D-wave Symmetry Of Order Parameter Research Articles

Anisotropy of the T vs. H phase diagram and the HO/LMAFM phase boundary in URu2−xFexSi2

The correlated f-electron compound URu2Si2 exhibits superconductivity (SC) with a critical temperature Tc = 1.5 K that coexists with the “hidden order” (HO) phase that forms below a characteristic temperature T0 = 17.5 K. The SC of URu2Si2 appears to be spin singlet chiral SC with d-wave order parameter symmetry, and the pairing of SCing electrons may involve spin excitations of the HO phase. Electrical resistance R measurements were performed on single crystal specimens of URu2−xFexSi2 with increasing x throughout the transition from the HO phase to the large moment antiferromagnetic LMAFM phase in high magnetic fields H oriented at various angles θ with respect to the tetragonal c-axis. Measurements of R(θ) at H = 20, 33, 40, and 45 T were conducted in the temperature range 0.33 ≤ T ≤ 20 K and showed θ-dependent behavior in the various phase transitions of URu2−xFexSi2 (HO, LMAFM, spin density wave, Fermi surface reconstruction, etc.). These phase transitions, as functions of T, H, and θ are plotted in a phase diagram of T vs. H//c = Hcosθ for multiple values of x and show that H//c, not θ is a tuning parameter of the URu2−xFexSi2 system throughout all Fe concentrations, as previously found by Scheereret al. for the URu2Si2 parent compound.

Stationary Josephson current as a tool to detect charge density waves in high-[formula omitted] oxides

Nonmonotonic and even sign-changing dependences on the temperature and the doping level were predicted for the stationary Josephson tunnel current Ic between superconductors with d-wave order parameter symmetry and partial gapping by charge density waves (CDWs). The junction electrodes were considered in the framework of the two-dimensional electron spectrum appropriate to high-Tc cuprates. The non-trivial behavior can be observed for certain relative electrode orientations. Hence, Ic-measurements in wide ranges of doping and temperature may serve as an indicator of CDW existence.

Disordered-based theory of pseudogap, superconducting gap, and Fermi arc of cuprates

A model for cuprate superconductors based on weakly coupled inhomogeneous electronic domains forming an array of Josephson junctions is studied. This approach provides physical insights to the most important properties of these materials like the pseudogap phase as forming by the onset of intradomains superconducting amplitudes and the zero resistivity critical temperature Tc due to phase coherence activated by Josephson coupling. The formation of the Fermi arcs and the dichotomy in k-space follow from the direction dependence of the junctions tunneling supercurrent and the quantum fluctuations of the d-wave order parameter symmetry on the CuO2 planes. This procedure reproduces the details of the cuprate Bi2212 phase diagram.

Impurity effects in quasiparticle spectrum of high-Tc superconductors (Review Article)

The revision is made of Green function methods that describe the dynamics of electronic quasiparticles in disordered superconducting systems with d-wave symmetry of order parameter. Various types of impurity perturbations are analyzed within the simplest T-matrix approximation. The extension of the common self-consistent T-matrix approximation (SCTMA) to the so-called group expansions in clusters of interacting impurity centers is discussed and hence the validity criteria for SCTMA are established. A special attention is paid to the formation of impurity resonance states and localized states near the characteristic points of energy spectrum, corresponding to nodal points on the Fermi surface.

Feasibility of a High Temperature Superconductor rf-SQUID Based on Biepitaxial Josephson Junction Technology

Recently, the observation of macroscopic quantum effects in high critical temperature superconductor (HTS) Josephson junctions (JJs) paved the way to the possible use of HTS in quantum hybrid circuits. Dissipation in HTS JJs has been proven to be below expectations, even in junction configurations designed to fully exploit the functionality of a d-wave order parameter symmetry, where low energy quasi-particles can be more harmful for coherence. We report on the design of YBaCuO rf-SQUIDs based on the properties of sub-micron biepitaxial junctions with variable inter face orientation with respect to the order parameters of the two electrodes. The study of the double well potential of such system may offer further insights for a deeper understanding of the dynamics of a HTS Josephson device. The rf-SQUID has been de signed to have independent controls for the barrier height between the wells and for the relative positions of the energy levels in different fluxoid wells. The flux state of the rf-SQUID is readout by an inductively coupled dc-SQUID magnetometer.

