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All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Status of Analysis and Manufacturability of Superconducting Wires with Low AC Losses

Superconductors can carry an order-of-magnitude higher current than room temperature copper wires and can do so with two orders-of-magnitude lower alternating current (AC) electrical losses. These advantages underlie our estimates that turboelectric propulsion of large aircraft can be enabled by superconducting machines. However, even the much smaller losses of superconductors pose thermal management issues at the low temperatures required for superconductivity, and predicting those losses and validating the predictions has been a developing process at NASA Glenn Research Center over the last decade. Since Glenn’s earliest assessments of the feasibility of fully superconducting machines for turboelectric propulsion, the available models of AC losses in superconductors have changed significantly, as well as the state of development of superconducting wire for the coils of electric machines. While the models available to us have improved significantly, the value of the AC losses predicted by these models have only increased as more fidelity was developed. The fabrication of medium temperature superconducting wires (Tc near 40 K) has advanced, and wires can be produced with finer filaments and tighter twisting than a decade ago. However, the ideal wire configurations, developed decades ago for low temperature superconductors (Tc < 25 K), still elude manufacturers of medium and high temperature (Tc > 77 K) superconductors. This report discusses the developments, the current limitations, and the expectations that future configurations of superconducting wire can yet be produced that will provide suitably low AC losses for the aircraft propulsion application. The report presents a basic discussion of the types of AC losses in superconductors, followed by a discussion of the evolution of our understanding of the practical consequences of those AC losses. Next, there is a discussion of the superconducting wire configurations that have been developed, which were partially guided by that understanding. A brief discussion of the modes of removing the heat produced by the losses is presented. Lastly, a comparison is presented between losses in currently available MgB2 wire and other important cases, including copper at room temperature, copper at liquid hydrogen temperature, and expected future MgB2 wire. Room temperature copper has 100 times the loss of today’s MgB2 and 300 times the expected loss of future MgB2. That implies we can expect much higher efficiency from fully superconducting machines than from machines with copper stators, and high efficiency targets remain the driver behind investment in MgB2 development and medium temperature superconductor research.

superconducting motors↗
DOE OSTI2023

Two-level systems in nucleated and non-nucleated epitaxial alpha-tantalum films

Building usefully coherent superconducting quantum processors depends on reducing losses in their constituent materials. Tantalum, like niobium, has proven utility as the primary superconducting layer within highly coherent qubits. However, unlike Nb, high temperatures are typically used to stabilize the desirable body-centered-cubic phase, α-Ta, during thin film deposition. It has long been known that a thin Nb layer permits the room-temperature nucleation of α-Ta, but here we observe the epitaxial process and present few-photon microwave loss measurements in Nb-nucleated Ta films. We compare resonators patterned from Ta films grown at high temperature (500 °C) and films nucleated at room temperature, in order to understand the impact of the crystalline order on quantum coherence. In both cases, films grew with Al 2 O 3 (001) ∥ Ta (110), indicating that the epitaxial orientation is independent of temperature and is preserved across the Nb/Ta interface. We use conventional low-power spectroscopy to measure two level system (TLS) loss as well as an electric-field bias technique to measure the effective dipole moments of TLS in the surfaces of resonators. In our measurements, Nb-nucleated Ta resonators had greater loss tangent (1.5 ± 0.1 × 10 -5 ) than non-nucleated (5 ± 1× 10 -6 ) in approximate proportion to defect densities as characterized by x-ray diffraction (0.27° vs 0.18° [110] reflection width) and electron microscopy (30 vs 70 nm domain size). Furthermore, the dependence of the loss tangent on domain size indicates that the development of more ordered Ta films is likely to lead to improvements in qubit coherence times. Moreover, low-temperature α-Ta epitaxy may enable the growth of microstate-free heterostructures, which would not withstand high temperature processing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1986

Electrical properties of Al-In-Sn alloys directionally solidified in high and low gravitational fields

The Al-In-Sn alloys were directionally solidified in the NASA KC-135 aircraft which flies a series of parabolas to generate high (high-g) and low (low-g) gravity forces parallel to the longitudinal growth axis. Thus, for a given sample, successive sections can be identified which were solidified in high-g and low-g. Measurements of the electronic properties of the samples reveal that: the resistivity of the low-g sections is larger (about a factor of 10) than that of the high-g sections; the low-g sections behave conductively like a semi-metal, while the high-g sections are essentially metallic; and both high-g and low-g sections are superconducting but the superconducting transition temperature of the low-g sections is 1 K higher than that of the high-g sections.

