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At least 703 records · Page 39

The Cosmic Ultraviolet Baryon Survey (CUBS) – III. Physical properties and elemental abundances of Lyman-limit systems at z < 1

ABSTRACT We present a systematic investigation of physical conditions and elemental abundances in four optically thick Lyman-limit systems (LLSs) at z = 0.36–0.6 discovered within the Cosmic Ultraviolet Baryon Survey (CUBS). Because intervening LLSs at z < 1 suppress far-UV (ultraviolet) light from background QSOs, an unbiased search of these absorbers requires a near-UV-selected QSO sample, as achieved by CUBS. CUBS LLSs exhibit multicomponent kinematic structure and a complex mix of multiphase gas, with associated metal transitions from multiple ionization states such as C ii, C iii, N iii, Mg ii, Si ii, Si iii, O ii, O iii, O vi, and Fe ii absorption that span several hundred km s−1 in line-of-sight velocity. Specifically, higher column density components (log N(H i)/cm−2≳ 16) in all four absorbers comprise dynamically cool gas with $\langle T \rangle =(2\pm 1) \times 10^4\,$K and modest non-thermal broadening of $\langle b_\mathrm{nt} \rangle =5\pm 3\,$km s−1. The high quality of the QSO absorption spectra allows us to infer the physical conditions of the gas, using a detailed ionization modelling that takes into account the resolved component structures of H i and metal transitions. The range of inferred gas densities indicates that these absorbers consist of spatially compact clouds with a median line-of-sight thickness of $160^{+140}_{-50}$ pc. While obtaining robust metallicity constraints for the low density, highly ionized phase remains challenging due to the uncertain $N\mathrm{(H\, {\small I})}$, we demonstrate that the cool-phase gas in LLSs has a median metallicity of $\mathrm{[\alpha /H]_{1/2}}=-0.7^{+0.1}_{-0.2}$, with a 16–84 percentile range of [α/H] = (−1.3, −0.1). Furthermore, the wide range of inferred elemental abundance ratios ([C/α], [N/α], and [Fe/α]) indicate a diversity of chemical enrichment histories. Combining the absorption data with deep galaxy survey data characterizing the galaxy environment of these absorbers, we discuss the physical connection between star-forming regions in galaxies and diffuse gas associated with optically thick absorption systems in the z < 1 circumgalactic medium.

Zahedy, Fakhri S. (ORCID:0000000178692551)↗

Kinematics of the H α and H β broad-line region in an SDSS sample of type-1 AGNs

Here, we investigate the kinematics of the part of the broad-line region (BLR) in active galactic nuclei (AGNs) emitting H β and H α emission lines. We explore the widths and asymmetries of the broad H β and H α emission lines in a sample of high-quality (i.e. high signal-to-noise ratio) spectra of type-1 AGN taken from the Data Release 16 of the Sloan Digital Sky Survey in order to explore possible deviation from the gravitationally bound motion. To find only the broad component of H β and H α, we use the FANTASY (Fully Automated pythoN Tool for AGN Spectra analYsis) code for the multicomponent modelling of the AGN spectra and for careful extraction of the broad emission-line parameters. Here, we show that based on the broad-line profiles widths and asymmetries, the BLR gas emitting H β and H α lines follows similar kinematics, and seems to be virialized in our sample of type-1 AGN.