Tunneling spectroscopy of layered superconductors: intercalated Li0.48(C4H8O)xHfNCl and De-intercalated HfNCl0.7

Tunneling measurements have been carried out on layered superconductors of the β(SmSI)-type -L i0.48(THF)xHfNCl (THF = C4H8O) and HfNCl0.7 - by means of break-junction and scanning tunneling spectroscopy. Break-junction technique reveals Bardeen-Cooper-Schrieffer (BCS) - like gap structures with typical gap values of 2Δ(4. 2K ) =1 1 −12 meV for Li0.48(THF)xHfNCl with the highest Tc = 25.5 K. Some of our measurements revealed multiple gaps and dip-hump structures, the largest gap 2Δ (4.2 K) ≈ 17-20 meV closing at Tc. This was shown both by break-junction and scanning-tunneling spectroscopy. From these experiments it stems that the highest obtained gap ratio 2Δ/kBTc ∼ 8 substantially exceeds the BCS weak-coupling limiting values: ≈3.5 and ≈4.3 for s-wave and d-wave order parameter symmetry, respectively. Such large 2Δ/kBTc ratios are rather unusual for conventional superconductors but quite common to high-Tc cuprates, as well as to organic superconductors. Our studies allowed to collect much more evidence concerning the huge pairing energy in those materials and to investigate in detail the complexity of their superconducting gap spectra. An origin of the observed phenomena still remains to be clarified.

RSFQ Circuitry Using Intrinsic <formula formulatype="inline"> <tex>$\pi$</tex> </formula>-Phase Shifts

The latching of temporary data is essential in the rapid single flux quantum (RSFQ) electronics family. Its pulse-driven nature requires two or more stable states in almost all cells. Storage loops must be designed to have exactly two stable states for binary data representation. In conventional RSFQ such loops are constructed to have two stable states, e.g. by using asymmetric bias currents. This bistability naturally occurs when phase-shifting elements are included in the circuitry, such as π-Josephson junctions or a π-phase shift associated with an unconventional (d-wave) order parameter symmetry. Both approaches can be treated completely analogously, giving the same results. We have demonstrated for the first time the correct operation of a logic circuit, a toggle-flip-flop, using rings with an intrinsic π-phase shift (π-rings) based on hybrid high-Tc to low-Tc Josephson junctions. Because of their natural bistability these π-rings improve the device symmetry, enhance operation margins and alleviate the need for bias current lines.

Macroscopic Quantum Phenomena in High Critical Temperature Superconducting Josephson Junctions

YBa2Cu3O7−δ grain boundary bi-epitaxial Josepshon junctions (JJs) allow a very clear demonstration of Josephson current variation with the misorientation angle, consistent with the d-wave symmetry of the superconducting order parameter in cuprate, high temperature superconductors. Our bi-epitaxial junctions show a strong suppression of the first harmonic, I1 sin o, of the current phase relation when tunneling from a lobe into a node of the superconducting gap function. In these configurations, the contribution of the second harmonic, I2 sin 2o, becomes of the same magnitude as the first one, giving rise to a characteristic two-well Josephson potential as a function of phase o instead of the usual single well. This characteristic intrinsic property has suggested proposals of a new class of qu-bit named “quiet” because of the existence a spontaneously degenerate fundamental state without the need of applying an external field. Our experiments probe the macroscopic quantum properties in a d-wave Josephson junction by measuring macroscopic quantum tunneling and energy level quantization. The switching current out of the zero voltage state is measured as a function of temperature down to 20 mK. The temperature variation of the width of an ensemble of switching events goes over from one, which is characteristic of a thermal activation of phase fluctuations to a temperature independent width which is a token of quantum tunneling of the phase. The transition regime is affected by the two-well potential in a 45∘ misorientation junction as the second harmonic term gives rise to additional thermal transitions. The difference between quantized energy levels in the harmonic potential was determined by microwave spectroscopy. From the broadening of energy levels, it was possible to extract a Q-value of about 40 for the phase oscillations. The relatively high Q indicates quantum coherence over a sizeable time in d-wave junctions and gives hopes for a realization of a “quiet” high-Tc qu-bit. The contributions of V. L. Ginzburg to several different fields of physics are impressive and long standing. In superconductivity the Ginzburg–Landau theory, for instance, still represents a very powerful approach to model a huge number of different physical systems. High Temperature Superconductors (HTS) have strongly influenced research of the last 20 years and their d-wave order parameter symmetry represents one of the most intriguing features from both the fundamental point of view and some types of innovative long-term applications.

Effect of gap suppression by superfluid current on the nonlinear microwave response ofd-wave superconductors

Recently several works have focused on the intrinsic nonlinear current in passive microwave filters as a tool for identifying d-wave order parameter symmetry in the high Tc cuprates. Evidence has been found for d-wave pairing in YBCO and further work has ensued. Most of the theoretical work has been limited to low temperature because it has not included the effect of the superfluid current on the energy gap. We find that this effect leads to important corrections above T~0.2Tc, while leaving the 1/T low temperature behavior intact. A twofold increase in the nonlinear coefficient at temperatures of order ~0.75 Tc is found, and as T->Tc the nonlinearity comes entirely from the effects of the superfluid current on the gap. Impurity scattering has been included and, in addition, signatures for the case of d+s-wave are presented.

