Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Dirac materials”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26

Anisotropic positive linear and sub-linear magnetoresistivity in the cubic type-II Dirac metal Pd 3 In 7

We report a transport study on Pd 3 In 7 which displays multiple Dirac type-II nodes in its electronic dispersion. Pd 3 In 7 is characterized by low residual resistivities and high mobilities, which are consistent with Dirac-like quasiparticles. For an applied magnetic field (μ 0 H) having a non-zero component along the electrical current, we find a large, positive, and linear in μ 0 H longitudinal magnetoresistivity (LMR). The sign of the LMR and its linear dependence deviate from the behavior reported for the chiral-anomaly-driven LMR in Weyl semimetals. Interestingly, such anomalous LMR is consistent with predictions for the role of the anomaly in type-II Weyl semimetals. In contrast, the transverse or conventional magnetoresistivity (CMR for electric fields E⊥μ 0 H) is large and positive, increasing by 10 3 –10 4 % as a function of μ 0 H while following an anomalous, angle-dependent power law ρ xx α (μ 0 H) n with n(θ) ≤ 1. The order of magnitude of the CMR, and its anomalous power-law, is explained in terms of uncompensated electron and hole-like Fermi surfaces characterized by anisotropic carrier scattering likely due to the lack of Lorentz invariance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Orbital Ingredients and Persistent Dirac Surface State for the Topological Band Structure in FeTe 0.55 Se 0.45

FeTe 0.55 Se 0.45 (FTS) occupies a special spot in modern condensed matter physics at the intersections of electron correlation, topology, and unconventional superconductivity. The bulk electronic structure of FTS is predicted to be topologically nontrivial due to the band inversion between the d x z and p z bands along Γ − Z . However, there remain debates in both the authenticity of the Dirac surface states (DSSs) and the experimental deviations of band structure from the theoretical band inversion picture. Here we resolve these debates through a comprehensive angle-resolved photoemission spectroscopy investigation. We first observe a persistent DSS independent of k z . Then, by comparing FTS with FeSe, which has no band inversion along Γ − Z , we identify the spectral weight fingerprint of both the presence of the p z band and the inversion between the d x z and p z bands. Furthermore, we propose a renormalization scheme for the band structure under the framework of a tight-binding model preserving crystal symmetry. Our results highlight the significant influence of correlation on modifying the band structure and make a strong case for the existence of topological band structure in this unconventional superconductor. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Exploration of two surfaces observed in Weyl semimetal BaMnSb 2

Single crystalline BaMnSb 2 is considered as a 3D Weyl semimetal with the 2D electronic structure containing Dirac cones from the Sb sheet. We report experimental investigation of low-temperature cleaved BaMnSb 2 surfaces using scanning tunneling microscopy/spectroscopy and low energy electron diffraction. By natural cleavage, we find two terminations: one is Ba (above the orthorhombically distorted Sb sheet) and another Sb2 (at the surface of the Sb/Mn/Sb sandwich layer). Both terminations show the 2×1 surface reconstructions, with drastically different morphologies and electronic properties, however. The reconstructed structures, defect types and nature of the electronic structures of the two terminations are extensively studied. The quasiparticle interference (QPI) analysis is conducted at the energy range between -2 V and 2 V, although no interesting states are observed near the Fermi level, the surface-projected electronic band structures strongly depend on the surface termination above 1.6 V. The existence of defects can greatly modify the local density of states to create electronic phase separations on the surface in the order of tens of nm scale. Our observation on the atomic structures of the terminations and the corresponding electronic structures provides critical information towards an understanding of topological properties of BaMnSb 2 .

