Local Superconducting Research Articles

Phase fluctuations in two-dimensional superconductors and pseudogap phenomenon

We study the phase fluctuations in the normal state of generic two-dimensional superconducting systems with $s$-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the two-dimensional Berezinskii-Kosterlitz-Thouless transition lead to a significant broadening of the single-particle spectrum, giving birth to the pseudogap phenomenon. Quantitatively, the broadening of spectral weights near the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the fermionic attractive-$U$ Hubbard model on the square lattice, using the unbiased determinant quantum Monte Carlo method and stochastic analytic continuation.

Scanning tunneling microscopy and spectroscopy characterization of Nb films for quantum applications

Niobium thin films are key components of superconducting microwave resonators. Interest in these devices has increased dramatically because of their application in quantum systems. Despite tremendous effort to improve their performance, loss mechanisms are still not well understood. Nb/substrate and Nb/air interfaces are likely culprits in contributing to decoherence and ultimately limiting the performance of superconducting devices. Here, we investigate the Nb/substrate interface by studying the effect of hydrogen-passivated H:Si(111) substrates on the local superconducting properties of ∼40 nm thick Nb films compared to Nb films grown on typical Si(001) substrates. Specifically, low-temperature scanning tunneling microscopy and spectroscopy are employed to compare nanoscale material properties. The atomically flat monohydride H:Si(111) substrates are found to yield a smoother and less defective interface with the Nb film. Correspondingly, the Nb films grown on H:Si(111) substrates present more uniform superconducting properties and exhibit less quasiparticle broadening.

Controlling Andreev Bound States with the Magnetic Vector Potential.

Tunneling spectroscopy measurements are often used to probe the energy spectrum of Andreev bound states (ABSs) in semiconductor-superconductor hybrids. Recently, this spectroscopy technique has been incorporated into planar Josephson junctions (JJs) formed in two-dimensional electron gases, a potential platform to engineer phase-controlled topological superconductivity. Here, we perform ABS spectroscopy at the two ends of planar JJs and study the effects of the magnetic vector potential on the ABS spectrum. We show that the local superconducting phase difference arising from the vector potential is equal in magnitude and opposite in sign at the two ends, in agreement with a model that assumes localized ABSs near the tunnel barriers. Complemented with microscopic simulations, our experiments demonstrate that the local phase difference can be used to estimate the relative position of localized ABSs separated by a few hundred nanometers.

Distribution of the order parameter in strongly disordered superconductors: An analytic theory

We developed an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to superconducting-insulator transition. Single-electron eigenstates are assumed to be Anderson-localized, with a large localization volume. Superconductivity develops due to coherent delocalization of originally localized pre-formed Cooper pairs. The key assumption of the theory is that each such pair is coupled to a large number $Z\gg1$ of similar neighboring pairs. We derived integral equations for the probability distribution $P\left(\Delta\right)$ of local superconducting order parameter $\Delta\left(\boldsymbol{r}\right)$ and analyzed their solutions in the limit of small dimensionless Cooper coupling constant $\lambda\ll1$. The shape of the order-parameter distribution is found to depend crucially upon the effective number of nearest neighbors $Z_{\text{eff}}=2\nu_{0}\Delta_{0}Z$. The solution we provide is valid both at large and small $Z_{\text{eff}}$; the latter case is nontrivial as the function $P\left(\Delta\right)$ is heavily non-Gaussian. The discovery of a broad parameter range where the distribution function $P\left(\Delta\right)$ is non-Gaussian but also non-critical (in the sense of SIT criticality) is one of our key findings. The analytic results are supplemented by numerical data, and good agreement between them is observed.