79 ASTRONOMY AND ASTROPHYSICS↗

First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies

ABSTRACT We present, for the first time, an observational test of the consistency relation for the large-scale structure (LSS) of the Universe through a joint analysis of the anisotropic two- and three-point correlation functions (2PCF and 3PCF) of galaxies. We parameterize the breakdown of the LSS consistency relation in the squeezed limit by Es, which represents the ratio of the coefficients of the shift terms in the second-order density and velocity fluctuations. Es ≠ 1 is a sufficient condition under which the LSS consistency relation is violated. A novel aspect of this work is that we constrain Es by obtaining information about the non-linear velocity field from the quadrupole component of the 3PCF without taking the squeezed limit. Using the galaxy catalogues in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, we obtain $E_{\rm s} = -0.92_{-3.26}^{+3.13}$, indicating that there is no violation of the LSS consistency relation in our analysis within the statistical errors. Our parameterization is general enough that our constraint can be applied to a wide range of theories, such as multicomponent fluids, modified gravity theories, and their associated galaxy bias effects. Our analysis opens a new observational window to test the fundamental physics using the anisotropic higher-order correlation functions of galaxy clustering.

79 ASTRONOMY AND ASTROPHYSICS↗

SPT-SZ MCMF: an extension of the SPT-SZ catalogue over the DES region

We present an extension to a Sunyaev–Zel’dovich Effect (SZE) selected cluster catalogue based on observations from the South Pole Telescope (SPT); this catalogue extends to lower signal to noise than the previous SPT–SZ catalogue and therefore includes lower mass clusters. Optically derived redshifts, centres, richnesses, and morphological parameters together with catalogue contamination and completeness statistics are extracted using the multicomponent matched filter (MCMF) algorithm applied to the S/N > 4 SPT–SZ candidate list and the Dark Energy Survey (DES) photometric galaxy catalogue. The main catalogue contains 811 sources above S/N = 4, has 91 per cent purity, and is 95 per cent complete with respect to the original SZE selection. It contains in total 50 per cent more clusters and twice as many clusters above z = 0.8 in comparison to the original SPT-SZ sample. The MCMF algorithm allows us to define subsamples of the desired purity with traceable impact on catalogue completeness. As an example, we provide two subsamples with S/N > 4.25 and S/N > 4.5 for which the sample contamination and cleaning-induced incompleteness are both as low as the expected Poisson noise for samples of their size. The subsample with S/N > 4.5 has 98 per cent purity and 96 per cent completeness and is part of our new combined SPT cluster and DES weak-lensing cosmological analysis. We measure the number of false detections in the SPT-SZ candidate list as function of S/N, finding that it follows that expected from assuming Gaussian noise, but with a lower amplitude compared to previous estimates from simulations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The impact of baryonic discs on the shapes and profiles of self-interacting dark matter haloes

We employ isolated N-body simulations to study the response of self-interacting dark matter (SIDM) haloes in the presence of the baryonic potentials. Dark matter self-interactions lead to kinematic thermalization in the inner halo, resulting in a tight correlation between the dark matter and baryon distributions. A deep baryonic potential shortens the phase of SIDM core expansion and triggers core contraction. This effect can be further enhanced by a large self-scattering cross-section. We find the final SIDM density profile is sensitive to the baryonic concentration and the strength of dark matter self-interactions. Assuming a spherical initial halo, we also study evolution of the SIDM halo shape together with the density profile. The halo shape at later epochs deviates from spherical symmetry due to the influence of the non-spherical disc potential, and its significance depends on the baryonic contribution to the total gravitational potential, relative to the dark matter one. In addition, we construct a multicomponent model for the Milky Way, including an SIDM halo, a stellar disc, and a bulge, and show it is consistent with observations from stellar kinematics and streams.

79 ASTRONOMY AND ASTROPHYSICS↗

A new RASS galaxy cluster catalogue with low contamination extending to z ∼ 1 in the DES overlap region

