High Pinning Force Values of a Fe(Se,Te) Single Crystal Presenting a Second Magnetization Peak Phenomenon

The magnetization M of an Fe(Se, Te) single crystal has been measured as a function of temperature T and dc magnetic field H. The sample properties have been analyzed in the case of a magnetic field parallel to its largest face H||ab. From the M(T) measurement, the T_c of the sample and a magnetic background have been revealed. The superconducting hysteresis loops M(H) were between 2.5 K and 15 K showing a tilt due to the presence of a magnetic signal measured at T > T_c. From the M(H) curves, the critical current density J_c(H) has been extracted at different temperatures showing the presence of a second magnetization peak phenomenon. By extracting and fitting the J_c(T) curves at different fields, a pinning regime crossover has been identified and shown to be responsible for the origin of the second magnetization peak phenomenon. Then, the different kinds of pinning centers of the sample were investigated by means of Dew-Hughes analysis, showing that the pinning mechanism in the sample can be described in the framework of the collective pinning theory. Finally, the values of the pinning force density have been calculated at different temperatures and compared with the literature in order to understand if the sample is promising for high-current and high-power applications.     

Drag Voltages in a Superconductor/Insulator/Ferromagnet Trilayer

The interaction between two spatially separated systems is of strong interest in order to study a wide class of unconventional effects at cryogenic temperatures. Here we report on drag transverse voltage effects in multilayered systems containing superconducting and ferromagnetic materials. The sample under test is a conventional superconductor/insulator/ferromagnet (S/I/F) trilayer in a cross configuration. S/F as well as S/N (here N stands for normal metal) bilayers in the same geometry are also analyzed for comparison. Current–voltage (I–V) characteristics measured at T = 4.2 K in the presence of a perpendicular magnetic field show strong peculiarities related to the interaction between the layers. The results are interpreted in terms of interaction effects between the layers.     

Enhancement of the critical current density in single-crystal Bi2Sr2CaCu2O8 superconductors by chemically induced disorder

The effect of metal substitution on the critical current densities of single-crystal PbxBi2-xSr2CaCu2O8 (x = 0 or x = 0.7) superconductors has been investigated. Substitution of lead was found to increase the average critical current density from 1 x 10(5) A/cm2 to 2 x 10(6) A/cm2 at 5 K in an applied magnetic field of 10 kilooersteds (1 oersted = 80 A/m). The order of magnitude increase in the critical current density was observed for temperatures up to the flux vortex lattice melting point; the flux lattice melting point was also found to increase to 30 K (from 22 K) in the lead-substituted materials. Diffraction and microscopy investigations of the structural parameters indicate that the fundamental atomic lattices are virtually the same for both materials. Scanning tunneling microscopy images demonstrate, however, that lead substitution causes significant disorder (or defects) in the one-dimensional superstructure found in Bi2Sr2CaCu2O8. Since crystal defects can increase the critical current density by pinning the motion of flux vortices, it is likely that this lead-induced disorder enhances vortex pinning. The lead-induced disorder is specific to the nonsuperconducting Bi-O layers, and thus our results suggest that chemical substitutions may be utilized to control selectively flux pinning and the critical current density in these materials.     

Magnetic and Magnetostrictive Properties of Ni50Mn20Ga27Cu3 Rapidly Quenched Ribbons

The influence of the rapid solidification technique and heat treatment on the martensitic transformation, magnetic properties, thermo- and magnetic induced strain and electrical resistivity is investigated for the Cu doped NiMnGa Heusler-based ferromagnetic shape memory ribbons. The martensitic transformation temperatures are unexpectedly low (below 90 K—which can be attributed to the disordered texture as well as to the uncertainty in the elements substituted by the Cu), preceded by a premartensitic transformation (starting at around 190 K). A thermal treatment slightly increases the transformation as well as the Curie temperatures. Additionally, the thermal treatment promotes a higher magnetization value of the austenite phase and a lower one in the martensite. The shift of the martensitic transformation temperatures induced by the applied magnetic field, quantified from thermo-magnetic and thermo-magnetic induced strain measurements, is measured to have a positive value of about 1 K/T, and is then used to calculate the transformation entropy of the ribbons. The magnetostriction measurements suggest a rotational mechanism in low fields for the thermal treated samples and a saturation tendency at higher magnetic fields, except for the temperatures close to the phase transition temperatures (saturation is not reached at 5 T), where a linear volume magnetostriction cannot be ruled out. Resistivity and magnetoresistance properties have also been measured for all the samples.     