The influence of CeO2 addition on microstructure and superconducting properties of GdBCO-Ag single grain bulk superconductors

Bulk single-grain GdBCO superconductors (nominal composition 1 mol GdBa2Cu3O7-δ + ½ mol Gd2BaCuO5 + 20 wt% Ag2O + Z wt% CeO2 (Z = 0.4, 1.0, 1.6) grown using the top-seeded melt-grow process are studied by differential thermal analysis, X-ray diffraction, scanning electron microscopy and magnetic measurement of local superconducting properties. The amount of CeO2 added is shown to have a significant effect on thermal behaviour, phase composition, microstructure and local superconducting properties. The observed behaviour is explained by the dissolution of Ce in the melt L' formed by monotectic melting of the samples. Ce dissolved in melt L' reduces the substitution of Ba by Gd in the Gd123 crystal lattice. This effect causes an increase in the superconducting transition temperature Tc with added CeO2, an increase in Tc with distance from the seed and influences the critical current density by chemical pinning. The obtained results open a new effective way to improve the superconducting properties of LREBCO bulk single-grain superconductors grown in air.

Nanoscale Superconducting States in the Fe-Based Filamentary Superconductor of Pr-Doped CaFe2As2.

The low-temperature scanning tunneling microscope and spectroscopy (STM/STS) are used to visualize superconducting states in the cleaved single crystal of 9% praseodymium-doped CaFe2As2 (Pr-Ca122) with Tc ≈ 30 K. The spectroscopy shows strong spatial variations in the density of states (DOS), and the superconducting map constructed from spectroscopy discloses a localized superconducting phase, as small as a single unit cell. The comparison of the spectra taken at 4.2 K and 22 K (below vs. close to the bulk superconducting transition temperature) from the exact same area confirms the superconducting behavior. Nanoscale superconducting states have been found near Pr dopants, which can be identified using dI/dV conductance maps at +300 mV. There is no correlation of the local superconductivity to the surface reconstruction domain and surface defects, which reflects its intrinsic bulk behavior. We, therefore, suggest that the local strain of Pr dopants is competing with defects induced local magnetic moments; this competition is responsible for the local superconducting states observed in this Fe-based filamentary superconductor.

Analysis of magnetic vortex dissipation in Sn-segregated boundaries in Nb3Sn superconducting RF cavities

We study mechanisms of vortex nucleation in ${\mathrm{Nb}}_{3}\mathrm{Sn}$ superconducting RF (SRF) cavities using a combination of experimental, theoretical, and computational methods. Scanning transmission electron microscopy imaging and energy dispersive spectroscopy of some ${\mathrm{Nb}}_{3}\mathrm{Sn}$ cavities show Sn segregation at grain boundaries in ${\mathrm{Nb}}_{3}\mathrm{Sn}$ with Sn concentration as high as $\ensuremath{\sim}35$ at. % and widths $\ensuremath{\sim}3$ nm in chemical composition. Using ab initio calculations, we estimate the effect excess tin has on the local superconducting properties of the material. We model Sn segregation as a lowering of the local critical temperature. We then use time-dependent Ginzburg-Landau theory to understand the role of segregation on magnetic vortex nucleation. Our simulations indicate that the grain boundaries act as both nucleation sites for vortex penetration and pinning sites for vortices after nucleation. Depending on the magnitude of the applied field, vortices may remain pinned in the grain boundary or penetrate the grain itself. We estimate the superconducting losses due to vortices filling grain boundaries and compare with observed performance degradation with higher magnetic fields. We estimate that the quality factor may decrease by an order of magnitude $({10}^{10} \mathrm{to} {10}^{9})$ at typical operating fields if 0.03% of the grain boundaries actively nucleate vortices. We additionally estimate the volume that would need to be filled with vortices to match experimental observations of cavity heating.

Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems

We study the superconducting proximity effect in inhomogeneous systems in which a disordered or quasicrystalline normal-state wire is connected to a BCS superconductor. We self-consistently compute the local superconducting order parameters in the real space Bogoliubov-de Gennes framework for three cases, namely, when states are i) extended, ii) localized or iii) critical. The results show that the spatial decay of the superconducting order parameter as one moves away from the normal-superconductor interface is power law in cases i) and iii), stretched exponential in case ii). In the quasicrystalline case, we observe self-similarity in the spatial modulation of the proximity-induced superconducting order parameter. To characterize fluctuations, which are large in these systems, we study the distribution functions of the order parameter at the center of the normal region. These are Gaussian functions of the variable (case i) or of its logarithm (cases ii and iii). We give arguments to explain the characteristics of the distributions and their scaling with system size for each of the three cases.