ABSTRACT We present the MARD-Y3 catalogue of between 1086 and 2171 galaxy clusters (52 per cent and 65 per cent new) produced using multicomponent matched filter (MCMF) follow-up in 5000 deg2 of DES-Y3 optical data of the ∼20 000 overlapping ROSAT All-Sky Survey source catalogue (2RXS) X-ray sources. Optical counterparts are identified as peaks in galaxy richness as a function of redshift along the line of sight towards each 2RXS source within a search region informed by an X-ray prior. All peaks are assigned a probability fcont of being a random superposition. The clusters lie at 0.02 < z < 1.1 with more than 100 clusters at z > 0.5. Residual contamination is 2.6 per cent and 9.6 per cent for the cuts adopted here. For each cluster we present the optical centre, redshift, rest frame X-ray luminosity, M500 mass, coincidence with NWAY infrared sources, and estimators of dynamical state. About 2 per cent of MARD-Y3 clusters have multiple possible counterparts, the photo-z’s are high quality with σΔz/(1 + z) = 0.0046, and ∼1 per cent of clusters exhibit evidence of X-ray luminosity boosting from emission by cluster active galactic nuclei. Comparison with other catalogues (MCXC, RM, SPT-SZ, Planck) is performed to test consistency of richness, luminosity, and mass estimates. We measure the MARD-Y3 X-ray luminosity function and compare it to the expectation from a fiducial cosmology and externally calibrated luminosity- and richness–mass relations. Agreement is good, providing evidence that MARD-Y3 has low contamination and can be understood as a simple two step selection – X-ray and then optical – of an underlying cluster population described by the halo mass function.

79 ASTRONOMY AND ASTROPHYSICS↗

Thermodynamic Modeling of Complex Solid Solutions in the Lu-H-N System via Graph Neural Network Accelerated Monte Carlo Simulations

Metal hydrides are important across diverse applications, such as hydrogen storage, batteries, gas sensors, nuclear reactions, and high-temperature superconductivity. Previous computational studies of metal hydrides under extreme pressures, e.g., 𝑂⁡(10 2 ) ⁢GPa, usually treat them as stoichiometric compounds without considering interstitial lattice disorder. As pressures become more moderate in the 𝑂⁡(10 0 ) ⁢GPa and below range, hydrogen disorder at interstitial lattice sites becomes prominent, e.g., in the N-doped Lu hydride that was recently claimed superconducting near 1 GPa. Further adding compositional complexity from alloying and/or multielement interstitial occupation makes elucidating pressure- and temperature-dependent observables intractable by first-principles calculations alone. We therefore propose a lattice graph neural-network surrogate modeling approach to predict configuration- and pressure-dependent equation-of-state properties. Their efficiency permits Monte Carlo simulations to calculate Gibbs energies and pressure-dependent phase diagrams, thereby revealing insights into the synthesis conditions required for achieving desired phase equilibria. We demonstrate this concept for the compositionally complex cubic Lu(H,N,Va) 3 system where three constituents (hydrogen, nitrogen and vacancy) have disordered multielement interstitial occupancies and insights into pressure-dependent phase equilibria are critically needed, e.g., N-doping levels can significantly lower dehydrogenation temperatures and provide a new strategy to optimize hydrogen-storage alloys. This work can improve the thermodynamic understanding of the Lu-H-N system and help rational synthesis of N-doped Lu hydrides, but more generally demonstrates an efficient approach to model pressure-dependent thermodynamics of multicomponent solid solutions.

Monte Carlo methods↗

Machine-learned quantum molecular dynamics calculations of warm dense equation of state and ionic transport coefficients of deuterated water

White dwarf models require accurate equations of state and ionic transport coefficients in the warm dense matter regime, where kinetic theory models and tabulated equations of state are often inaccurate. In this work, spectral-partitioned density functional theory and machine-learned interatomic potentials are combined to perform large-scale, first-principles quantum molecular dynamics simulations of deuterated water (D 2 O) near the principal Hugoniot. This approach retains Kohn-Sham accuracy while achieving orders-of-magnitude speedup, yielding converged equation of state and transport properties over a broad pressure and temperature range. The results reveal the thermodynamic conditions under which ionic transport models for interdiffusivity and shear viscosity converge and identify those in closest agreement with density functional theory benchmarks at temperatures in the warm dense matter regime. The present framework extends first-principles transport calculations to higher temperatures than previously achieved, and provides an efficient, scalable, and general approach for studying transport properties in complex multicomponent mixtures.