Indication of Strongly Correlated Electron Transport and Mott Insulator in Disordered Multilayer Ferritin Structures (DMFS)

Electron tunneling in ferritin and between ferritin cores (a transition metal (iron) oxide storage protein) in disordered arrays has been extensively documented, but the electrical behavior of those structures in circuits with more than two electrodes has not been studied. Tests of devices using a layer-by-layer deposition process for forming multilayer arrays of ferritin that have been previously reported indicate that strongly correlated electron transport is occurring, consistent with models of electron transport in quantum dots. Strongly correlated electrons (electrons that engage in strong electron-electron interactions) have been observed in transition metal oxides and quantum dots and can create unusual material behavior that is difficult to model, such as switching between a low resistance metal state and a high resistance Mott insulator state. This paper reports the results of the effect of various degrees of structural homogeneity on the electrical characteristics of these ferritin arrays. These results demonstrate for the first time that these structures can provide a switching function associated with the circuit that they are contained within, consistent with the observed behavior of strongly correlated electrons and Mott insulators.     

Magnetic stripes and skyrmions with helicity reversals

It was recently realized that topological spin textures do not merely have mathematical beauty but can also give rise to unique functionalities of magnetic materials. An example is the skyrmion--a nano-sized bundle of noncoplanar spins--that by virtue of its nontrivial topology acts as a flux of magnetic field on spin-polarized electrons. Lorentz transmission electron microscopy recently emerged as a powerful tool for direct visualization of skyrmions in noncentrosymmetric helimagnets. Topologically, skyrmions are equivalent to magnetic bubbles (cylindrical domains) in ferromagnetic thin films, which were extensively explored in the 1970s for data storage applications. In this study we use Lorentz microscopy to image magnetic domain patterns in the prototypical magnetic oxide-M-type hexaferrite with a hint of scandium. Surprisingly, we find that the magnetic bubbles and stripes in the hexaferrite have a much more complex structure than the skyrmions and spirals in helimagnets, which we associate with the new degree of freedom--helicity (or vector spin chirality) describing the direction of spin rotation across the domain walls. We observe numerous random reversals of helicity in the stripe domain state. Random helicity of cylindrical domain walls coexists with the positional order of magnetic bubbles in a triangular lattice. Most unexpectedly, we observe regular helicity reversals inside skyrmions with an unusual multiple-ring structure.     

Valley Chern numbers and boundary modes in gapped bilayer graphene

Electronic states at domain walls in bilayer graphene are studied by analyzing their four- and two-band continuum models, by performing numerical calculations on the lattice, and by using quantum geometric arguments. The continuum theories explain the distinct electronic properties of boundary modes localized near domain walls formed by interlayer electric field reversal, by interlayer stacking reversal, and by simultaneous reversal of both quantities. Boundary mode properties are related to topological transitions and gap closures, which occur in the bulk Hamiltonian parameter space. The important role played by intervalley coupling effects not directly captured by the continuum model is addressed using lattice calculations for specific domain wall structures.     

Field-Induced Transversely Isotropic Shear Response of Ellipsoidal Magnetoactive Elastomers

Magnetoactive elastomers (MAEs) claim a vital place in the class of field-controllable materials due to their tunable stiffness and the ability to change their macroscopic shape in the presence of an external magnetic field. In the present work, three principal geometries of shear deformation were investigated with respect to the applied magnetic field. The physical model that considers dipole-dipole interactions between magnetized particles was used to study the stress-strain behavior of ellipsoidal MAEs. The magneto-rheological effect for different shapes of the MAE sample ranging from disc-like (highly oblate) to rod-like (highly prolate) samples was investigated along and transverse to the field direction. The rotation of the MAE during the shear deformation leads to a non-symmetric Cauchy stress tensor due to a field-induced magnetic torque. We show that the external magnetic field induces a mechanical anisotropy along the field direction by determining the distinct magneto-mechanical behavior of MAEs with respect to the orientation of the magnetic field to shear deformation.     