A framework for the description of charge order, pseudo and superconducting gap, critical temperature and pairing interaction in cuprate superconductors

A unified phenomenological description framework is proposed for the evaluation of some of the most important observables of the cuprate superconductors: the pseudogap (PG) ΔPG, the local superconducting amplitudes ΔSC(ri), the critical temperature Tc and charge ordering (CO) parameters. Recent detailed measurements of CO structures and CO wavelengths λCO are faithfully reproduced by solutions of a Cahn–Hilliard differential equation with a free energy potential VGL that produces alternating small charge modulations. The charge oscillations induce atomic fluctuations that mediate the SC pair interaction proportional to the VGL amplitude. The local SC amplitude and phase θi are connected by Josephson coupling EJ(rij) and the SC long-range order transition occurs when . The calculated results of the wavelength λCO, ΔPG, and Tc calculations are in good agreement with a variety of experiments.

Inhomogeneity of SmBCO bulk superconductors grown in air

The local superconducting properties and microstructure of SmBCO bulk single-grain superconductors with the addition of different quantities of BaO2 were studied. The single-grain bulk SmBCO superconductors were fabricated via the top-seeded melt growth process in air. Increasing transition temperature, critical current density and the narrowing superconducting transition width were observed with BaO2 addition. It was shown that the transition temperature and critical current density depend on the distance from the seed. Microstructural analysis showed that the reaction of Ba with the supporting ZrO2 bars is responsible for the gradient of Ba concentration in the peritectic melt, and consequent changes in Sm/Ba substitution in the Sm123 crystal lattice lead to the inhomogeneity of local superconducting properties.

Two-particle spectral function for disordered s -wave superconductors: Local maps and collective modes

We make the first testable predictions for the local two-particle spectral function of a disordered s-wave superconductor, probed by scanning Josephson spectroscopy (sjs), providing complementary information to scanning tunneling spectroscopy (sts). We show that sjs provides a direct map of the local superconducting order parameter that is found to be anticorrelated with the gap map obtained by sts. Furthermore, this anticorrelation increases with disorder. For the momentum resolved spectral function, we find the Higgs mode shows a non-dispersive subgap feature at low momenta, spectrally separated from phase modes, for all disorder strengths. The amplitude-phase mixing remains small at low momenta even when disorder is large. Remarkably, even for large disorder and high momenta, the amplitude-phase mixing oscillates rapidly in frequency and hence do not affect significantly the purity of the Higgs and phase dominated response functions.

Local superconductivity in vanadium iron arsenide

We investigate the chemical substitution of group 5 into BaFe2As2 (122) iron arsenide, in the effort to understand why Fe-site hole doping of this compound (e.g., using group 5 or 6) does not yield bulk superconductivity. We find an increase in c-lattice parameter of the BaFe2As2 with the substitution of V, Nb, or Ta; the reduction in c predicts the lack of bulk superconductivity [1] that is confirmed here through transport and magnetization results. However, our spectroscopy measurements find a coexistence of antiferromagnetic and local superconducting nanoscale regions in V-122, observed for the first time in a transition-metal hole-doped iron arsenide. In BaFe2As2, there is a complex connection between local parameters such as composition and lattice strain, average lattice details, and the emergence of bulk quantum states such as superconductivity and magnetism. [1] L. M. N. Konzen, and A. S. Sefat, J. Phys.: Condens. Matter 29 (2017), 083001.