36 MATERIALS SCIENCE↗

Andreev Reflection and Klein Tunneling in High-Temperature Superconductor-Graphene Junctions

Scattering processes in quantum materials emerge as resonances in electronic transport, including confined modes, Andreev states, and Yu-Shiba-Rusinov states. However, in most instances, these resonances are driven by a single scattering mechanism. Here, in this paper, we show the appearance of resonances due to the combination of two simultaneous scattering mechanisms, one from superconductivity and the other from graphene p-n junctions. These resonances stem from Andreev reflection and Klein tunneling that occur at two different interfaces of a hole-doped region of graphene formed at the boundary with superconducting graphene due to proximity effects from Bi 2 Sr 2 Ca 1 Cu 2 O 8+δ . The resonances persist with gating from p + -p and p-n configurations. The suppression of the oscillation amplitude above the bias energy which is comparable to the induced superconducting gap indicates the contribution from Andreev reflection. Our experimental measurements are supported by quantum transport calculations in such interfaces, leading to analogous resonances. Our results put forward a hybrid scattering mechanism in graphene–high-temperature superconductor heterojunctions of potential impact for graphene-based Josephson junctions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Extrinsic n-type doping of Cd 3 As 2 thin films

Cd 3 As 2 provides an excellent platform for studying the physics of three-dimensional Dirac semimetals due to its stability as well as its compatibility with thin film growth. Crystals made using both bulk and thin film synthesis are unintentionally doped n-type, and other than introducing Zn to reduce the carrier concentration, no efforts have been reported to alter this intrinsic doping without major changes to the band structure. Here, group VI elements Te and Se are introduced during epitaxy to increase the electron concentration of the films. Starting from an unintentionally doped electron concentration of 1–2 × 10 17 cm -3 , concentrations of up to 3 × 10 18 cm -3 are achieved. Analysis of Shubnikov–de Haas oscillations reveals good agreement in calculated effective mass and Fermi velocity of highly doped films with unintentionally doped single crystals with similar electron concentrations. The density functional theory is also performed to study the effects of group VI substitutions and confirms no strong perturbations in the electronic structure. This work ultimately demonstrates tunability in the carrier concentration using extrinsic dopants without substantial changes in the band structure, allowing for intentional design of Fermi-level position for device applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magic-angle semimetals with chiral symmetry

Here, we construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation. In real space, this is realized with a quasiperiodic hopping term. This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states (DOS) and subdiffusive transport when the quasiperiodic hopping is strongest. We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique “unfreezing” transition. This unfreezing transition in momentum space generates flat bands with a dramatically renormalized bandwidth in the metallic phase similar to the phenomena of the band structure of twisted bilayer graphene at the magic angle. We characterize the nature of this transition numerically as well as analytically in terms of the formation of a band of topological zero modes. For pure quasiperiodic hopping, we provide strong numerical evidence that the low-energy DOS develops a divergence and the eigenstates exhibit Chalker (quantum-critical) scaling despite the model not being random. At particular commensurate limits the model realizes higher-order topological insulating phases. We discuss how these systems can be realized in experiments on ultracold atoms and metamaterials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effect of Fermi surface topology change on the Kagome superconductor CeRu 2 under pressure

The cubic Laves phase compound CeRu 2 with a Kagome substructure of Ru has been investigated to understand myriad fascinating phenomena resulting from competition among its various physical and geometric features. Such phenomena include flat bands, van Hove singularities, Dirac cones, reentrant superconductivity, magnetism, the Fulde–Ferrell–Larkin–Ovchinnikov state, valence fluctuations, time-irreversible anisotropic s-state superconductivity, etc. Extensive studies have thus been carried out since 1958 when the highly unusual coexistence of superconductivity and ferromagnetism was proposed for the mixed compounds (Ce,Gd)Ru 2 . Activity has accelerated in recent years due to increasing interest in topological states in superconductors. However, there has been little investigation of the mutual influence of these fascinating states. Therefore, we systematically investigated the superconductivity and possible Fermi surface topological change in CeRu 2 via magnetic, resistivity, and structural measurements under pressure up to ~168 GPa. An unusual phase diagram that suggests an intriguing interplay between the compound’s superconducting order and Fermi surface topological order has been constructed. A resurgence in its superconducting transition temperature was observed above 28 GPa. Our experiments have identified a structural transition above 76 GPa and a few tantalizing phase transitions driven by high pressure. Our high-pressure results further suggest that superconductivity and Fermi surface topology in CeRu 2 are strongly intertwined.

