Symmetry of the order parameter in the high-Tc superconductor YBa2Cu3O7- δ

Evidence for d-wave superconductivity of infinite-layer nickelates from low-energy electrodynamics

The discovery of superconductivity in infinite-layer nickelates established another category of unconventional superconductors that shares structural and electronic similarities with cuprates. However, key issues of the superconducting pairing symmetry, gap amplitude and superconducting fluctuations are yet to be addressed. Here we utilize static and ultrafast terahertz spectroscopy to address these. We demonstrate that the equilibrium terahertz conductivity and non-equilibrium terahertz responses of an optimally Sr-doped nickelate film (superconducting transition temperature of Tc = 17 K) are in line with the electrodynamics of d-wave superconductivity in the dirty limit. The gap-to-Tc ratio (2Δ/kBTc) is found to be 3.4, indicating that the superconductivity falls in the weak coupling regime. In addition, we observed substantial superconducting fluctuations near Tc that do not extend into the deep normal state as the optimally hole-doped cuprates do. Our results support a d-wave system that closely resembles the electron-doped cuprates.

Unequivocal Identification of Spin-Triplet and Spin-Singlet Superconductors with Upper Critical Field and Flux Quantization

Spin-triplet superconductors play central roles in Majorana physics and quantum computing but are difficult to identify. We show the methods of kink-point upper critical field and flux quantization in superconducting rings can unequivocally identify spin-singlet, spin-triplet in centrosymmetric superconductors, and singlet-triplet admixture in noncentrosymmetric superconductors, as realized in γ-BiPd, β-Bi_{2}Pd, and α-BiPd, respectively. Our findings are essential for identifying triplet superconductors and exploring their quantum properties.

Energy recovery linac based fully coherent light source

Energy recovery linac (ERL) holds great promise for generating high repetition-rate and high brightness electron beams. The application of ERL to drive a free-electron laser is currently limited by its low peak current. In this paper, we consider the combination of ERL with the recently proposed angular-dispersion induced microbunching technique to generate fully coherent radiation pulses with high average brightness and tunable pulse length. Start-to-end simulations have been performed based on a low energy ERL (600 MeV) for generating coherent EUV radiation pulses. The results indicate an average brightness over 10²⁵ phs/s/mm²/mrad²/0.1%BW and average power of about 100 W at 13.5 nm or 20 W with the spectral resolution of about 0.5 meV with the proposed technique. Further extension of the proposed scheme to shorter wavelength based on an ERL complex is also discussed.

Unveiling Nanoscale Compositional and Structural Heterogeneities of Highly Textured Mg0.7Ti0.3Hy Thin Films

Thin films often exhibit fascinating properties, but the understanding of the underlying mechanism behind such properties is not simple. This is partially because of the limited structural information available. The hurdle in obtaining such information is especially high for textured thin films such as Mg-rich Mg_xTi_1-x, a promising switchable smart coating material. Although these metastable thin films are seen as solid solution alloys by conventional crystallographic methods, their hydrogen-induced optical transition is hardly understood by a solid solution model. In this study, we collect atomic pair distribution function (PDF) data for a Mg_0.7Ti_0.3H_y thin film in situ on hydrogenation and successfully resolve TiH₂ clusters of an average size of 30 Å embedded in the Mg matrix. This supports the chemically segregated model previously proposed for this system. We also observe the emergence of a previously unknown intermediate face-centered tetragonal phase during hydrogenation of the Mg matrix. This phase appears between Mg and MgH₂ to reduce lattice mismatch, thereby preventing pulverization and facilitating rapid hydrogen uptake. This work may shed new light on the hydrogen-induced properties of Mg-rich Mg_xTi_1-x thin films.

Observation of half-quantum flux in the unconventional superconductor β-Bi2Pd

Magnetic flux quantization is one of the defining properties of a superconductor. We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting β-Bi₂Pd thin films. The half-quantum fluxoid manifests itself as a π phase shift in the quantum oscillation of the superconducting critical temperature. This result verifies unconventional superconductivity of β-Bi₂Pd and is consistent with a spin-triplet pairing symmetry. Our findings may have implications for flux quantum bits in the context of quantum computing.