Expert consensus on the application of the magnetic anchoring and traction technique in thoracoscopic and laparoscopic surgery

Introduction The mutual interference between surgical instruments in tho-racoscopic and laparoscopic surgery and the effective exposure of the surgical field are important factors affecting surgical op-erability[1].Magnetic anchoring and traction is one of the core techniques of magnetic surgery,which uses magnetic materials to generate force through indirect contact to achieve traction expo-sure of the target organs[2](Fig.1).     

Influence of Magnetite Nanoparticles Shape and Spontaneous Surface Oxidation on the Electron Transport Mechanism

The spontaneous oxidation of a magnetite surface and shape design are major aspects of synthesizing various nanostructures with unique magnetic and electrical properties, catalytic activity, and biocompatibility. In this article, the roles of different organic modifiers on the shape and formation of an oxidized layer composed of maghemite were discussed and described in the context of magnetic and electrical properties. It was confirmed that Fe₃O₄ nanoparticles synthesized in the presence of triphenylphosphine could be characterized by cuboidal shape, a relatively low average particle size (9.6 ± 2.0 nm), and high saturation magnetization equal to 55.2 emu/g. Furthermore, it has been confirmed that low-frequency conductivity and dielectric properties are related to surface disordering and oxidation. The electric energy storage possibility increased for nanoparticles with a disordered and oxidized surface, whereas the dielectric losses in these particles were strongly related to their size. The cuboidal magnetite nanoparticles synthesized in the presence of triphenylphosphine had an ultrahigh electrical conductivity (1.02 × 10⁻⁴ S/cm at 10 Hz) in comparison to the spherical ones. At higher temperatures, the maghemite content altered the behavior of electrons. The electrical conductivity can be described by correlated barrier hopping or overlapping large polaron tunneling. Interestingly, the activation energies of electrons transport by the surface were similar for all the analyzed nanoparticles in low- and high-temperature ranges.     

Signatures of quantum criticality in pure Cr at high pressure

The elemental antiferromagnet Cr at high pressure presents a new type of naked quantum critical point that is free of disorder and symmetry-breaking fields. Here we measure magnetotransport in fine detail around the critical pressure, P_c ∼ 10 GPa, in a diamond anvil cell and reveal the role of quantum critical fluctuations at the phase transition. As the magnetism disappears and T → 0, the magntotransport scaling converges to a non-mean-field form that illustrates the reconstruction of the magnetic Fermi surface, and is distinct from the critical scaling measured in chemically disordered Cr∶V under pressure. The breakdown of itinerant antiferromagnetism only comes clearly into view in the clean limit, establishing disorder as a relevant variable at a quantum phase transition.     

Coupling of hydrogenic tunneling to active-site motion in the hydrogen radical transfer catalyzed by a coenzyme B12-dependent mutase

Hydrogen transfer reactions catalyzed by coenzyme B(12)-dependent methylmalonyl-CoA mutase have very large kinetic isotope effects, indicating that they proceed by a highly quantal tunneling mechanism. We explain the kinetic isotope effect by using a combined quantum mechanical/molecular mechanical potential and semiclassical quantum dynamics calculations. Multidimensional tunneling increases the magnitude of the calculated intrinsic hydrogen kinetic isotope effect by a factor of 3.6 from 14 to 51, in excellent agreement with experimental results. These calculations confirm that tunneling contributions can be large enough to explain even a kinetic isotope effect >50, not because the barrier is unusually thin but because corner-cutting tunneling decreases the distance over which the system tunnels without a comparable increase in either the effective potential barrier or the effective mass for tunneling.     

Quantum critical scaling at the edge of Fermi liquid stability in a cuprate superconductor

In the high-temperature cuprate superconductors, the pervasiveness of anomalous electronic transport properties suggests that violation of conventional Fermi liquid behavior is closely tied to superconductivity. In other classes of unconventional superconductors, atypical transport is well correlated with proximity to a quantum critical point, but the relative importance of quantum criticality in the cuprates remains uncertain. Here, we identify quantum critical scaling in the electron-doped cuprate material La(2-x)Ce(x)CuO(4) with a line of quantum critical points that surrounds the superconducting phase as a function of magnetic field and charge doping. This zero-temperature phase boundary, which delineates a metallic Fermi liquid regime from an extended non-Fermi liquid ground state, closely follows the upper critical field of the overdoped superconducting phase and gives rise to an expanse of distinct non-Fermi liquid behavior at finite temperatures. Together with signatures of two distinct flavors of quantum fluctuations, these facts suggest that quantum criticality plays a significant role in shaping the anomalous properties of the cuprate phase diagram.     