36 MATERIALS SCIENCE↗

Electronic and magnetic properties of hole-doped topological kagome Fe 1−𝑥 ⁢Mn 𝑥 ⁢Sn thin films

We have investigated the electronic and magnetic structures of topological kagome Fe 1−𝑥 ⁢Mn 𝑥 ⁢Sn (0 ≤ 𝑥 ≤ 0.3) thin films via neutron diffraction, electronic transport measurements, and ab initio density functional theory (DFT) to understand the interplay between hole doping, magnetism, and the electronic structures. Temperature-dependent neutron diffraction measurements on parent FeSn reveal the Néel temperature to be 𝑇 N ∼ 355 K and the underlying A-type antiferromagnetic ordering is associated with a wave vector 𝒒 = (001/2). Upon Mn doping to 𝑥 = 0.15, 𝑇 N decreases slightly while the magnetic ordering vector remains the same. Resistivity measurements show metallic characteristics and in-plane anisotropy down to 10 K for all the investigated samples. The effects of hole doping are mapped in terms of electronic ground state calculations via DFT which show that the Dirac point is moved closer to the Fermi level (𝐸 F ) and the flat bands get pushed away from 𝐸 F upon hole doping. However, a comparison between hole-doped Fe 1−𝑥⁢ Mn 𝑥⁢ Sn and electron-doped Fe 1−𝑥 ⁢Co 𝑥 ⁢Sn indicates that the Néel temperature does not scale with the position of 𝐸 F relative to the flat band. Furthermore, our results establish the antiferromagnetic state of FeSn and Fe 1−𝑥 ⁢Mn 𝑥⁢ Sn films at room temperature, laying the groundwork for future studies of magnetism in kagome heterostructures.

36 MATERIALS SCIENCE↗

Twisted symmetric trilayer graphene: Single-particle and many-body Hamiltonians and hidden nonlocal symmetries of trilayer moiré systems with and without displacement field

Here, we derive the Hamiltonian for trilayer moiré systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror symmetry with respect to the middle layer. We provide a full symmetry analysis of the noninteracting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high-velocity Dirac fermions, and we identify a hidden nonlocal symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of noninteracting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wave functions and derive the full many-body Hamiltonian of the system. We also provide an efficient parametrization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the U (2) × U (2) spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large U (4) × U (4) × U (4) × U (4) symmetry in the chiral limit. Moreover, by identifying a symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

2-dimensional systems↗

Controllable Formation of Threefold-Coordinated Oxygen in Graphene by Low-Energy Ion Implantation

The atomically precise engineering of impurities in graphene and the understanding of their structural and carrier-dependent electronic properties at the nanoscale are crucial for advancing graphene-based nanoelectronics, catalysis, and energy technologies. Here, we demonstrate controllable incorporation of the elusive 3-fold-coordinated O substitutions into graphene using low-energy O + ion implantation under ultrahigh-vacuum conditions. By combining high-resolution scanning tunneling microscopy and spectroscopy (STM/S), bond-resolved noncontact atomic force microscopy techniques, and density functional theory (DFT) calculations, we resolve both the structural and electronic properties of the O-related defects. The STM/S measurements, corroborated by DFT calculations, uncover a characteristic impurity state that is energetically pinned to the Dirac point across different charge-carrier doping regimes. Molecular dynamics simulations further reveal the distribution of implantation-induced configurations and identify the formation of 3-fold-coordinated O dopants. Furthermore, this work provides a viable route to incorporate 3-fold-coordinated O dopants and opens new opportunities for controlled defect engineering in graphene.