79 ASTRONOMY AND ASTROPHYSICS↗

Competing Electronic Ground States in the Heavy-Fermion Superconductor CeRh 2 As 2

CeRh 2 ⁢As 2 is rare among superconductors, in that the magnetic field tunes it between two distinct superconducting phases. Combined with a lack of local inversion symmetry and an upper critical field exceeding the Pauli paramagnetic limit, this excitingly suggests triplet multicomponent superconductivity. Preceding the superconducting onset, 𝑓-electron correlations cause long-range order, attributed both to local antiferromagnetism and itinerant (quadrupole) density waves. A magnetic field provides a significant perturbation of the 𝑓 electrons and may reveal the nature of the many-body correlations. Therefore, we report comprehensive magnetization and magnetotransport studies on microstructured devices in fields of up to 73 T. Applied along the 𝑐 axis, the field causes a low-temperature change of majority (hole) carrier density at 𝜇 0⁢ 𝐻 ≈ 2⁢4 T. By contrast, in-plane fields produce a cascade of phase transitions; the field-induced in-plane conductivity anisotropy and lack of accompanying magnetic features, plus the closed-dome nature of the overall phase boundary is consistent with a hierarchy of field-induced density-wave states.

36 MATERIALS SCIENCE↗

Compressive sensing lattice dynamics. I. General formalism

Ab initio calculations have been successfully used for evaluating lattice dynamical properties of solids within the (quasi)harmonic approximation (i.e., assuming noninteracting phonons with infinite lifetimes), but it remains difficult to treat anharmonicity in all but the simplest compounds. We detail a systematic information-theory-based approach to deriving ab initio anharmonic force constants: Compressive sensing lattice dynamics (CSLD). The non-negligible terms that are necessary to reproduce the first-principles calculated interatomic forces are automatically selected by minimizing the ℓ 1 norm (sum of absolute values) of the scaled force constants. Here, by using efficient sampling of the configuration space using a modest number of atomic configurations with quasirandom displacements, CSLD is well suited for deriving accurate anharmonic potentials for complex multicomponent compounds with large unit cells. We demonstrate the power and generality of CSLD by calculating the phonon lifetimes and thermal transport properties of type-I Si clathrates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

$\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals

In this work, we uncover the properties of complex tensor ($\textit{d}$-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-$\frac{3}{2}$ fermions at a fourfold linear band-crossing point. Although the general theory of $\textit{d}$-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-$\frac{3}{2}$ nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the “cyclic state,” well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic $\textit{d}$-wave superconductors where the $\textit{d}$-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantifying multipoint ordering in alloys

A central problem in multicomponent lattice systems is to systematically quantify multipoint ordering. Ordering in such systems is often described in terms of pairs, even though this is not sufficient when three-point and higher-order interactions are included in the Hamiltonian. Current models and parameters for multipoint ordering are often only applicable for very specific cases or require approximating a subset of correlated occupational variables on a lattice as being uncorrelated. In this paper, cluster order parameters are introduced to systematically quantify arbitrary multipoint ordering motifs in substitutional systems through direct calculations of normalized cluster probabilities. These parameters can describe multipoint chemical ordering in crystal systems with multiple sublattices, multiple components, and systems with reduced symmetry. These are defined in this paper and applied to quantify four-point chemical ordering motifs in platinum/palladium alloy nanoparticles that are of practical interest to the synthesis of catalytic nanocages. Impacts of chemical ordering on nanocage stability are discussed. It is demonstrated that approximating four-point probabilities from superpositions of lower-order pair probabilities is not sufficient in cases where three- and four-body terms are included in the energy expression. Furthermore, conclusions about the formation mechanisms of nanocages may change significantly when using common pair approximations.

