Nodal Direction Research Articles

Quantum size effects in ultra-thin YBa2Cu3O7 − x films

The d-wave symmetry of the order parameter with zero energy gap in nodal directions stands in the way of using high-temperature superconductors for quantum applications. We investigate the symmetry of the order parameter in ultra-thin YBa2Cu3O7 − x (YBCO) films by measuring the electrical transport properties of nanowires aligned at different angles relative to the main crystallographic axes. The anisotropy of the nanowire critical current in the nodal and antinodal directions reduces with the decrease in the film thickness. The Andreev reflection spectroscopy of the nanoconstrictions shows the presence of a thickness-dependent energy gap that does not exist in bulk YBCO. We find that the thickness-dependent energy gap appears due to the quantum size effects in ultra-thin YBCO films that open the energy gap along the entire Fermi surface. The fully gapped state of the ultra-thin YBCO films makes them a promising platform for quantum applications, including quantum computing and quantum communications.

Evidence for a finite-momentum Cooper pair in tricolor d-wave superconducting superlattices

Fermionic superfluidity with a nontrivial Cooper-pairing, beyond the conventional Bardeen-Cooper-Schrieffer state, is a captivating field of study in quantum many-body systems. In particular, the search for superconducting states with finite-momentum pairs has long been a challenge, but establishing its existence has long suffered from the lack of an appropriate probe to reveal its momentum. Recently, it has been proposed that the nonreciprocal electron transport is the most powerful probe for the finite-momentum pairs, because it directly couples to the supercurrents. Here we reveal such a pairing state by the non-reciprocal transport on tricolor superlattices with strong spin-orbit coupling combined with broken inversion-symmetry consisting of atomically thin d-wave superconductor CeCoIn5. We find that while the second-harmonic resistance exhibits a distinct dip anomaly at the low-temperature (T)/high-magnetic field (H) corner in the HT-plane for H applied to the antinodal direction of the d-wave gap, such an anomaly is absent for H along the nodal direction. By carefully isolating extrinsic effects due to vortex dynamics, we reveal the presence of a non-reciprocal response originating from intrinsic superconducting properties characterized by finite-momentum pairs. We attribute the high-field state to the helical superconducting state, wherein the phase of the order parameter is spontaneously spatially modulated.

Exploring spin-polarization in Bi-based high-Tc cuprates

The role of spin–orbit interaction has been recently reconsidered in high-T_{c} cuprates, stimulated by the recent experimental observations of spin-polarized electronic states. However, due to the complexity of the spin texture reported, the origin of the spin polarization in high-T_{c} cuprates remains unclear. Here, we present the spin- and angle-resolved photoemission spectroscopy (ARPES) data on the facing momentum points that are symmetric with respect to the Gamma point, to ensure the intrinsic spin nature related to the initial state. We consistently found the very weak spin polarization only along the nodal direction, with no indication of spin-splitting of the band. Our findings thus call for a revision of the simple application of the spin–orbit interaction, which has been treated within the standard framework of the Rashba interaction in high-T_{c} cuprates.

Effect of Anisotropic Impurity Scattering in D-Wave Superconductors

In d x 2–y 2 -wave superconductors, the effect of s-wave point disorder has been extensively studied in literature. We study the anisotropic disorder in the form of with fk = cos(2θ) (θ the azimuthal angle of k), as proposed to be caused by apical oxygen vacancies in overdoped La-based cuprate films, under the Born approximation. The disorder self-energy and d-wave pairing affect each other and must be solved simultaneously self-consistently. We find that the self-energy is reduced at low frequencies and thus weakens the pair-breaking effect. This frequency dependence vanishes in the dirty limit for which the disorder is well described by a scattering rate . One consequence of the disorder effect is that the gap-to-T c ratio 2Δ(0)/T c is greatly enhanced by the d-wave disorder, much larger than the s-wave disorder and the clean BCS value 4.28. Lastly, we generalize the d-wave scattering rate to a general form around each nodal direction θ 0. We find the density of states ρ(ω)–ρ(0)∝|ω| (ω 2) for all α ≥ 1 (α < 1) in the limit of ω → 0. As a result, the superfluid density ρ s exhibits two and only two possible scaling behaviors: ρ s(0)–ρ s(T)∝ T (T 2) for α ≥ 1 (α < 1) in the low temperature limit.

Critical Current Density in d-Wave Hubbard Superconductors.