Directly visualizing the sign change of d-wave superconducting gap in Bi2Sr2CaCu2O8+δ by phase-referenced quasiparticle interference

The superconducting state is formed by the condensation of Cooper pairs and protected by the superconducting gap. The pairing interaction between the two electrons of a Cooper pair determines the gap function. Thus, it is pivotal to detect the gap structure for understanding the mechanism of superconductivity. In cuprate superconductors, it has been well established that the gap may have a d-wave function. This gap function has an alternative sign change in the momentum space. It is however hard to visualize this sign change. Here we report the measurements of scanning tunneling spectroscopy in Bi2Sr2CaCu2O8+δ and conduct the analysis of phase-referenced quasiparticle interference (QPI). We see the seven basic scattering vectors that connect the octet ends of the banana-shaped contour of Fermi surface. The phase-referenced QPI clearly visualizes the sign change of the d-wave gap. Our results illustrate an effective way for determining the sign change of unconventional superconductors.

Two-leg ladder systems with dipole-dipole Fermion interactions

The ground-state phase diagram of a two-leg fermionic dipolar ladder with inter-site interactions is studied using density matrix renormalization group (DMRG) techniques. We use a state-of-the-art implementation of the DMRG algorithm and finite size scaling to simulate large system sizes with high accuracy. We also consider two different model systems and explore stable phases in half and quarter filling factors. We find that in the half filling, the charge and spin gaps emerge in a finite value of the dipole-dipole and on-site interactions. In the quarter filling case, s-wave superconducting state, charge density wave, homogenous insulating and phase separation phases occur depend on the interaction values. Moreover, in the dipole-dipole interaction, the D-Mott phase emerges when the hopping terms along the chain and rung are the same, whereas, this phase has been only proposed for the anisotropic Hubbard model. In the half filling case, on the other hand, there is either charge-density wave or charged Mott order phase depends on the orientation of the dipole moments of the particles with respect to the ladder geometry.

Analysing magnetism using scanning SQUID microscopy

Scanning superconducting quantum interference device microscopy (SSM) is a scanning probe technique that images local magnetic flux, which allows for mapping of magnetic fields with high field and spatial accuracy. Many studies involving SSM have been published in the last few decades, using SSM to make qualitative statements about magnetism. However, quantitative analysis using SSM has received less attention. In this work, we discuss several aspects of interpreting SSM images and methods to improve quantitative analysis. First, we analyse the spatial resolution and how it depends on several factors. Second, we discuss the analysis of SSM scans and the information obtained from the SSM data. Using simulations, we show how signals evolve as a function of changing scan height, SQUID loop size, magnetization strength, and orientation. We also investigated 2-dimensional autocorrelation analysis to extract information about the size, shape, and symmetry of magnetic features. Finally, we provide an outlook on possible future applications and improvements.

Double Helix Nodal Line Superconductor

Time-reversal invariant superconductors in three dimensions may contain nodal lines in the Brillouin zone, which behave as Wilson loops of 3D momentum-space Chern-Simons theory of the Berry connection. Here we study the conditions of realizing linked nodal lines (Wilson loops), which yield a topological contribution to the thermal magnetoelectric coefficient that is given by the Chern-Simons action. We find the essential conditions are the existence of torus or higher genus Fermi surfaces and spiral spin textures. We construct such a model with two torus Fermi surfaces, where a generic spin-dependent interaction leads to double-helix-like linked nodal lines as the superconductivity is developed.

Optical studies of high-temperature superconducting cuprates

The optical studies of high-temperature superconducting cuprates (HTSC) are reviewed. From the doping dependence of room temperature spectra, a dramatic change of the electronic state from a Mott (charge transfer) insulator to a Fermi liquid has been revealed. Additionally, the unusual 2D nature of the electronic state has been found. The temperature dependence of the optical spectra provided a rich source of information on the pseudogap, superconducting gap, Josephson plasmon, transverse Josephson plasma mode and precursory superconductivity. Among these issues, Josephson plasmons and transverse Josephson plasma mode were experimentally discovered by optical measurements, and thus are unique to HTSC. The effect of the spin/charge stripe order is also unique to HTSC, reflecting the conducting nature of the stripe order in this system. The pair-breaking due to the stripe order seems stronger in the out-of-plane direction than in the in-plane one.