Curreri, P. A.↗
NASA NTRS1987

Electrical properties of Al-In-Sn alloys directionally solidified in high and low gravitational fields

The Al-In-Sn alloys were directionally solidified in the NASA KC-135 aircraft which flies a series of parabolas to generate high (high-g) and low (low-g) gravity forces parallel to the longitudinal growth axis. Thus, for a given sample, successive sections can be identified which were solidified in high-g and low-g. Measurements of the electronic properties of the samples reveal that: the resistivity of the low-g sections is larger (about a factor of 10) than that of the high-g sections; the low-g sections behave conductively like a semi-metal, while the high-g sections are essentially metallic; and both high-g and low-g sections are superconducting but the superconducting transition temperature of the low-g sections is 1 K higher than that of the high-g sections.

Wu, M. K.↗
DOE OSTI2021

Development of High-efficiency and Cost-effective Forged Ingot Niobium Technology for Science Frontiers and Accelerator Applications

Development of Forged Ingot Niobium Technology: Worlds science frontier programs and SRF accelerator applications demand high performance and cost-effective SRF accelerator technology [1-8]. Fine-grain (FG) and Large-grain (LG) ingot niobium technologies have been very well developed and implemented in all the present-day accelerator projects. However, forged ingot niobium technology which is the focus of this development proposal will be much more cost-effective and expected to have several technical advantages. FG niobium sheet production is very complex involving more than ten processing steps making them prone to contamination. As a result, they are very expensive to produce and require stringent QA procedure to be ready for SRF cavity production. The accelerating cavity process steps are also numerous and require strict procedures in order to achieve high accelerating gradients and quality factors needed for science frontier programs. LG niobium disc production, directly sliced from the ingot, is relatively simple and straight forward to keep surface cleanness. The disc production cost is significantly low compared to FG niobium sheet production. However, there are (some) draw backs due to non-homogeneity of the grain boundary distribution, resulting in non-uniform mechanical properties and complex cavity fabrication, although the LG cavities achieve the expected high-gradient performance goals with lower cost. Medium-grain (MG) niobium disk production may be realized with a new approach/process, the disc directly sliced from the forged ingot, involves a simpler process steps contributing major production cost reduction [9]. These discs are expected to be superior as they tend to be homogenous with uniform sub millimeter grains and mechanical properties. We are eagerly looking forward to developing the forged ingot niobium SRF accelerator technology for the benefit of the world-wide science frontier programs, green energy subcritical nuclear energy systems and a wide variety of industrial applications including the production of radio isotopes and nuclear transmutation applications. Measurement of thermal characteristics of the forged ingot niobium: Measurement of the thermal diffusivity, D, of superconducting MG niobium is important to be understood in comparison with FG sheet and LG disc, as well as that of advanced composite material of Nb3Sn film sputtered on forged ingot Nb, which will be determined using transient pump-probe thermo-modulation [10,11]. Transient thermo-modulation is based on using an ultrafast laser pulse to heat the superconducting materials by a few K, then a synchronized laser pulse probes the reflectance of the heated material. For thin films on a substrate (e.g, 100-nm Nb3Sn on Nb), it takes <100 ps for the heat to reach the substrate by diffusion. Therefore, an ultrafast method is needed to probe D of the studied material. D will be measured from room temperature to liquid helium temperatures. Fundamental Research: The increase