In this work, the Generalized Hubbard Model on a square lattice is applied to evaluate the electrical current density of high critical temperature d-wave superconductors with a set of Hamiltonian parameters allowing them to reach critical temperatures close to 100 K. The appropriate set of Hamiltonian parameters permits us to apply our model to real materials, finding a good quantitative fit with important macroscopic superconducting properties such as the critical superconducting temperature (Tc) and the critical current density (Jc). We propose that much as in a dispersive medium, in which the velocity of electrons can be estimated by the gradient of the dispersion relation ∇ε(k), the electron velocity is proportional to ∇E(k) in the superconducting state (where E(k)=(ε(k)-μ)2+Δ2(k) is the dispersion relation of the quasiparticles, and k is the electron wave vector). This considers the change of ε(k) with respect to the chemical potential (μ) and the formation of pairs that gives rise to an excitation energy gap Δ(k) in the electron density of states across the Fermi level. When ε(k)=μ at the Fermi surface (FS), only the term for the energy gap remains, whose magnitude reflects the strength of the pairing interaction. Under these conditions, we have found that the d-wave symmetry of the pairing interaction leads to a maximum critical current density in the vicinity of the antinodal k-space direction (π,0) of approximately 1.407236×108 A/cm2, with a much greater current density along the nodal direction (π2,π2) of 2.214702×109 A/cm2. These results allow for the establishment of a maximum limit for the critical current density that could be attained by a d-wave superconductor.

Deviations from the extended London model at high magnetic fields in YBa2Cu3O7

We report on the evolution with the magnetic field and the temperature of the vortex lattice (VL) in fully oxygenated ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ as studied by time-of-flight small-angle neutron scattering. Using the High Field Magnet/Extreme Environment Diractometer beamline at Helmholtz-Zentrum Berlin, we have obtained data up to 25.9 T---much higher than data available previously. Our VL structure results are consistent with the progressive suppression by the field of the superconductivity along the crystallographic $\mathbf{b}$ (CuO chain) direction and an accompanying shift of the nodal directions as the field is increased. The intensity of the diffracted signal reveals the spatial variation of magnetization caused by the VL (the ``form factor''). Instead of a rapid falloff with the field, as seen in superconductors with smaller upper critical fields, we find that the form factor is almost constant with the field above $\ensuremath{\sim}12$ T. We speculate that this is due to Pauli paramagnetic effects.

Imperfect symmetry of real annular combustors: beating thermoacoustic modes and heteroclinic orbits

In jet engines and gas turbines, the annular shape of the combustion chamber allows the appearance of self-oscillating azimuthal thermoacoustic modes. We report experimental evidence of a new type of modal dynamics characterised by periodic switching of the spinning direction and develop a theoretical model that fully reproduces this phenomenon and explains the underlying mechanisms. It is shown that tiny asymmetries of the geometry, the mean temperature field, the thermoacoustic response of the flames or the acoustic impedance of the walls, present in any real systems, can induce these heteroclinic orbits. The model also explains experimental observations showing a statistically dominant spinning direction despite the absence of swirling flow, or pairs of preferred nodal line directions.

Superconductivity in the three-band model of cuprates: nodal direction characteristics and influence of intersite interactions

The three-band Emery model is applied to study the selected principal features of the d-wave superconducting phase in the copper-based compounds. The electron–electron correlations are taken into account by the use of the diagrammatic expansion of the Guztwiller wave function (DE-GWF method). The nodal Fermi velocity, Fermi momentum, and effective mass are all determined in the paired state and show relatively good agreement with the available experimental data, as well as with the corresponding single-band calculations. Additionally, the influence of the next-nearest neighbor oxygen–oxygen hopping and intersite Coulomb repulsion terms on the superconducting phase is analyzed.

Unified theory of spin and charge excitations in high- Tc cuprate superconductors: A quantitative comparison with experiment and interpretation

We provide a unified interpretation of both paramagnon and plasmon modes in high-$T_c$ copper-oxides, and verify it quantitatively against available resonant inelastic $x$-ray scattering (RIXS) data across the hole-doped phase diagram. Three-dimensional extended Hubbard model, with included long-range Coulomb interactions and doping-independent microscopic parameters for both classes of quantum fluctuations, is used. Collective modes are studied using VWF+$1/\mathcal{N}_f$ approach which extends variational wave function (VWF) scheme by means of an expansion in inverse number of fermionic flavors ($1/\mathcal{N}_f$). We show that intense paramagnons persist along the anti-nodal line from the underdoped to overdoped regime and undergo rapid overdamping in the nodal direction. Plasmons exhibit a three-dimensional character, with minimal energy corresponding to anti-phase oscillations on neighboring $\mathrm{CuO_2}$ planes. The theoretical spin- and charge excitation energies reproduce semi-quantitatively RIXS data for $\mathrm{(Bi, Pb)_2 (Sr, La)_2 CuO_{6+\delta}}$. The present VWF+$1/\mathcal{N}_f$ analysis of dynamics and former VWF results for static quantities combine into a consistent description of the principal properties of hole-doped high-$T_c$ cuprates as strongly correlated systems.