Theoretical approach to resonant inelastic x-ray scattering in iron-based superconductors at the energy scale of the superconducting gap

We develop a phenomenological theory to predict the characteristic features of the momentum-dependent scattering amplitude in resonant inelastic x-ray scattering (RIXS) at the energy scale of the superconducting gap in iron-based super-conductors. Taking into account all relevant orbital states as well as their specific content along the Fermi surface we evaluate the charge and spin dynamical structure factors for the compounds LaOFeAs and LiFeAs, based on tight-binding models which are fully consistent with recent angle-resolved photoemission spectroscopy (ARPES) data. We find a characteristic intensity redistribution between charge and spin dynamical structure factors which discriminates between sign-reversing and sign-preserving quasiparticle excitations. Consequently, our results show that RIXS spectra can distinguish between s± and s++ wave gap functions in the singlet pairing case. In addition, we find that an analogous intensity redistribution at small momenta can reveal the presence of a chiral p-wave triplet pairing.

Chiral superconductors

Chiral superconductivity is a striking quantum phenomenon in which an unconventional superconductor spontaneously develops an angular momentum and lowers its free energy by eliminating nodes in the gap. It is a topologically non-trivial state and, as such, exhibits distinctive topological modes at surfaces and defects. In this paper we discuss the current theory and experimental results on chiral superconductors, focusing on two of the best-studied systems, Sr2RuO4, which is thought to be a chiral triplet p-wave superconductor, and UPt3, which has two low-temperature superconducting phases (in zero magnetic field), the lower of which is believed to be chiral triplet f-wave. Other systems that may exhibit chiral superconductivity are also discussed. Key signatures of chiral superconductivity are surface currents and chiral Majorana modes, Majorana states in vortex cores, and the possibility of half-flux quantum vortices in the case of triplet pairing. Experimental evidence for chiral superconductivity from μSR, NMR, strain, polar Kerr effect and Josephson tunneling experiments are discussed.

ARPES measurements of the superconducting gap of Fe-based superconductors and their implications to the pairing mechanism

Its direct momentum sensitivity confers to angle-resolved photoemission spectroscopy (ARPES) a unique perspective in investigating the superconducting gap of multi-band systems. In this review we discuss ARPES studies on the superconducting gap of high-temperature Fe-based superconductors. We show that while Fermi-surface-driven pairing mechanisms fail to provide a universal scheme for the Fe-based superconductors, theoretical approaches based on short-range interactions lead to a more robust and universal description of superconductivity in these materials. Our findings are also discussed in the broader context of unconventional superconductivity.

The diamond superconducting quantum interference device

Diamond is an electrical insulator in its natural form. However, when doped with boron above a critical level (∼0.25 atom %) it can be rendered superconducting at low temperatures with high critical fields. Here we present the realization of a micrometer-scale superconducting quantum interference device (μ-SQUID) made from nanocrystalline boron-doped diamond (BDD) films. Our results demonstrate that μ-SQUIDs made from superconducting diamond can be operated in magnetic fields as large as 4 T independent of the field direction. This is a decisive step toward the detection of quantum motion in a diamond-based nanomechanical oscillator.

Interplay between static and dynamic properties of semifluxons in YBa2Cu3O(7-delta) 0-pi Josephson junctions

We have investigated the static and dynamic properties of long YBa2Cu3O(7-delta) 0-pi Josephson junctions and compared them with those of conventional 0 junctions. Scanning SQUID microscope imaging has revealed the presence of a semifluxon at the phase discontinuity point in 0-pi Josephson junctions. Zero field steps have been detected in the current-voltage characteristics of all junctions. Comparison with simulation allows us to attribute these steps to fluxons traveling in the junction for conventional 0 junctions and to fluxon-semifluxon interactions in the case of 0-pi Josephson junctions.