Influence of crystalline structure on rf dissipation in superconducting niobium

Bulk niobium is the most common material used in the fabrication of rf superconducting cavities for accelerators. Predicting and reducing the rf surface dissipation in these cavity structures is mandatory, since it has a tremendous cost impact on the large accelerator projects. In this paper the author hopes to demonstrate that sources of dissipation usually attributed to external causes (mainly flux trapping during cooldown and hydrides precipitates) are related to the same type of crystalline defects that affect the local superconducting properties and can be at the source of early vortex penetration at the surface. We also want to show how these types of defects can explain some of the discrepancies observed from other laboratories in niobium cavity doping experiments. Understanding the origin and the role of these defects could provide direction for improving material specifications as well as improving fabrication control from sheet material to completed cavity. In particular, we will demonstrate that dislocation entanglements, due to the fabrication damage layer, have the strongest impact for the pinning behavior of trapped flux, as well as hydrogen segregation in cavity niobium. The author wishes to present to the superconducting radio frequency (SRF) accelerator community the synthesis of experimental results scattered in the literature, completed with some personal results. The results of this effort provide a new perspective on recently published work in the domain of SRF cavity doping and sensitivity to trapped flux during cooldown. I will also try to draw whenever possible, some conclusions about other types of superconductors used for SRF applications including $\mathrm{Nb}/\mathrm{Cu}$ thin films and to discuss their possible change of behavior with field or frequency. I will concentrate on surface and material science aspects since the experimental results on rf cavities have already been treated elsewhere.

Investigation of Dayem Bridge NanoSQUIDs Made by Xe Focused Ion Beam

Superconducting QUantum Interference Devices (SQUIDs) based on nanobridge junctions have shown increasing promise for single particle detection. This paper describes the development of the fabrication of improved and reproducible nanobridge junctions fabricated by focused ion beam (FIB) milling from niobium thin films. Although the very low noise properties of nanobridge SQUIDs are well known, the nature of the milling process is little understood at the level of local superconducting properties. In this paper, we report the results for nanobridge Josephson devices and SQUIDs, which we believe are the first to be made by Xenon (Xe) FIB milling. Temperature-dependent current–voltage behavior, microwave-induced Shapiro steps, and SQUID response to magnetic fields have been measured. We make preliminary comparisons with nominally identical devices milled from Nb thin films using either Xe or Ga ions.

Spiral magnetic order and topological superconductivity in a chain of magnetic adatoms on a two-dimensional superconductor

We study the magnetic and electronic phases of a 1D magnetic adatom chain on a 2D superconductor. In particular, we confirm the existence of a `self-organized' 1D topologically non-trivial superconducting phase within the set of subgap Yu-Shiba-Rusinov (YSR) states formed along the magnetic chain. This phase is stabilized by incommensurate spiral correlations within the magnetic chain that arise from the competition between short-range ferromagnetic and long-range antiferromagnetic electron-induced exchange interactions, similar to a recent study for a 3D superconductor [M. Schecter et al. Phys. Rev. B 93, 140503(R) 2016]. The exchange interaction along diagonal directions are also considered and found to display behavior similar to a 1D substrate when close to half filling. We show that the topological phase diagram is robust against local superconducting order parameter suppression and weak substrate spin-orbit coupling. Lastly, we study the effect of a direct ferromagnetic exchange coupling between the adatoms, and find the region of spiral order in the phase diagram to be significantly enlarged in a wide range of the direct exchange coupling.

Low-field magnetoresponse of strongly disordered two-dimensional superconductors

We show that inhomogeneities in the spatial distribution of Cooper pairs and in the phase of the local superconducting order parameter in the vicinity of a superconductor-normal state transition (SNT) in two dimensions can be highly sensitive to a perpendicular magnetic field. We focus on the role of orbital effects in the field-dependence of local superfluid stiffness and superconducting phase disorder in homogeneously-disordered two-dimensional superconductor thin films. The relative importance of these orbital effects is analyzed in different physical regimes dominated by Coulomb blockade, thermal phase fluctuations and Aharanov-Bohm phase disorder respectively. Following this approach, we obtain explicit expressions for the field dependence of magnetoresistance and superfluid stiffness near the SNT, and attempt an understanding of some recent experimental findings.