36 MATERIALS SCIENCE↗

Coupling between bulk thermal defects and surface segregation dynamics

Surface segregation is a phenomenon that depends on the delicate interplay between thermodynamic driving forces and kinetic obstacles, for which elevated temperature is often needed to enhance the atom mobility and reach equilibrium. Using the classic system of Cu 3 Au ( 100 ) under nonisothermal conditions, in this study, we show an adatom process underlying transient surface segregation dynamics through the temperature-change-driven creation and annihilation of thermal vacancies in the bulk and the resulting bulk-surface mass exchanges. This is demonstrated by monitoring the surface composition evolution of Cu 3 Au ( 100 ) with temperature changes between 250 and 500 ° C , showing that the increase in temperature decreases monotonically the surface Au concentration as a result of the transfer of more Cu than Au from the bulk to the surface to form Cu-rich clusters of adatoms. Such a bulk thermal defect effect is expected to be universal in inducing the disparity in the bulk-surface mass exchanges of dissimilar atoms in multicomponent materials because of the inherent differences in the vacancy formation energies of the constituent atoms.

36 MATERIALS SCIENCE↗

Spatially inhomogeneous superconductivity in UTe 2

The newly discovered superconductor UTe 2 is a strong contender for a topological spin-triplet state wherein a multicomponent order parameter arises from two nearly degenerate superconducting states. A key issue is whether both of these states intrinsically exist at ambient pressure. Through thermal expansion and calorimetry, we show that UTe 2 at ambient conditions exhibits two detectable transitions only in some samples, and the size of the thermal expansion jump at each transition varies when the measurement is performed in different regions of the sample. This result indicates that the two transitions arise from two spatially separated regions that are inhomogeneously mixed throughout the volume of the sample, each with a discrete superconducting transition temperature (T c ). Notably, samples with higher T c only show a single transition at ambient pressure. Above 0.3 GPa, however, two transitions are invariably observed in ac calorimetry. Our results not only point to a nearly vertical line (constant pressure) in the pressure-temperature phase diagram but also provide a consistent scenario for the sample dependence of UTe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Composition-transferable machine learning potential for LiCl-KCl molten salts validated by high-energy x-ray diffraction

Unraveling the liquid structure of multicomponent molten salts is challenging due to the difficulty in conducting and interpreting high-temperature diffraction experiments. Here, motivated by this challenge, we developed composition-transferable Gaussian approximation potential (GAP) for molten LiCl-KCl. A DFT-SCAN accurate GAP is active-learned from only ~1100 training configurations drawn from 10 unique mixture compositions enriched with metadynamics. The GAP-computed structures show strong agreement across high-energy x-ray diffraction experiments, including for a eutectic not explicitly included in model training, thereby opening the possibility of composition discovery.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, s -wave charge- 4 e , and d -wave charge- 4 e states

Electronically ordered states that break multiple symmetries can melt in multiple stages, similarly to liquid crystals. In a partially melted phase, known as vestigial phase, a bilinear made out of combinations of the multiple components of the primary order parameter condenses. Multicomponent superconductors are thus natural candidates for vestigial order since they break both the U⁡(1)-gauge and also time-reversal or lattice symmetries. Here, we use group theory to classify all possible real-valued and complex-valued bilinears of a generic two-component superconductor on a tetragonal or hexagonal lattice. While the more widely investigated real-valued bilinears correspond to vestigial nematic or ferromagnetic order, the little explored complex-valued bilinears correspond to a vestigial charge-4e condensate, which itself can have an underlying s-wave, d x 2 –y 2 -wave, or d xy -wave symmetry. To properly describe the fluctuating regime of the superconducting Ginzburg-Landau action and thus access these competing vestigial phases, we employ both a large-N and a variational method. We show that while vestigial order can be understood as a weak-coupling effect in the large-N approach, it is akin to a moderate-coupling effect in the variational method. Despite these distinctions, both methods yield similar results in wide regions of the parameter space spanned by the quartic Landau coefficients. Specifically, we find that the nematic and ferromagnetic phases are the leading vestigial instabilities, whereas the various types of charge-4⁢e order are attractive albeit subleading vestigial channels. The only exception is for the hexagonal case, in which the nematic and s-wave charge-4e vestigial states are degenerate. Finally, we discuss the limitations of our approach, as well as the implications of our results for the realization of exotic charge-4⁢e states in material candidates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

