements over the past decade enable significant new science in the simulation of high-temperature "cuprate" superconductors. We describe the method of dynamic cluster approximation with quantum Monte Carlo, along with its computational requirements. We then show the unique capabilities of the X1 for supporting this method and delivering near optimal performance. This allows us to study systematically the cluster size dependence of the superconductivity in the conventional two-dimensional Hubbard model, which is commonly believed to describe high-temperature superconductors. Due to the non-locality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, converged results are found that display a finite temperature instability to d-wave superconductivity. The results we report here demonstrate for the first time that superconductivity is possible in a system of strongly correlated electrons without the need of a phonon mediated attractive interaction.

Enhancing Tc within phonon mediated coexistence of s + d wave superconductivity in cuprates

The high superconducting transition temperatures T c of oxide cuprates and their proximity to an antiferromagnetic ground state have frequently been attributed to unconventional pairing mechanisms and a d-wave superconducting order parameter. Even though effects due to the lattice have been observed experimentally, their role on superconductivity is mainly questioned. Here it will be shown that some features of hole doped superconducting cuprates can be well modeled by combining two order parameters of different symmetry, i.e. s + d, which interact through phonon induced interband scattering. A polaronic type phase (charge density wave like) precedes the superconducting state and signals the onset of the pseudogap state. Both effects, interband interactions and polaronic level shift are shown to substantially enhance T c.

Raman study of carrier-overdoping effects on the gap in high-Tcsuperconducting cuprates

Raman scattering in the heavily overdoped (Y,Ca)Ba_2Cu_3O_{7-d} (T_c = 65 K) and Bi_2Sr_2CaCu_2O_{8+d} (T_c = 55 K) crystals has been investigated. For the both crystals, the electronic pair-breaking peaks in the A_{1g} and B_{1g} polarizations were largely shifted to the low energies close to a half of 2Delta_0, Delta_0 being the maximum gap. It strongly suggests s-wave mixing into the d-wave superconducting order parameter and the consequent manifestation of the Coulomb screening effect in the B_{1g}-channel. Gradual mixing of s-wave component with overdoping is not due to the change of crystal structure symmetry but a generic feature in all high-T_c superconducting cuprates.

Fluctuating Order Parameter in Doped Cuprate Superconductors

We discuss the static fluctuations of the d-wave superconducting order parameter Δ in CuO 2 planes, due to quasiparticle scattering by charged dopants. The analysis of two-particle anomalous Green functions at T = 0 permits to estimate the mean-square fluctuation δ2 = <Δ2> - <Δ>2, averaged in random dopant configurations, to the lowest order in doping level c. Since Δ is found to saturate with growing doping level while δ remains to grow, this can explain the collapse of Tc at overdoping. Also we consider the spatial correlations <Δ(0)Δ(R)> for order parameter in different points of the plane.

Antiferromagnetic vortex core in HTSC studied by spatially resolved NMR

Spatially resolved NMR is used to probe the magnetism in the vortex state of Tl2Ba2CuO6+δ (Tc=85 K). We found that (1): T1−1 at 205Tl is extremely enhanced toward to the vortex core, (2): T1 process becomes largely inhomogeneous nearby the vortex core, and (3): the T-dependence of T1−1 at the vortex core region shows a peak at T=20 K. These results indicate a clear evidence of the local AF order inside the vortex core. The suppression of the d-wave superconducting order parameter leads to the nucleation of islands with the local AF order.

Antiferromagnetic vortex core in HTSC studied by spatially resolved NMR

Spatially-resolved NMR is used to probe the magnetism in the vortex state of nearly optimally doped high- T c cuprate Tl 2Ba 2CuO 6+ δ ( T c =85 K ). We found that (1) the nuclear spin–lattice relaxation rate T 1 −1 at 205 Tl is extremely enhanced toward the vortex core and (2) T 1 process become largely inhomogeneous in the vortex state and (3) the temperature dependence of T 1 −1 at the vortex core region shows a peak at T∼20 K . These results indicates a clear evidence of the antiferromagnetic (AF) order inside the vortex core, and that the suppression of the d-wave superconducting order parameter leads to the nucleation of islands with AF order.