Analysis of ground states of0−πlong Josephson junctions

We investigate analytically a long Josephson $0\ensuremath{-}\ensuremath{\pi}$ junction with several $0$ and $\ensuremath{\pi}$ facets which are comparable to the Josephson penetration length ${\ensuremath{\lambda}}_{J}.$ Such junctions can be fabricated exploiting (a) the d-wave order-parameter symmetry of cuprate superconductors; (b) the spacial oscillations of the order parameter in superconductor-insulator-ferromagnet-superconductor structures with different thicknesses of ferromagnetic layer to produce 0 or $\ensuremath{\pi}$ coupling; or (c) the structure of the corresponding sine-Gordon equations and substituting the phase $\ensuremath{\pi}$ discontinuities by the artificial current injectors. We investigate analytically the possible ground states in such a system and show that there is a critical facet length ${a}_{c},$ which separates the states with half-integer flux quanta (semifluxons) from the trivial ``flat phase state'' without magnetic flux. We analyze different branches of the bifurcation diagram, derive a system of transcendental equations which can be effectively solved to find the crossover distance ${a}_{c}$ (bifurcation point), and present the solutions for different number of facets and the edge facets length.

Paramagnetic effect inYBa2Cu3O7−xgrain-boundary junctions

A detailed investigation of the magnetic response of YBaCuO grain boundary Josephson junctions has been carried out using both radio-frequency measurements and Scanning SQUID Microscopy. In a nominally zero-field-cooled regime we observed a paramagnetic response at low external fields for 45 degree asymmetric grain boundaries. We argue that the observed phenomenology results from the d-wave order parameter symmetry and depends on Andreev bound states.

Hexagonal and square flux line lattices in CeCoIn5.

Using small-angle neutron scattering, we have imaged the magnetic flux line lattice (FLL) in the d-wave heavy-fermion superconductor CeCoIn5. At low fields we find a hexagonal FLL. Around 0.6 T this undergoes what is most likely a first-order transition to square symmetry, with the nearest neighbors oriented along the gap node directions. This orientation of the square FLL is consistent with theoretical predictions based on the d-wave order parameter symmetry.

Coexistence of Andreev bound states and Josephson current in YBa 2Cu 3O 7 break-junctions

To favour the ab-plane contribution to the tunneling current, we have used the break junction technique on highly epitaxial (dc sputtered) YBa 2Cu 3O 7 thin films, with T c≥ 91K and ΔT c≤ 0.5K. One particularly intriguing feature of the conductance spectra is the presence of a zero bias peak that can be related to the formation of Andreev bound states (ABS) in the quasi-particle density of states, according to recent models about the d-wave symmetry of the HTS order parameter. We report data in which the Josephson current and the ABS are observed simultaneously appearing as a narrow conductance peak at zero bias overimposed on a wider one. The Josephson current shows modulation in magnetic field, typical of inhomogeneous current distribution due to the fracture faceting.

Microwave surface impedance of high-quality YBa 2Cu 3O 7− x thin films

The parallel plate resonator method has been used for measuring high quality YBa 2Cu 3O 7− x (YBCO) thin films. The surface resistance and the real part of the conductivity show a non-monotonic behaviour with a broad peak around 45 K. The penetration depth and the real part of the conductivity vary linearly at low temperatures. The lowest penetration depth linear fitting has a slope value of 2.2 to 2.5 Å/K up to 20 K which is lower than previous measurements on YBCO single crystals. An interpretation of this smaller slope in terms of the generally accepted d-wave order parameter symmetry presents difficulties.

Penetration depth measurement in high quality thin films

The parallel plate resonator method has been used for measuring high quality \(\) (YBCO) thin films, which have low temperature residual losses comparable to those previously obtained in single crystals. The surface resistance and the real part of the conductivity show a non-monotonic behaviour with a broad peak around 45 K. The penetration depth and the real part of the conductivity vary linearly at low temperatures. The lowest penetration depth linear fitting has a slope value of \(\) to \(\) up to 20 K which is lower than previous measurements on YBCO single crystals. An interpretation of this smaller slope in terms of the generally accepted d-wave order parameter symmetry presents difficulties.

Effect of impurity scattering on a d + s wave superconductor: low temperature behavior of penetration depth

Currently there exist several experimental reports on high- T c oxides which favor d-wave order parameter symmetry. However, several others would support an s-wave gap. Recent measurements of the penetration depth in YBa 2 Cu 3 O 7 − δ single crystals show large differences in a and b directions in the basal plane, which implies that orthorhombicity due to the chains is not small. As an attempt to understand current experimental results we consider an order parameter with d + s wave symmetry, which can arise naturally as a deviation from d-wave due to the presence of orthorhombicity. We provide a detailed study of the characteristics of such an order parameter in the low temperature behavior of the penetration depth in the presence of non-magnetic impurity scattering. The results are discussed in comparison with d-wave and anisotropic s-wave cases.