of rf loss in SRF cavities is related to trapping of residual magnetic field during the cavity cool-down. The study suggested that the micro structure plays the role in flux trapping sensitivity. The research includes the flux trapping and expulsion study as forged ingot niobium goes through several mechanical deformations, crystallization leading to the optimal SRF cavity performance. Furthermore, the cavity made from FG, MG, and LG sheet/disc will be compared to understand the optimal re-crystallization temperature that cavity needed to be heat treated which minimize the flux trapping and increase SRF cavity performance. References: 1. S. Belomestnykh, Overview of recent SRF developments for ERLs, presented at the SRF 2015, Whistler, BC, Canada (2015). 2. A. Yamamoto, M. Yamanaka and G. Myneni, Ingot Nb based SRF Technology for the International Linear Collider, in Science and Technology of Ingot Niobium for Superconducting Radio Frequency Applications, AIP Conf. Proc. 1687, 030005-1 ? 03005-6, 2015 3. Report of the Workshop on Energy and Environmental Applications of Accelerators, DOE Workshop Report. https://science.osti.gov/-/media/hep/pdf/Reports/2020/CASM_WorkshopReport.pdf? la=en&hash=AEB0B318ED0436B1C5FF4EE0FDD6DEB84C2F15B2 4. G. Ciovati, et al., Design of a cw, low-energy, high-power superconducting linac for environmental applications, Phys. Rev. Accel. Beams 21, 091601 (2018). 5. P. Dhakal, et al., Effect of high temperature heat treatments on the quality factor of a large-grain superconducting radio-frequency niobium cavity, Phys. Rev. ST Accel. Beams 16, 042001 (2013). 6. P. Kneisel et al., Review of ingot niobium as a material for superconducting radio frequency accelerating cavities, Nuclear Instruments and Methods in Physics Research A 774, 133 (2015). 7. G. Ciovati, P. Dhakal, and G. R, Myneni, Superconducting radio-frequency cavities made from medium and low-purity niobium ingots, Supercond. Sci. Technol. 29, 064002 (2016). 8. M. Drury et al., commissioning of the prototype C75 cavities in a CEBAF cryomodule, in Proc. of IPAC 2018, Vancouver, BC, Canada (2018) 9. Feasibility of forged-ingot niobium disc and SRF cavity fabrication technology recently demonstrated in cooperation of ATI, BSCE, and KEK (2020). 10. Hani E. Elsayed-Ali, ?Measurements of heat transport in thin films by ultrafast laser-based techniques,? 3rd International Conference on Thermal Issues in Emerging Technologies Theory and Applications, Cairo, Egypt, pp. 347 ? 350 (2010). DOI: 10.1109/ThETA17616.2010 11. W. M. G. Ibrahim, H. E. Elsayed-Ali, M. Schinn, and C. A. Bonner, Jr., ?Ultrafast investigation of electron dynamics in multilayer metals,? Int. J. Heat and Mass Transfer, 47(10?11), 2261?2268 (2004).

Myneni, G.↗
DOE OSTI2021

High-T c Superconducting Memory Cell

In this paper, operational principles of a cryogenic memory cell that utilizes high-temperature superconductors (high-T c ) are presented. Such a cell consists of three inductively coupled Josephson junctions coupled via inductors. Design and operational logic of this type of cell were recently introduced and demonstrated for low temperature 4 K environment. The basic memory cell operations (read, write, reset) can be implemented on the same simple circuit and both destructive and non-destructive memory cell operations can be realized. Here, we present the design principles and computational validation of basic memory cell operations (write, read, and reset) for the high-T c memory cell. In conclusion, our results for the high-T c memory cell operations show very good resemblance with the previously presented low-temperature 4 K memory cell operations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Robust charge-density-wave correlations in the electron-doped single-band Hubbard model

There is growing evidence that the hole-doped single-band Hubbard and t–J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Materials preparation, single-crystal growth, and the phase diagram of the cuprate high-temperature superconductor La 1.6-x Nd 0.4 Sr x CuO 4