3-fold-coordinated oxygen↗

Electronic structure and magnetism of pristine, defected, and strained $\mathrm{Ti_2N}$ $\mathrm{MX}$ene

Here, from first principles electronic structure calculations, we unravel the evolution of structural, electronic, and magnetic properties of pristine, defected, and strained titanium nitride MXene with different functional groups (-F, -O, -H, and -OH). The formation and cohesive energies reveal their chemical stability. The dynamical stability of Ti 2 N mono-layer is also confirmed by phonon calculations. The MAX phase and defect free functionalized MXenes are metallic except for oxygen terminated (Ti 2 NO 2 ) one which is 100% spin polarized half-metallic ferromagnet. The spin–orbit coupling significantly influences the bare MXene (Ti 2 N) to exhibit Dirac topology and band inversion near the high symmetry directions. The strain effect sways the Fermi level thereby shifting it towards lower energy state under compression and towards higher energy state under tensile strain in Ti 2 NH 2 . The Ti 2 NO 2 exhibits exotic electronic structure not only in pristine but also in strained and defected structures. Its half-metallic nature changes to semi-metallic under 1% compression and it is completely destroyed under 2% compression. In single vacancy defect, its band structure remarkably transforms from half-metallic to semi-conducting with large band gap in 12.5% Ti, weakly semi-conducting in 5.5% Ti, and semi-metallic in 12.5% O. The 25% N defect changes its half-metallic characteristic to metallic. Further, the 12.5% Co substitution preserves its half-metallic character, whereas Mn substitution allows it to convert half-metallic characteristic into weak semi-metallic characteristic preserving ferromagnetism. However, Cr substitution converts half-metallic ferromagnetic state to half-metallic anti-ferromagnetic state. The understanding made here on collective structural stability, and electronic band structure, and magnetic phenomena in novel 2D Ti 2 N derived MXenes open up their possibility in designing them for synthesis.

36 MATERIALS SCIENCE↗

Edge‐Driven Fringe‐Field Effects, Reduced Screening, and Bandgap Widening in Graphene Nanoribbons Enable Single‑Molecule Sensitivity

Graphene nanoribbons (GNRs) offer promising platforms for single‐molecule sensing due to their quasi‐1D channels and discrete electronic states, providing superior sensitivity toward molecular perturbations. While prior studies emphasize smoother edges as essential for optimal performance, the potential benefits of controlled edge roughness remain largely unexplored. Additionally, most investigations focus on GNR arrays, leaving critical edge‐ and width‐dependent factors, including fringe fields, bandgap widening, interactions between adsorbing molecules and GNR atoms, density of states (DOS) suppression, and electrostatic screening lengths, and their collective impact on sensitivity, poorly understood. Here, in this work, we fabricated field‐effect transistors using individual GNRs (widths: 200–20 nm) and characterized their response to molecular adsorption with perfluorooctanoic acid as the model analyte. Narrower ribbons displayed significantly enhanced sensitivity, yielding a coverage‐normalized response of 116 ± 10 mV per molecule in 20 nm‐wide GNRs (from calibrated ensemble Dirac‐point shifts). Experimental and theoretical analyses reveal that this heightened sensitivity arises from stronger fringe fields, width‐dependent quantum confinement effects, reduced DOS, and increased edge roughness that facilitates molecular anchoring, enhanced orbital overlap, and improved charge transfer efficiency. Our findings challenge the conventional assumption that smoother edges inherently enhance sensor performance, demonstrating that controlled edge disorder substantially boosts molecular sensitivity in GNR sensors.