Time-resolved ARPES on cuprates: Tracking the low-energy electrodynamics in the time domain

The pursuit of a comprehensive understanding of the dynamical nature of intertwined orders in quantum matter has fueled the development of several new experimental techniques, including time- and angle-resolved photoemission spectroscopy (TR-ARPES). In this regard, the study of copper-oxide high-temperature superconductors, prototypical quantum materials, has furthered both the technical advancement of the experimental technique, as well as the understanding of their correlated dynamical properties. Here, we provide a brief historical overview of the TR-ARPES investigations of cuprates, and review what specific information can be accessed via this approach. We then present a detailed discussion of the transient evolution of the low-energy spectral function both along the gapless nodal direction and in the near-nodal superconducting gap region, as probed by TR-ARPES on Bi-based cuprates.

Positive Seebeck Coefficient in Highly Doped La2−xSrxCuO4 (x = 0.33); Its Origin and Implication

We present a study of the thermoelectric (Seebeck and Nernst) response in heavily overdoped, non-superconducting La$_{1.67}$Sr$_{0.33}$CuO$_4$. In spite of the electron-like curvature of the Fermi surface, the Seebeck coefficient is positive at low temperatures. Such a feature, previously observed in copper, silver, gold and lithium, is caused by a non-trivial energy dependence of the scattering time. We argue that this feature implies a strong asymmetry between the lifetime of occupied and unoccupied states along the zone diagonals and such an electron-hole asymmetry impedes formation of Cooper pairs along the nodal direction in the superconducting ground state emerging at lower doping levels.

Ubiquitous suppression of the nodal coherent spectral weight in Bi-based cuprates

High-temperature superconducting cuprates exhibit an intriguing phenomenology for the low-energy elementary excitations. In particular, an unconventional temperature dependence of the coherent spectral weight (CSW) has been observed in the superconducting phase by angle-resolved photoemission spectroscopy (ARPES), both at the antinode where the d-wave paring gap is maximum, as well as along the gapless nodal direction. Here, we combine equilibrium and time-resolved ARPES to track the temperature dependent meltdown of the nodal CSW in Bi-based cuprates with unprecedented sensitivity. We find the nodal suppression of CSW upon increasing temperature to be ubiquitous across single- and double-layer Bi cuprates, and uncorrelated to superconducting and pseudogap onset temperatures. We quantitatively model both the lineshape of the nodal spectral features and the anomalous suppression of CSW within the Fermi-Liquid framework, establishing the key role played by the normal state electrodynamics in the description of nodal quasiparticles in superconducting cuprates.

New 3D Diffusion Code Based on The Nodal Polynomial Expansion

Nodal Expansion Method (NEM) is widely employed in the neutronic design of nuclear reactors core. The main reason is its higher computational performance and efficiency when compared with the conventional fine mesh difference method or finite element method. The NEM diffusion calculation uses coarse spatial meshes and the size can lie in assembly scale. This is the key for the computational efficiency and high accuracy calculations. The NEM consists mainly of basis polynomial function expansion for each nodal direction. The Nodal Expansion Method (NEM), as proposed by Finnemann in 1977, has been used to solve the multigroup neutron diffusion equations in three-dimensional (3D) rectangular geometry. The weighted residual technique has been applied to determine the higher order coupling coefficients. Resulting from the combination of nodal and finite element methods, NEM provides rigorously accurate equations obtained by integrating the neutron balance equation. The two group coarse mesh 3D IAEA benchmark has been simulated by NEM3D-1A using different nodes sizes. The VENTURE