One branch of the La-214 family of cuprate superconductors, La 1.6-x Nd 0.4 Sr x CuO 4 (NdLSCO), has been of significant and sustained interest, in large part because it displays the full complexity of the phase diagram for canonical hole-doped, high TC superconductivity, while also displaying relatively low superconducting critical temperatures. The low superconducting TC’s imply that experimentally accessible magnetic fields can suppress the superconductivity to zero temperature. In particular, this has enabled various transport and thermodynamic studies of the T = 0 ground state in Nd-LSCO, free of superconductivity, across the critical doping p* = 0.23 where the pseudogap phase ends. The strong dependence of its superconducting properties on its crystal symmetry has itself motivated careful studies of the Nd-LSCO structural phase diagram. This paper provides a systematic study and summary of the materials preparation and characterization of both single crystal and polycrystalline samples of Nd-LSCO. Single-phase polycrystalline samples with x spanning the range from 0.01 to 0.40 have been synthesized, and large single crystals of La 1.6-x Nd 0.4 Sr x CuO 4 for select x across the region (0.07, 0.12, 0.17, 0.19, 0.225, 0.24, and 0.26) were grown by the optical floating zone method. Furthermore, systematic neutron and X-ray diffraction studies on these samples were performed at both low and room temperatures, 10 K and 300 K, respectively. These studies allowed us to follow the various structural phase transitions and propose an updated structural phase diagram for NdLSCO. In particular, we found that the low-temperature tetragonal (LTT) phase ends at a critical doping p LTT = 0.255±0.005, clearly separated from p*.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Use of Refractory-Volatile Element Deep Eutectic Regions to Grow Single Crystalline Intermetallic Compounds

Compounds containing both refractory and volatile elements present a unique challenge for crystal growth, given the conflicting realities of high melting temperatures and high vapor pressures. Nevertheless, the discovery of superconductivity in FeAs and FeSe based materials and a Weyl semimetal state in TaP are motivations to explore compounds containing such pairs. Here, we discuss use of the low-melting single phase liquid regions above deep M-X eutectics (M=transition metal, X=P, S) as the basis for high temperature solutions for growing intermetallic compounds containing volatile-refractory pairs. We show that Ni-P, Pd-P, Pt-P, and Pd-S compositions form single phase melts at moderate temperatures below 1000 °C and with minimal vapor pressure. We first present the simple case of growing Ni 2 P from Ni-P and next discuss the more complicated growth of RPd 3 S 4 (R=La, Ce, Nd, Eu) from a Pd-S melt. We show how frit-disc alumina crucible sets allow for contamination-free capture of decanted liquid and its reuse in subsequent experiments, demonstrating a fractionation of the CePd 3 S 4 growth to determine the optimal conditions for crystal growth. We conclude by using the single phase liquid regions above the Pt-P and Pd-P eutectics to grow single crystals of MPt 5 P (M=Mn, Fe) and MnPd 5 P. As these materials have primarily been studied in polycrystalline form, we give an overview of the magnetic and transport properties of our single crystals. The examples outlined here illustrate the utility of using the single phase liquid above deep metal-X eutectics for solution growth and materials discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

Reaction of YBa2Cu3O(7-beta) with Gold, Silver, Bismuth and Lead: Substitution Chemistry and Composite Fabrication