36 MATERIALS SCIENCE↗

Quantum oscillations with angular dependence in PdTe 2 single crystals

The layered transition-metal dichalcogenide PdTe 2 has been discovered to possess bulk Dirac points as well as topological surface states. By measuring the magnetization (up to 7 T) and magnetic torque (up to 35 T) in single crystalline PdTe2, we observe distinct de Haas–van Alphen (dHvA) oscillations. Eight frequencies are identified with H||c, with two low frequencies (F α = 8 T and F β = 117 T) dominating the spectrum. The effective masses obtained by fitting the Lifshitz–Kosevich (LK) equation to the data are $m_α^* =0.059m_0$ and $m_β^* =0.067m_0$ where $m_0$ is the free electron mass. The corresponding Landau fan diagrams allow the determination of the Berry phase for these oscillations resulting in values of ~0.67π for the 3D α band (hole-type) (down to the 1st Landau level) and ~0.23π–0.73π for the 3D β band (electron-type) (down to the 3rd Landau level). By investigating the angular dependence of the dHvA oscillations, we find that the frequencies and the corresponding Berry phase (Φ B ) vary with the field direction, with a Φ B ~ 0 when H is 10°–30° away from the ab plane for both α and β bands. Finally, the multiple band nature of PdTe 2 is further confirmed from Hall effect measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Band structure, superconductivity, and polytypism in AuSn 4

The orthorhombic compound AuSn 4 is compositionally similar to the Dirac node arc semimetal PtSn 4 . AuSn 4 is, contrary to PtSn 4 , superconducting with a critical temperature of T c = 2.35 K. Recent measurements present indications for quasi-two-dimensional superconducting behavior in AuSn 4 . Here we present measurements of the superconducting density of states and the band structure of AuSn 4 through scanning tunneling microscopy and angular resolved photoemission spectroscopy (ARPES). The superconducting gap values in different portions of the Fermi surface are spread around Δ 0 = 0.4 meV, which is close to but somewhat larger than Δ = 1.76k B T c expected from BCS theory. We observe superconducting features in the tunneling conductance at the surface up to temperatures about 20% larger than bulk T c . The band structure calculated with density functional theory follows well the results of ARPES. The crystal structure presents two possible stackings of Sn layers, giving two nearly degenerate polytypes. This makes AuSn 4 a rather unique case with a three-dimensional electronic band structure but properties ressembling those of low-dimensional layered compounds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Coexisting kagome and heavy fermion flat bands in YbCr 6 Ge 6

Flat bands, electronic states with nearly dispersionless energy-momentum structure, provide fertile ground for unconventional quantum phases. Recent observations of flat bands at the Fermi level in kagome metals open the possibility of unifying topology and correlation-driven heavy-fermion physics. Here we show that topology and heavy-fermion correlations coexist in the layered kagome metal YbCr 6 Ge 6 . At high temperatures, an intrinsic kagome flat band—arising from frustrated hopping on the kagome lattice—dominates the Fermi level. Upon cooling, localized Yb 4f-states hybridize with the topological kagome flat bands, transforming this state into momentum-independent Kondo resonance states across the entire Brillouin zone. Topological analysis of the hybridization gaps reveals filling-tunable weak and strong topological Kondo-insulating regimes, and identifies a topological Dirac–Kondo semimetal. Taken together, these results identify YbCr 6 Ge 6 as a prototype of a topological heavy-fermion system and a platform where geometric frustration, strong correlations, and topology converge, with broad implications for correlated quantum matter.

36 MATERIALS SCIENCE↗

Type-II Weyl nodes, flat bands, and evidence for a topological Hall-effect in the new ferromagnet FeCr 3 Te 6