Eigenrays in 3D heterogeneous anisotropic media, Part I: Kinematics

ABSTRACTWe present a new ray bending approach, referred to as the Eigenray method, for solving two‐point boundary‐value kinematic and dynamic ray tracing problems in 3D smooth heterogeneous general anisotropic elastic media. The proposed Eigenray method is aimed to provide reliable stationary ray path solutions and their dynamic characteristics, in cases where conventional initial‐value ray shooting methods, followed by numerical convergence techniques, become challenging. The kinematic ray bending solution corresponds to the vanishing first traveltime variation, leading to a stationary path between two fixed endpoints (Fermat's principle), and is governed by the nonlinear second‐order Euler–Lagrange equation. The solution is based on a finite‐element approach, applying the weak formulation that reduces the Euler–Lagrange second‐order ordinary differential equation to the first‐order weighted‐residual nonlinear algebraic equation set. For the kinematic finite‐element problem, the degrees of freedom are discretized nodal locations and directions along the ray trajectory, where the values between the nodes are accurately and naturally defined with the Hermite polynomial interpolation. The target function to be minimized includes two essential penalty (constraint) terms, related to the distribution of the nodes along the path and to the normalization of the ray direction. We distinguish between two target functions triggered by the two possible types of stationary rays: a minimum traveltime and a saddle‐point solution (due to caustics). The minimization process involves the computation of the global (all‐node) traveltime gradient vector and the traveltime Hessian matrix. The traveltime Hessian is used for the minimization process, analysing the type of the stationary ray, and for computing the geometric spreading of the entire resolved stationary ray path. The latter, however, is not a replacement for the dynamic ray tracing solution, since it does not deliver the geometric spreading for intermediate points along the ray, nor the analysis of caustics. Finally, we demonstrate the efficiency and accuracy of the proposed method along three canonical examples.

Transport and Point Contact Measurements on Pr1-xCexPt4Ge12 Superconducting Polycrystals.

We performed a detailed investigation of the superconducting properties of polycrystalline Pr1−xCexPt4Ge12 pellets. We report the effect of Ce substitution, for x = 0.07, on magnetic field phase diagram H-T. We demonstrate that the upper critical field is well described by the Ginzburg–Landau model and that the irreversibility field line has a scaling behaviour similar to cuprates. We also show that for magnetic fields lower than 0.4 T, the activation energy follows a power law of the type 𝐻−1/2, suggesting a collective pinning regime with a quasi-2D character for the Ce-doped compound with x = 0.07. Furthermore, by means of a point contact Andreev reflection spectroscopy setup, we formed metal/superconductor nano-junctions as small as tens of nanometers on the PrPt4Ge12 parent compound (x = 0). Experimental results showed a wide variety of conductance features appearing in the dI/dV vs. V spectra, all explained in terms of a modified Blonder–Tinkham–Klapwijk model considering a superconducting order parameter with nodal directions as well as sign change in the momentum space for the sample with x = 0. The numerical simulations of the conductance spectra also demonstrate that s-wave pairing and anisotropic s-waves are unsuitable for reproducing experimental data obtained at low temperature on the un-doped compound. Interestingly, we show that the polycrystalline nature of the superconducting PrPt4Ge12 sample can favour the formation of an inter-grain Josephson junction in series with the point contact junction in this kind of experiments.

A unified form of low-energy nodal electronic interactions in hole-doped cuprate superconductors

Using angle resolved photoemission spectroscopy measurements of Bi2Sr2CaCu2O8+δ over a wide range of doping levels, we present a universal form for the non-Fermi liquid electronic interactions in the nodal direction in the exotic normal state phase. It is described by a continuously varying power law exponent versus energy and temperature (hence named a Power Law Liquid or PLL), which with doping varies smoothly from a quadratic Fermi Liquid in the overdoped regime, to a linear Marginal Fermi Liquid at optimal doping, to a non-quasiparticle non-Fermi Liquid in the underdoped regime. The coupling strength is essentially constant across all regimes and is consistent with Planckian dissipation. Using the extracted PLL parameters we reproduce the experimental optics and resistivity over a wide range of doping and normal-state temperature values, including the T* pseudogap temperature scale observed in the resistivity curves. This breaks the direct link to the pseudogapping of antinodal spectral weight observed at similar temperature scales and gives an alternative direction for searches of the microscopic mechanism.

Sources of uncertainties and artifacts in back-projection results

Summary Back-projecting high-frequency (HF) waves is a common procedure for imaging rupture processes of large earthquakes (i.e. Mw &gt; 7.0). However, obtained back-projection (BP) results could suffer from large uncertainties since high-frequency seismic waveforms are strongly affected by factors like source depth, focal mechanisms, and the Earth's 3D velocity structures. So far, these uncertainties have not been thoroughly investigated. Here, we use synthetic tests to investigate the influencing factors for which scenarios with various source and/or velocity set-ups are designed, using either Tohoku-Oki (Japan), Kaikoura (New Zealand), Java/Wharton Basin (Indonesia) as test areas. For the scenarios, we generate either 1D or 3D teleseismic synthetic data, which are then back-projected using a representative BP method, MUltiple SIgnal Classification (MUSIC). We also analyze corresponding real cases to verify the synthetic test results. The Tohoku-Oki scenario shows that depth phases of a point source can be back-projected as artifacts at their bounce points on the earth's surface, with these artifacts located far away from the epicenter if earthquakes occur at large depths, which could significantly contaminate BP images of large intermediate-depth earthquakes. The Kaikoura scenario shows that for complicated earthquakes, composed of multiple sub-events with varying focal mechanisms, BP tends to image sub-events emanating large amplitude coherent waveforms, while missing sub-events whose P nodal directions point to the arrays, leading to discrepancies either between BP images from different arrays, or between BP images and other source models. Using the Java event, we investigate the impact of 3D source-side velocity structures. The 3D bathymetry together with a water layer can generate strong and long-lasting coda waves, which are mirrored as artifacts far from the true source location. Finally, we use a Wharton Basin outer-rise event to show that the wavefields generated by 3D near trench structures contain frequency-dependent coda waves, leading to frequency-dependent BP results. In summary, our analyses indicate that depth phases, focal mechanism variations, and 3D source-side structures can affect various aspects of BP results. Thus, we suggest that target-oriented synthetic tests, for example, synthetic tests for subduction earthquakes using more realistic 3D source-side velocity structures, should be conducted to understand the uncertainties and artifacts before we interpret detailed BP images to infer earthquake rupture kinematics and dynamics.