Strong Interfacial Perpendicular Magnetic Anisotropy in Exchange-Biased NiO/Co/Au and NiO/Co/NiO Layered Systems

The ability to induce and control the perpendicular magnetic anisotropy (PMA) of ferromagnetic layers has been widely investigated, especially those that offer additional functionalities (e.g., skyrmion stabilization, voltage-based magnetization switching, rapid propagation of domain walls). Out-of-plane magnetized ferromagnetic layers in direct contact with an oxide belong to this class. Nowadays, investigation of this type of system includes antiferromagnetic oxides (AFOs) because of their potential for new approaches to applied spintronics that exploit the exchange bias (EB) coupling between the ferromagnetic and the AFO layer. Here, we investigate PMA and EB effect in NiO/Co/Au and NiO/Co/NiO layered systems. We show that the coercive and EB fields increase significantly when the Co layer is coupled with two NiO layers, instead of one. Surrounding the Co layer only with NiO layers induces a strong PMA resulting in an out-of-plane magnetized system can be obtained without a heavy metal/ferromagnetic interface. The PMA arises from a significant surface contribution (0.74 mJ/m²) that can be enhanced up to 0.99 mJ/m² by annealing at moderate temperatures (~450 K). Using field cooling processes for both systems, we demonstrate a wide-ranging control of the exchange bias field without perturbing other magnetic properties of importance.     

Transverse Anderson Localization in Disordered Glass Optical Fibers: A Review

Disordered optical fibers show novel waveguiding properties that can be used for various device applications, such as beam-multiplexed optical communications and endoscopic image transport. The strong transverse scattering from the transversely disordered optical fibers results in transversely confined beams that can freely propagate in the longitudinal direction, similar to conventional optical fibers, with the advantage that any point in the cross section of the fiber can be used for beam transport. For beam multiplexing and imaging applications, it is highly desirable to make the localized beam radius as small as possible. This requires large refractive index differences between the materials that define the random features in the disordered fiber. Here, disordered glass-air fibers are briefly reviewed, where randomly placed airholes in a glass matrix provide the sufficiently large refractive index difference of 0.5 for strong random transverse scattering. The main future challenge for the fabrication of an optimally disordered glass-air fibers is to increase the fill-fraction of airholes to nearly 50% for maximum beam confinement.     

Structural Analysis of the Menangle Virus P Protein Reveals a Soft Boundary between Ordered and Disordered Regions

The paramyxoviral phosphoprotein (P protein) is the non-catalytic subunit of the viral RNA polymerase, and coordinates many of the molecular interactions required for RNA synthesis. All paramyxoviral P proteins oligomerize via a centrally located coiled-coil that is connected to a downstream binding domain by a dynamic linker. The C-terminal region of the P protein coordinates interactions between the catalytic subunit of the polymerase, and the viral nucleocapsid housing the genomic RNA. The inherent flexibility of the linker is believed to facilitate polymerase translocation. Here we report biophysical and structural characterization of the C-terminal region of the P protein from Menangle virus (MenV), a bat-borne paramyxovirus with zoonotic potential. The MenV P protein is tetrameric but can dissociate into dimers at sub-micromolar protein concentrations. The linker is globally disordered and can be modeled effectively as a worm-like chain. However, NMR analysis suggests very weak local preferences for alpha-helical and extended beta conformation exist within the linker. At the interface between the disordered linker and the structured C-terminal binding domain, a gradual disorder-to-order transition occurs, with X-ray crystallographic analysis revealing a dynamic interfacial structure that wraps the surface of the binding domain.     