Analysis of the local superconducting properties in YBCO coated conductors with striations

In order to realize economical applications, it is important to reduce the ac loss of 2G high-temperature superconductor coated conductors. It seems to be reasonable that a multi-filamentary wire can decrease the magnetization loss. In this study, we prepared two samples of YBCO coated conductors with striations. We measured local superconducting properties of both samples by using Low Temperature Scanning Laser and Hall Probe Microscopy (LTSLHPM). The distribution of the local critical temperature of samples was analyzed from experimental results of Low Temperature Scanning Laser Microscopy (LTSLM) near the superconducting transition temperature. According to LTSLM results, spatial distributions of the local critical temperature of both samples are homogeneous. The local current density and the local magnetization in samples were explored from measuring stray fields by using Scanning Hall Probe Microscopy (SHPM). From SHPM results, the remanent field pattern of the one bridge sample in an external magnetic field confirms the Bean's critical state model and the three bridge sample has similar remanent field pattern of the one bridge sample. The local magnetization curve in the three bridge sample was measured from external fields from -500 Oe to 500 Oe. We visualized that the distribution of local hysteresis loss are related in the distribution of the remanent field of the three bridge sample. Although the field dependence of the critical current density must be taken into account, the relation of the local hysteresis loss and the remanent field from Bean's model was useful.

Scanning SQUID microscopy of local superconductivity in inhomogeneous combinatorial ceramics.

Although combinatorial solid-state chemistry promises to be an efficient way to search for new superconducting compounds, the problem of determining which compositions are strongly diamagnetic in a mixed-phase sample is challenging. By means of reactions in a system of randomly mixed starting components (Ca, Sr, Ba, La, Y, Pb, Bi, Tl, and Cu oxides), samples were produced that showed an onset of diamagnetic response above 115 K in bulk measurements. Imaging of this diamagnetic response in ceramic samples by scanning SQUID microscopy (SSM) revealed local superconducting areas with sizes down to as small as the spatial resolution of a few micrometers. In addition, locally formed superconducting matter was extracted from mixed-phase samples by magnetic separation. The analysis of single grains (d<80 μm) by X-ray diffraction, elemental analysis, and bulk SQUID measurements allowed Tl2Ca3Ba2Cu4O12, TlCaBaSrCu2O(7-δ), BaPb(0.5)Bi(0.25)Tl(0.25)O(3-δ), TlBa2Ca2Cu3O9, Tl2Ba2CaCu2O8, and YBa2Cu3O7 phases to be identified. SSM, in combination with other diagnostic techniques, is therefore shown to be a useful instrument to analyze inhomogeneous reaction products in the solid-state chemistry of materials showing magnetic properties.

Multiple-gap structure in electric-field-induced surface superconductivity

Local superconducting gap structure is studied as a function of nanoscale depth in electric-field-induced surface superconductivity such as in $\mathrm{SrT}\phantom{\rule{0.5pt}{0ex}}{\mathrm{iO}}_{3}$. We examine solutions of the Bogoliubov--de Gennes equation in two limiting confinement potential cases of an electric field with and without screening effects. As unique properties different from bulk superconductivity, there appear in-gap states even for isotropic $s$-wave pairing, due to the multiple-gap structure of sub-band-dependent surface superconductivity. These determine the depth dependence of local superconductivity.

Describing How the Superconducting Transition in La2CuO4+y Is Related to the i-O Phase Separation

The phase separation of oxygen interstitial in the spacer layers separating the CuO2 planes in the high critical temperature superconductor La2CuO4+y was studied by Poccia et al. (Nat. Mater. 10:733, 2011). We model this transition by the electronic charge in the planes that can be described by the Cahn–Hilliard theory, with the formation of clusters of low and high densities separated by potential barriers. The charge diffusion into bound regions minimizes the energy and favors the formation of Cooper pairs. Self-consistent calculations yield local dependent superconducting amplitudes Δsc(r), and the resistivity transition at Tc is driven by Josephson coupling among these nanoscale clusters.