Enhancement of penetration field in vortex matter in mesoscopic superconductors due to Andreev bound states

We study the penetration field $H_{\rm P}$ for vortex nanocrystals nucleated in micron-sized samples with edges aligned along the nodal and anti-nodal directions of the d-wave superconducting parameter of Bi$_2$Sr$_2$CaCu$_2$O$_{8 - \delta}$. Here we present evidence that the $H_{\rm P}$ for nanocrystals nucleated in samples with edges parallel to the nodal direction is larger than for the antinodal case, $\sim 72$\,\% at low temperatures. This finding supports the theoretical proposal that surface Andreev bound states appearing in a sample with edges parallel to the nodal direction would produce an anomalous Meissner current that increases the Bean-Livingston barrier for vortex penetration.This has been detected thanks to the nucleation of vortex nanocrystals with a significant surface-to-volume ratio.

Torsional chiral magnetic effect due to skyrmion textures in a Weyl superfluid He3−A

We investigate torsional chiral magnetic effect (TCME) induced by skyrmion-vortex textures in the A phase of the superfluid $^3$He. In $^3$He-A, Bogoliubov quasiparticles around point nodes behave as Weyl fermions, and the nodal direction represented by the $\ell$-vector may form a spatially modulated texture. $\ell$-textures generate a chiral gauge field and a torsion field directly acting on the chirality of Weyl-Bogoliubov quasiparticles. It has been clarified by G. E. Volovik [Pi'sma Zh. Eksp. Teor. Fiz. {\bf 43}, 428 (1986)] that, if the $\ell$-vector is twisted, the chiral gauge field is responsible for the chiral anomaly, leading to an anomalous current along ${\ell}$. Here we show that, even for non-twisted $\ell$-vector fields, a torsion arising from $\ell$-textures brings about contributions to the equilibrium currents of Weyl-Bogoliubov quasiparticles along ${\rm curl}{\ell}$. This implies that while the anomalous current appears only for the twisted (Bloch-type) skyrmion of the $\ell$-vector, the extra mass current due to TCME always exists regardless of the skyrmion type. Solving the Bogoliubov-de Gennes equation, we demonstrate that both Bloch-type and N\'{e}el-type skyrmions induce chiral fermion states with spectral asymmetry, and possess spatially inhomogeneous structures of Weyl bands in the real coordinate space. Furthermore, we discuss the contributions of Weyl-Bogoliubov quasiparticles and continuum states to the mass current density in the vicinity of the topological phase transition. In the weak coupling limit, continuum states give rise to backflow to the mass current generated by Weyl-Bogoliubov quasiparticles, which makes a non-negligible contribution to the orbital angular momentum. As the topological transition is approached, the mass current density is governed by the contribution of continuum states.

Origin of the Fermi arcs in cuprates: a dual role of quasiparticle and pair excitations

Angle resolved photoemission spectroscopy (ARPES) mesurements in cuprates have given key information on the temperature and angle dependence of the gap (d-wave order parameter, Fermi arcs and pseudogap). We show that these features can be understood in terms of a Bose condensation of interacting pairons (preformed hole pairs which form in their local antiferromagnetic environment). Starting from the basic properties of the pairon wavefunction, we derive the corresponding k-space spectral function. The latter explains the variation of the ARPES spectra as a function of temperature and angle up to T*, the onset temperature of pairon formation. While Bose excitations dominate at the antinode, the fermion excitations dominate around the nodal direction, giving rise to the Fermi arcs at finite temperature. This dual role is the key feature distinguishing cuprate from conventional superconductivity.