A tunneling spectroscopy study of the pairing symmetry in the electron-doped Pr(1-x)LaCe(x)CuO(4-y)

We have performed scanning tunneling spectroscopy and point contact spectroscopy measurements on the electron-doped superconductor Pr(1-x)LaCe(x)CuO(4-y) (x = 0.12, T(c) is approximately equal 25 K). We address the question of the symmetry of the order parameter and of the amplitude of the energy gap. We compare three possible scenarios, i.e. isotropic s-wave, 'anisotropic' s-wave, and d-wave. Evidence for a d-wave symmetry of the order parameter is given. From the temperature evolution of the dI/dV versus V characteristics we extract a BCS-like temperature dependence of the superconducting energy gap Δ. Despite the variety of measured spectra we give a consistent explanation for the whole set of data, indicating Δ = (3.6 ± 0.2) meV and a ratio 2Δ/K(B)T(C) is approximately equal 3.5 ±0.2. In particular, point contact characteristics showing gap-like features at higher voltages have been interpreted by considering the formation of an intergrain Josephson junction in series with the point contact junction. Further confirmation of the correctness of the model is given by the behavior of the critical current of the intergrain Josephson junction versus temperature which follows the Ambegaokar-Baratoff behavior.

A high resolution magneto-optical system for imaging of individual magnetic flux quanta

A high-resolution magneto-optical imaging system is described. In this system magneto-optical Kerr effect is utilized for resolving individual flux quanta in a type II superconductor. Using an ultra thin EuSe indicator a spatial resolution of 0.8 microm is achieved.

Imaging of order parameter induced pi phase shifts in cuprate superconductors by low-temperature scanning electron microscopy

Low-temperature scanning electron microscopy (LTSEM) has been used to image the supercurrent distribution in ramp-type Josephson junctions between Nb and either the electron-doped cuprate Nd_{2-x}Ce_{x}CuO_{4-y} or the hole-doped cuprate YBa_{2}Cu_{3}O_{7}. For zigzag-shaped devices in the short junction limit the critical current is strongly suppressed at zero applied magnetic field. The LTSEM images show that this is due to the Josephson current counterflow in neighboring 0 and pi facets, which is induced by the d_{x;{2}-y;{2}} order parameter in the cuprates. Thus, LTSEM provides imaging of the sign change of the superconducting order parameter, which can also be applied to other types of Josephson junctions.

An integrated superconductive magnetic nanosensor for high-sensitivity nanoscale applications

An integrated magnetic nanosensor based on a niobium dc SQUID (superconducting quantum interference device) for nanoscale applications is presented. The sensor, having a washer shape with a hole of 200 nm and two Josephson-Dayem nanobridges of 80 nm × 100 nm, consists of a Nb(30 nm)/Al(30 nm) bilayer patterned by electron beam lithography (EBL) and shaped by lift-off and reactive ion etch (RIE) processes. The presence of the niobium coils, integrated on-chip and tightly coupled to the SQUID, allows us to easily excite the sensor in order to get the voltage-flux characteristics and to flux bias the SQUID at its optimal point. The measurements were performed at liquid helium temperature. A voltage swing of 75 µV and a maximum voltage-flux transfer coefficient (responsivity) as high as 1 mV/Φ(0) were directly measured from the voltage-flux characteristic. The noise measurements were performed in open loop mode, biasing the SQUID with a dc magnetic flux at its maximum responsivity point and using direct-coupled low-noise readout electronics. A white magnetic flux noise spectral density as low as 2.5 μΦ(0) Hz(-1/2) was achieved, corresponding to a magnetization or spin sensitivity in units of the Bohr magneton of 100 spin Hz(-1/2). Possible applications of this nanosensor can be envisaged in magnetic detection of nanoparticles and small clusters of atoms and molecules, in the measurement of nanoobject magnetization, and in quantum computing.

Nuclear magnetic resonance study of the electron-doped high-temperature superconducting cuprates

Nuclear magnetic resonance (NMR) measurements have been made on two of the electron-doped high-temperature superconducting cuprates (HTSCs), Pr(2-x)Ce(x)CuO(4) and Sr(0.9)La(0.1)CuO(2) that represent the two known electron-doped structures. The results are compared with the more-studied hole-doped HTSCs. We show that the electron and hole-doped HTSCs probe a similar antiferromagnetic spin fluctuation spectrum in the normal state, which provides support for theories of superconductivity where the pairing is mediated by antiferromagnetic spin fluctuations and the superconducting order parameter has a [Formula: see text] symmetry. Contrary to results from underdoped and hole-doped HTSCs, there is no evidence for a normal-state pseudogap in the NMR data from measurements on the electron-doped HTSCs. Therefore, the electron-doped HTSCs can be better compared with overdoped and hole-doped HTSCs where the normal-state pseudogap is absent. The antiferromagnetic spin fluctuation spectrum as probed by the Cu spin-lattice relaxation rate, is independent of the doped electrons per Cu. A similar effect is observed in the overdoped and hole-doped HTSC, Y(1-x)Ca(x)Ba(2)Cu(3)O(7-delta) for a hole concentration range of approximately 0.063. The anomalous Cu NMR linewidth anisotropy observed in the electron-doped HTSCs suggests a small and static spin variation for temperatures up to room temperature.