The interplay between linearly dispersing, or Dirac-like, and flat electronic bands, for instance, in the kagome ferromagnets, has attracted attention due to a possible interplay between topology and electronic correlations. Here, we report the synthesis, structural, electrical, and magnetic properties of a single-crystalline ferromagnetic compound, namely Fe 1/3 ⁢CrTe 2 or FeCr 3 ⁢Te 6 , which crystallizes in the 𝑃$\overline{3}$⁢𝑚⁢1 space group instead of the 𝐼⁢2/𝑚 previously reported for FeCr 2 ⁢Te 4 . Electronic band structure calculations reveal type-II Dirac nodes and relatively flat bands near the Fermi level (ε 𝐹 ). This compound shows onset Curie temperature 𝑇 c ≃ 120K, followed by an additional ferromagnetic transition near 𝑇 c2 ∼ 92.5K. Below 𝑇 c , FeCr 3 ⁢Te 6 displays a pronounced anomalous Hall effect, as well as sizable coercive fields that exceed 𝜇 0 ⁢𝐻=1 T at low 𝑇⁢s. However, a scaling analysis indicates that the anomalous Hall effect results from a significant intrinsic contribution, as expected from the calculations, and also from the extrinsic mechanism, i.e., scattering. The extrinsic contribution probably results from occupational disorder at the 1b Fe-site within the van der Waals gap of the CrTe 2 host. We also observe evidence for a topological Hall component superimposed onto the overall Hall response, suggesting the presence of chiral spin textures akin to skyrmions in this centrosymmetric system. Their possible presence will require experimental confirmation.

36 MATERIALS SCIENCE↗

Monolayer Superconductivity and Tunable Topological Electronic Structure at the Fe(Te,Se)/Bi 2 Te 3 Interface

The interface between 2D topological Dirac states and an s-wave superconductor is expected to support Majorana-bound states (MBS) that can be used for quantum computing applications. Realizing these novel states of matter and their applications requires control over superconductivity and spin-orbit coupling to achieve spin-momentum-locked topological interface states (TIS) which are simultaneously superconducting. While signatures of MBS have been observed in the magnetic vortex cores of bulk FeTe 0.55 Se 0.45 , inhomogeneity and disorder from doping make these signatures unclear and inconsistent between vortices. In this work, superconductivity is reported in monolayer (ML) FeTe 1–y Se y (Fe(Te,Se)) grown on Bi 2 Te 3 by molecular beam epitaxy (MBE). Spin and angle-resolved photoemission spectroscopy (SARPES) directly resolve the interfacial spin and electronic structure of Fe(Te,Se)/Bi 2 Te 3 heterostructures. For y = 0.25, the Fe(Te,Se) electronic structure is found to overlap with the Bi 2 Te 3 TIS and the desired spin-momentum locking is not observed. In contrast, for y = 0.1, reduced inhomogeneity measured by scanning tunneling microscopy (STM) and a smaller Fe(Te,Se) Fermi surface with clear spin-momentum locking in the topological states are found. Hence, it is demonstrated that the Fe(Te,Se)/Bi 2 Te 3 system is a highly tunable platform for realizing MBS where reduced doping can improve characteristics important for Majorana interrogation and potential applications.

36 MATERIALS SCIENCE↗

Geometric transport signatures of strained multi-Weyl semimetals

The minimal coupling of strain to Dirac and Weyl semimetals, and its modeling as a pseudogauge field has been extensively studied, resulting in several proposed topological transport signatures. In this work, we study the effects of strain on higher winding number Weyl semimetals and show that strain is not a pseudogauge field for any winding number larger than one. Here we focus on the double-Weyl semimetal as an illustrative example to show that the application of strain splits the higher winding number Weyl nodes and produces an anisotropic Fermi surface. Specifically, the Fermi surface of the double-Weyl semimetal acquires nematic order. By extending chiral kinetic theory for such nematic fields, we determine the effective gauge fields acting on the system and show how strain induces anisotropy and affects the geometry of the semiclassical phase space of the double-Weyl semimetal. Further, the strain-induced deformation of the Weyl nodes results in transport signatures related to the covariant coupling of the strain tensor to the geometric tensor associated with the Weyl nodes giving rise to strain-dependent dissipative corrections to the longitudinal as well as the Hall conductance. Thus, by extension, we show that in multi-Weyl semimetals, strain produces geometric signatures rather than topological signatures. Further, we highlight that the most general way to view strain is as a symmetry-breaking field rather than a pseudogauge field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