Multicomponent quantum Hall systems with internal degrees of freedom provide a fertile ground for the emergence of exotic quantum liquids. Here, we investigate the possibility of non-Abelian topological order in the half-filled fractional quantum Hall (FQH) bilayer system driven by the tunneling effect between two layers. By means of the state-of-the-art density-matrix renormalization group, we unveil “fingerprint” evidence of the non-Abelian Moore-Read Pfaffian state emerging in the intermediate-tunneling regime, including the ground-state degeneracy on the torus geometry and the topological entanglement spectroscopy (entanglement spectrum and topological entanglement entropy) on the spherical geometry, respectively. Remarkably, the phase transition from the previously identified Abelian (331) Halperin state to the non-Abelian Moore-Read Pfaffian state is determined to be continuous, which is signaled by the continuous evolution of the universal part of the entanglement spectrum, and discontinuities in the excitation gap and the derivative of the ground-state energy. Our results not only provide a “proof-of-principle” demonstration of realizing a non-Abelian state through coupling different degrees of freedom, but also open up a possibility in FQH bilayer systems for detecting different chiral p-wave pairing states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Field-induced magnetic phase transitions and metastable states in Tb 3 Ni

In this study we report the detailed study of magnetic phase diagrams, low-temperature magnetic structures, and the magnetic field effect on the electrical resistivity of the binary intermetallic compound ${\mathrm{Tb}}_{3}\mathrm{Ni}$. The incommensurate magnetic structure of the spin-density-wave type described with magnetic superspace group $P{112}_{1}/a{1}^{{'}}(ab0)0ss$ and propagation vector ${\mathbf{k}}_{\mathrm{IC}}=\left[0.506,0.299,0\right]$ was found to emerge just below Néel temperature ${T}_{\mathrm{N}}=61$ K. Further cooling below 58 K results in the appearance of multicomponent magnetic states: (i) a combination of ${\mathbf{k}}_{1}=\left[\frac{1}{2},\frac{1}{2},0\right]$ and ${\mathbf{k}}_{\mathrm{IC}}$ in the temperature range 51 < T < 58 K; (ii) a mixed magnetic state of ${\mathbf{k}}_{\mathrm{IC}}, {\mathbf{k}}_{1}$, and ${\mathbf{k}}_{2}=\left[\frac{1}{2},\frac{1}{4},0\right]$ with the partially locked-in incommensurate component in the temperature range 48 < T < 51 K; and (iii) a low-temperature magnetic structure that is described by the intersection of two isotropy subgroups associated with the irreducible representations of two coupled primary order parameters (OPs) ${\mathbf{k}}_{2}=\left[\frac{1}{2},\frac{1}{4},0\right]$ and ${\mathbf{k}}_{3}=\left[\frac{1}{2},\frac{1}{3},0\right]$ and involves irreducible representations of the secondary OPs ${\mathbf{k}}_{1}=\left[\frac{1}{2},\frac{1}{2},0\right]$ and ${\mathbf{k}}_{4}=\left[\frac{1}{2},0,0\right]$ below 48 K. An external magnetic field suppresses the complex low-temperature antiferromagnetic states and induces metamagnetic transitions towards a forced ferromagnetic state that are accompanied by a substantial magnetoresistance effect due to the magnetic superzone effect. Finally, the forced ferromagnetic state induced after application of an external magnetic field along the $b$ and $c$ crystallographic axes was found to be irreversible below 3 and 8 K, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