Spontaneous supercurrent induced by ferromagnetic pi junctions

We present magnetization measurements of mesoscopic superconducting niobium loops containing a ferromagnetic (PdNi) pi junction. The loops are prepared on top of the active area of a micro-Hall sensor based on high mobility GaAs/AlGaAs heterostructures. We observe asymmetric switching of the loop between different magnetization states when reversing the sweep direction of the magnetic field. This provides evidence for a spontaneous current induced by the intrinsic phase shift of the pi junction. In addition, the presence of the spontaneous current near zero applied field is directly revealed by an increase of the magnetic moment with decreasing temperature, which results in half integer flux quantization in the loop at low temperatures.

d-Wave-induced Josephson current counterflow in YBa2Cu3O7/Nb zigzag junctions

Well-defined zigzag-shaped ramp-type Josephson junctions between YBa2Cu3O7 and Nb have been studied. The magnetic field dependencies of the critical currents provide evidence for d-wave--induced alternations in the direction of the Josephson current between neighboring sides of the zigzag structure. The arrays present controllable model systems to study the influences of pi facets in high-angle high- T(c) grain boundaries. From the characteristics, we estimate a possible imaginary s-wave admixture to the order parameter of the YBa2Cu3O7 to be below 1%.

Phase-sensitive evidence for d-wave pairing symmetry in electron-doped cuprate superconductors

We present phase-sensitive evidence that the electron-doped cuprates Nd(1.85)Ce(0.15)CuO(4-y) (NCCO) and Pr(1.85)Ce(0.15)CuO(4-y) (PCCO) have d-wave pairing symmetry. This evidence was obtained by observing the half-flux quantum effect, using a scanning SQUID microscope, in c-axis-oriented films of NCCO or PCCO epitaxially grown on tricrystal [100] SrTiO3 substrates designed to be frustrated for a d(x(2)-y(2)) order parameter. Samples with two other configurations, designed to be unfrustrated for a d-wave superconductor, do not show the half-flux quantum effect.

Observation of spontaneous flux generation in a multi-josephson-junction loop

We describe observations of spontaneous flux generation inside a YBa(2)Cu(3)O(7-delta) loop made of 214 Josephson junctions in series. The flux is generated spontaneously during cooldown into the superconducting state. The experiment is motivated by the Kibble-Zurek scenario of formation of topological defects in condensed matter systems. The transition from decoupled superconducting segments into a coherent loop is determined by the strength of thermal fluctuations in the junctions. Values of the flux measured at the end of each cooldown follow a normal distribution, and are consistent with the instantaneous phase differences across the junctions adding up as the loop becomes coherent.

Temperature Dependence of the Half-Integer Magnetic Flux Quantum

The temperature dependence of the half-integer magnetic flux quantum effect in thin-film tricrystal samples of the high-critical-temperature cuprate superconductor YBa(2)Cu(3)O(7-delta) was measured and found to persist from a temperature of 0.5 kelvin through a critical temperature of about 90 kelvin, with no change in total flux. This result implies that d-wave symmetry pairing predominates in this cuprate, with a small component of time-reversal symmetry breaking, if any, over the entire temperature range.

SCANNING SQUID MICROSCOPY

▪ Abstract  The scanning SQUID microscope (SSM) is a powerful tool for imaging magnetic fields above sample surfaces. It has the advantage of high sensitivity and bandwidth and the disadvantages of relatively modest spatial resolution and the requirement of a cooled SQUID sensor. We describe the various implementations of this type of instrument and discuss a number of applications, including magnetic imaging of short circuits in integrated circuits, corrosion currents in aluminum, and trapped flux in superconductors.