The reaction of YBa2Cu3O(7-beta) with Au, Ag, Bi, and Ph ions or metal is described. Three types of materials were produced: a well-defined series of homogeneous superconductors was obtained for Au ion substitution with little effect on T(sub c); attempted Ag and Bi ion substitution resulted in multi-phase samples with slightly enhanced T(sub c); finally, attempts to produce superconducting metal/superconducting ceramic composites with Pb and Bi powders resulted in multi-phase samples with drastically diminished superconducting properties. For Au- substituted superconductors, YBa2(Cu(l-x)Au(x))3O(7-beta), a substitution series (x = 0 - 0.1) has been synthesized. For x = 0.1 there was no change in the a and b lattice parameters (a = 3.826 A and b = 3.889 A) but a 0.06 A c axis expansion to 11.75 A was observed. The valence of Cu and Au in YBa2Au(0.3)Cu(2.7)O(7-beta) was investigated using X-ray Absorption Near-Edge Structure (XANES). X-ray studies indicate that Au goes into the Cu(l) site and Cu K edge XANES shows that this has little effect on the oxidation state of the remaining copper. A small effect on T(sub c) is observed (T(sub c) = 89 K for x = 0.10). Ag and Bi addition results in a rise in T(sub c) and a decrease in (delta)T(sub c) at low levels (x = 0.10 Ag, T(sub c) = 94 K and (delta)T(sub c) = 0.5 K; x = 0.02 Bi, T(sub c) = 94 K and (delta)T(sub c) = 1K) relative to typical values for YBa2Cu3O(7-beta) (T(sub c) = 91 K, (delta)T(sub c) = 2 K). Attempts at fabrication of Pb- and Pb(1-x)Bi(x)-superconductor composites are described. Cold pressing followed by low temperature (200 C) sintering resulted in a composite which excluded flux below 90 K but did not show zero electrical resistance until the metal (alloy) superconducting transition. X-ray diffraction showed the presence of pervoskite and metal. Processing at moderate (450 C) or high (950 C) temperatures resulted in oxygen-depleted pervoskite and/or metal oxides. These materials displayed greatly degraded superconducting properties. Processing at 800 C resulted in high T(sub c) only for composites containing greater than 90% weight fraction ceramic. Reaction of metal with YBa2Cu3O(7-beta) formed superconducting lead/bismuth-based oxides and other binary oxides.

Hepp, Aloysius F.↗
DOE OSTI2021

Orbitally selective resonant photodoping to enhance superconductivity

Signatures of superconductivity at elevated temperatures above T c in high-temperature superconductors have been observed near 1/8 hole doping for photoexcitation with infrared or optical light polarized either in the CuO 2 plane or along the c axis. While the use of in-plane polarization has been effective for incident energies aligned to specific phonons, c-axis laser excitation in a broad range between 5 μm and 400 nm was found to affect the superconducting dynamics in striped La 1.88 5Ba 0.115 CuO 4 , with a maximum enhancement in the 1/ω dependence to the conductivity observed at 800 nm. This broad energy range, specifically 800 nm, is not resonant with any phonon modes, yet induced electronic excitations appear to be connected to superconductivity at energy scales well above the typical gap energies in the cuprates. A critical question is, What can be responsible for such an effect at 800 nm? Using time-dependent exact diagonalization, we demonstrate that the holes in the CuO 2 plane can be photoexcited into the charge reservoir layers at resonant wavelengths within a multiband Hubbard model. This orbitally selective photoinduced charge transfer effectively changes the in-plane doping level, which can lead to an enhancement of T c near the 1/8 anomaly.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Investigation of the effect of structural defects from hydride precipitation on superconducting properties of high purity SRF cavity Nb using magneto-optical and electron imaging methods

Abstract Nb is an elemental superconductor with a critical temperature of 9.3 K and is widely used to fabricate superconducting radiofrequency (SRF) cavities for particle accelerators. However, microstructural defects in Nb, such as grain boundaries (GBs) and dislocations, can act as pinning centers for magnetic flux that can degrade SRF cavity performance. Hydrogen contamination is also detrimental to SRF cavity performance due to the formation of normal conducting hydrides during cool down. In this study, disc shaped Nb bi-crystals extracted from high-purity large-grain Nb slices were investigated to study the effects of GBs, hydrogen, and dislocations on superconducting properties. Grain orientation and GB misorientation were measured using Laue x-ray diffraction and electron backscattered diffraction (EBSD) analyses. Cryogenic magneto-optical imaging was used to directly observe magnetic flux penetration below T c = 9.3 K. Damage caused by low temperature precipitation of hydrides and their dissolution upon reheating after cryogenic cycles was examined using electron channeling contrast imaging, and EBSD. The relationships between hydride formation, dislocation content, GBs, cryo-cooling, heat treatment (HT), and flux penetration indicate that both GB character and hydrogen content affect magnetic flux penetration. Such flux penetration could be facilitated by dislocation structures and low angle GBs resulting from hydride precipitation and HT.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Thermal Conductivity of Electroplated Copper Onto Bulk Niobium at Cryogenic Temperatures