From the Cover: Using thermal boundary conditions to engineer the quantum state of a bulk magnet

The degree of contact between a system and the external environment can alter dramatically its proclivity to quantum mechanical modes of relaxation. We show that controlling the thermal coupling of cubic-centimeter–sized crystals of the Ising magnet LiHo_xY_1-xF₄ to a heat bath can be used to tune the system between a glassy state dominated by thermal excitations over energy barriers and a state with the hallmarks of a quantum spin liquid. Application of a magnetic field transverse to the Ising axis introduces both random magnetic fields and quantum fluctuations, which can retard and speed the annealing process, respectively, thereby providing a mechanism for continuous tuning between the destination states. The nonlinear response of the system explicitly demonstrates quantum interference between internal and external relaxation pathways.The coupling of a sample to its environment is both a fundamental theoretical concept and a powerful experimental tool in classical thermodynamics. For quantum systems, contact between the internal degrees of freedom and the external world, often referred to as the “bath,” can change the measured outcome completely. Typically, such experiments involve a small number of particles sensitive to subtle changes in the external incoherent environment, such as ultracold atoms confined in precisely controlled optical potentials (1–3). With the search for viable solid-state qubits for quantum computing, the control of bath-induced decoherence in solids also has become an important topic for engineers and condensed-matter physicists. Approaches have centered on the nuclear spin bath (4–6), modifying it either with isotopic substitution (7) or radio frequency pulses (8), and on electrical control of the exchange interaction between electron spins in coupled quantum dots (9). The question of the importance of coupling to an external bath, as provided by a cryostat, has not been researched as intensively. Here, we show that by engineering the thermal boundary conditions for a macroscopic magnetic crystal, it is possible to select distinct low temperature states. Conditions of constant energy, as opposed to constant temperature, yield relatively fewer low energy contributions to the fluctuation spectrum and decouple the spin excitations responsible for that spectrum into separate oscillators. The experiments show the importance of thermal heat sinking for quantum annealing, also referred to as adiabatic quantum computation (10–13), as well as new protocols for generating quantum cluster states (14).The LiHo_xY_1-xF₄ family of insulating magnetic salts provides a physical manifestation of the simplest quantum mechanical spin model, the Ising model in transverse field (15). Pure LiHoF₄ (16, 17) is a ferromagnet with Curie temperature, T_C = 1.53 K. External magnetic fields can produce the longitudinal and transverse fields in the model, chemical substitution of Ho³⁺ ions by the nonmagnetic species Y³⁺ provides quenched disorder, and the anisotropy of the dipolar coupling produces random internal transverse fields (18–21) as well as competing ferromagnetic and antiferromagnetic interactions. The combination of site dilution and external fields yields a wide variety of collective magnetic states, ranging from random field ferromagnet at x = 0.44 (22) to quantum spin glass at x = 0.167 (23). We focus here on the dilute limit of x = 0.045, for which there have been seemingly contradictory findings concerning the ground state.The primary diagnostic of the ground state has been the AC magnetic susceptibility, whose imaginary part χ″(f) is the quotient of the long-wavelength magnetic fluctuation spectrum, S(f), and the Bose factor, (n(hf) + 1) = 1/(1-exp-hf/kT), where h and k are Planck’s and Boltzmann’s constants, respectively. For our experiments, hf<<kT and hence χ″(f) = hf/kT S(f). The frequency at which the imaginary part peaks indicates the characteristic relaxation rate of the system, which for spin dynamics dominated by thermal activation over energy barriers will vary in accord with the Arrhenius law, (15, 24, 25), precisely what we see for temperatures 0.15 K < T < 1 K. Below T ∼ 0.15 K, deviations from Arrhenius behavior emerge (15, 24, 25); however, the nature of the deviations and their interpretation has been contested (26). One class of experiments found a low-frequency narrowing of the spectrum with decreasing T (24, 27, 28), accompanied by the magnetic equivalent of optical hole burning in the nonlinear response, where effectively isolated, mesoscopic clusters of spins can be addressed and manipulated using a pump/probe technique (24). A magnetic field applied transverse to the Ising axis introduces quantum fluctuations, and can influence the relaxation pathways of the coherent clusters (28). Moreover, muon spin-relaxation (µSR) studies have shown that the persistent spin-fluctuation rate remains constant down to T = 0.02 K, consistent with a spin-liquid ground state (29). By contrast, a second class of magnetic susceptibility studies found that LiHo_0.045Y_0.955F₄ behaved as a paramagnet approaching a spin–glass transition, which extrapolation suggests to occur at T_g ∼0.04 K, with a magnetic fluctuation spectrum that broadened symmetrically as the temperature was lowered (25). In this picture, the characteristic dissipative response moves more quickly to low frequency as the system as a whole freezes.The most significant distinction between the two classes of susceptibility experiments is the heat sinking of the sample to the cryostat. For the measurements yielding a spin liquid, a single crystal measuring (5 × 5 × 10) mm³ was heat sunk by sapphire rods pressed against the sample on either end of the long axis (24); in the spin–glass case a (0.57 × 0.77 × 7.7) mm³ sample was glued to a sapphire rod running along its length (25). The sapphire rods are then thermally anchored to the mixing chamber of the dilution refrigerator, coupling them to the environmental heat bath. If the thermal boundary conditions of the sample change appreciably, then the internal state of the system also may be expected to change. Just as the application of a transverse magnetic field affects the spin cluster dynamics and their coupling to the external world in this system (28), thermal boundary conditions can enhance or destroy isolated spin degrees of freedom, tune the system between classical and quantum mechanical limits (30), and alter the relative energies of competing ground states.     

Observation of a superfluid Hall effect

Measurement techniques based upon the Hall effect are invaluable tools in condensed-matter physics. When an electric current flows perpendicular to a magnetic field, a Hall voltage develops in the direction transverse to both the current and the field. In semiconductors, this behavior is routinely used to measure the density and charge of the current carriers (electrons in conduction bands or holes in valence bands)--internal properties of the system that are not accessible from measurements of the conventional resistance. For strongly interacting electron systems, whose behavior can be very different from the free electron gas, the Hall effect's sensitivity to internal properties makes it a powerful tool; indeed, the quantum Hall effects are named after the tool by which they are most distinctly measured instead of the physics from which the phenomena originate. Here we report the first observation of a Hall effect in an ultracold gas of neutral atoms, revealed by measuring a Bose-Einstein condensate's transport properties perpendicular to a synthetic magnetic field. Our observations in this vortex-free superfluid are in good agreement with hydrodynamic predictions, demonstrating that the system's global irrotationality influences this superfluid Hall signal.     

Thermal-activated protein mobility and its correlation with catalysis in thermophilic alcohol dehydrogenase

Temperature-dependent hydrogen-deuterium (H/D) exchange of the thermophilic alcohol dehydrogenase (htADH) has been studied by using liquid chromatography-coupled mass spectrometry. Analysis of the changes in H/D exchange patterns for the protein-derived peptides suggests that some regions of htADH are in a rigid conformational substate at reduced temperatures with limited cooperative protein motion. The enzyme undergoes two discrete transitions at approximately 30 and 45 degrees C to attain a more dynamic conformational substate. Four of the five peptides exhibiting the transition above 40 degrees C are in direct contact with the cofactor, and the NAD(+)-binding affinity is also altered in this temperature range, implicating a change in the mobility of the cofactor-binding domain >45 degrees C. By contrast, the five peptides exhibiting the transition at 30 degrees C reside in the substrate-binding domain. This transition coincides with a change in the activation energy of k(cat) for hydride transfer, leading to a linear correlation between k(cat) and the weighted average exchange rate constant k(HX(WA)) for the five peptides. These observations indicate a direct coupling between hydride transfer and protein mobility in htADH, and that an increased mobility is at least partially responsible for the reduced E(act) at high temperature. The data provide support for the hypothesis that protein dynamics play a key role in controlling hydrogen tunneling at enzyme active sites.     

Effective Magnetic Field Dependence of the Flux Pinning Energy in FeSe0.5Te0.5 Superconductor

The role of a layered structure in superconducting pinning properties is still at a debate. The effects of the vortex shape, which can assume for example a staircase form, could influence the interplay with extrinsic pinning coming from the specific defects of the material, thus inducing an effective magnetic field dependence. To enlighten this role, we analysed the angular dependence of flux pinning energy U(H,θ) as a function of magnetic field in FeSe_0.5Te_0.5 thin film by considering the field components along the ab-plane of the crystal structure and the c-axis direction. U(H,θ) has been evaluated from magneto-resistivity measurements acquired at different orientations between the applied field up to 16 T and FeSe_0.5Te_0.5 thin films grown on a CaF₂ substrate. We observed that the U(H,θ) shows an anisotropic trend as a function of both the intensity and the direction of the applied field. Such a behaviour can be correlated to the presence of extended defects elongated in the ab-planes, thus mimicking a layered superconductor, as we observed in the microstructure of the compound. The comparison of FeSe_0.5Te_0.5 with other superconducting materials provides a more general understanding on the flux pinning energy in layered superconductors.