Superconducting radio-frequency (SRF) cavities made of high-purity bulk niobium are widely used in modern particle accelerators. The development of metallic outer coatings with high thermal conductivity would have a beneficial impact in terms of improved thermal stability, reduced material cost and for the development of conduction-cooled, cryogen-free SRF cavities. Several high-purity, fine-grain Nb samples have been coated with 2-4 mm thick copper by electroplating. Measurements of the thermal conductivity of the bimetallic Nb/Cu samples in the range 2 ? 7 K showed values of the order of 1 kW/(m K) at 4.3 K. Very good adhesion between copper and niobium was achieved by depositing a thin Cu layer by cold spray on the niobium, prior to electroplating the bulk Cu layer.

Dhakal, P.↗
DOE OSTI2021

Thermal Conductivity of Electroplated Copper Onto Bulk Niobium at Cryogenic Temperatures

Superconducting radio-frequency (SRF) cavities made of high-purity bulk niobium are widely used in modern particle accelerators. The development of metallic outer coatings with high thermal conductivity would have a beneficial impact in terms of improved thermal stability, reduced material cost and for the development of conduction-cooled, cryogen-free SRF cavities. Several high-purity, fine-grain Nb samples have been coated with 2-4 mm thick copper by electroplating. Measurements of the thermal conductivity of the bimetallic Nb/Cu samples in the range 2 ? 7 K showed values of the order of 1 kW/(m K) at 4.3 K. Very good adhesion between copper and niobium was achieved by depositing a thin Cu layer by cold spray on the niobium, prior to electroplating the bulk Cu layer.

Dhakal, P.↗
DOE OSTI2024

Signatures of ambient pressure superconductivity in thin film La 3 Ni 2 O 7

Recently, the bilayer nickelate La 3 Ni 2 O 7 has been discovered as a new superconductor with transition temperature T c near 80 K under high pressure. Despite extensive theoretical and experimental work to understand the nature of its superconductivity, the requirement of extreme pressure restricts the use of many experimental probes and limits its application potential. Here, in this work, we present signatures of superconductivity in La 3 Ni 2 O 7 thin films at ambient pressure, facilitated by the application of epitaxial compressive strain. The onset T c varies approximately from 26 K to 42 K, with higher T c values correlating with smaller in-plane lattice constants. We observed the co-existence of other Ruddlesden-Popper phases within the films and dependence of transport behavior with ozone annealing, suggesting that the observed low zero resistance T c of around 2 K can be attributed to stacking defects, grain boundaries, and oxygen stoichiometry. This finding initiates numerous opportunities to stabilize and study superconductivity in bilayer nickelates at ambient pressure, and to facilitate the broad understanding of the ever-growing number of high temperature and unconventional superconductors in the transition metal oxides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Nematic superconductivity in a one-dimensional system of massless fermions

The superconducting properties of the one-dimensional model of “relativistic” fermions with attraction generated by antiferromagnetic (Heisenberg) pair superexchange spin interaction are studied. Namely, we demonstrate that such a pairing in this system takes place in the nematic channel, with extended s-wave symmetry, where the attraction between fermions mostly takes place when the fermions occupy the nearest sites. It is demonstrated, that the zero-temperature properties of such a system are rather different from the “standard” case of superconductivity with local attraction. For instance, the order parameter has an unusual helical momentum dependence, ∼e −ika ⁠, where a is the lattice parameter and the dependence of the gap on doping has a bell shape, qualitatively similar to cuprate high-T c superconductors. Finally, the smooth transition from the overlapping pair to the local pair regime (or BCS–BEC crossover) in the nematic phase takes place at much lower values of doping as compared to the local pairing case, i.e., the “relativistic 1D” nematic superconductor is much less “friendly” to the local pairs. In conclusion, we also discuss the possible relation of the properties of this model to the superconducting properties of twisted graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