Gap Amplitude Research Articles

D-wave charge-4e superconductivity from fluctuating pair density waves

We present a theory for charge-4e superconductivity as a leading low-temperature instability with a nontrivial d-wave symmetry. We show that in several microscopic models for the pair-density-wave (PDW) state, when the PDW wave vectors connect special parts of the Fermi surface, the predominant interaction is in the bosonic pairing channel mediated by exchanging low-energy fermions. This bosonic pairing interaction is repulsive in the s-wave channel but attractive in the d-wave one, leading to a d-wave charge-4e superconductor. By analyzing the Ginzburg-Landau free energy including higher-order fluctuation effects of PDW, we find that the charge-4e superconductivity emerges as a vestigial order of PDW, and sets in via a first-order transition. Both the gap amplitude and the transition temperature decay monotonically with increasing superfluid stiffness of the PDW order. Our work provides a microscopic mechanism of higher-charge condensates with unconventional ordering symmetry in strongly-correlated materials.

Superconductivity of Co-Doped CaKFe4As4 Investigated via Point-Contact Spectroscopy and London Penetration Depth Measurements.

The iron-based superconductors (IBSs) of the recently discovered 1144 class, unlike many other IBSs, display superconductivity in their stoichiometric form and are intrinsically hole doped. The effects of chemical substitutions with electron donors are thus particularly interesting to investigate. Here, we study the effect of Co substitution in the Fe site of CaKFe4As4 single crystals on the critical temperature, on the energy gaps, and on the superfluid density by using transport, point-contact Andreev-reflection spectroscopy (PCARS), and London penetration depth measurements. The pristine compound (Tc≃36 K) shows two isotropic gaps whose amplitudes (Δ1 = 1.4-3.9 meV and Δ2 = 5.2-8.5 meV) are perfectly compatible with those reported in the literature. Upon Co doping (up to ≈7% Co), Tc decreases down to ≃20 K, the spin-vortex-crystal order appears, and the low-temperature superfluid density is gradually suppressed. PCARS and London penetration depth measurements perfectly agree in demonstrating that the nodeless multigap structure is robust upon Co doping, while the gap amplitudes decrease as a function of Tc in a linear way with almost constant values of the gap ratios 2Δi/kBTc.

A Gap Nonlinearity Compensation Strategy for Non-Direct-Drive Servo Systems

In this paper, a gap nonlinear compensation strategy is proposed for the full closed-loop control structure of non-direct-drive servo motor systems. Firstly, an improved deadband model containing the initial value of the gap is proposed, and two gap amplitude identification methods, namely, incremental torque and velocity difference integral, are compared. Then, for the full closed-loop structure, based on the describing function and the stability theory of the nonlinear system, the limit-loop oscillating frequency and the influencing factors are predicted, which are related to the system control stiffness and independent of the gap amplitude; finally, the state-feedback control is proposed, and the feedback coefficients are designed by using the pole configuration, making the system a pseudo-linear system. Simulation and experimental verification show that the method can suppress the limit loop oscillation, attenuate the system shock, and have a certain robustness.

Piezoelectric-triboelectric energy harvester with elastic double-side stoppers

An impact-based piezoelectric and triboelectric energy harvester with elastic double-side stoppers for wideband operation and efficient energy capture is proposed. The coupled nonlinear governing equations of the energy harvesting system are derived based on Hertz's contact model. The dynamic behavior of the energy harvester is enriched from linear to nonlinear regime by introducing stoppers to broaden the energy harvesting frequency range. The dynamic mechanism and energy harvesting performance of the harvester are explored through frequency sweeps, which identify comprehensive dynamic states and evaluate the energy harvesting performance. The time history diagram, phase diagram, Poincaré mapping and bifurcation diagram are used to discuss the single-period, double-period, multi-period and chaotic period vibrations of the energy harvester. Detailed parametric studies investigate the effects of the initial gap, mass ratio, stopper stiffness and excitation amplitude on the voltage and power output. Four models with different stoppers are compared to identify the best energy harvesting performance. Results show that compared with the cantilever without stopper, the proposed model with elastic double-side stoppers significantly broadens the resonance frequency region by 172.5 %, and increases the output cumulative voltage by 0.89 V. A maximum voltage of 1.2 V with a 0.6-V-bandwidth of 6.9 Hz is achieved when the energy harvester is actuated at 0.8 g acceleration. The RMS voltage of triboelectric nanogenerator is highest at 25 Hz, reaching 1.99 V, and the peak-to-peak output voltage reaches 15.59 V.

Spectral Analysis of Proton Eigenfunctions in Crystalline Environments

The Schrödinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and non-quadratic potentials, in both one-dimensional and three-dimensional scenarios. Numerical computation of the energy spectrum of bound eigenfunctions in both cases reveals intriguing structures, including bound states with degeneracy matching the site number Nw, reminiscent of a finite harmonic oscillator spectrum. In contrast to electronic energy bands, the proton system displays a greater number of possible bound states due to the significant mass of protons. Extending previous research, this study rigorously determines the constraints on the energy gap and oscillation amplitude of the previously identified coherent states. The deviations in energy level spacing identified in the computed spectrum, leading to the minor splitting of electromagnetic modes, are analyzed and found not to hinder the onset of coherence. Finally, a more precise value of the energy gap is determined for the proton coherent states, ensuring their stability against thermal decoherence up to the melting temperature of the hosting metal.

Superconducting and charge-ordered states in the anisotropic t–J–U model

Motivated by the effect of symmetry breaking in cuprates superconductors YBa2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}Cu3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document}O7-δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{7-\\delta }$$\\end{document}, we employ the renormalized mean-field theory to study the presence of uniform superconducting and charge-ordered states in two anisotropic t–J–U models, either with hopping strength anisotropy or antiferromagnetic interaction anisotropy. In the case of uniform superconducting state, compared with the isotropic t–J–U model with only dx2-y2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d_{x^2-y^2}$$\\end{document}-wave superconducting state, there is an additional s-wave superconducting state in the model with hopping strength anisotropy. Meanwhile, the hopping anisotropy may enhance the critical Coulomb interaction Uc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$U_c$$\\end{document} at the Mott insulator to the Gossamer superconductor transition point, and strong hopping anisotropy may weaken the superconducting state. In the case of a charge-ordered state, hopping anisotropy may suppress the amplitude of the charge density waves and pair density waves, which originate from local Coulomb interactions. These results indicate that the effects of hopping anisotropy and local Coulomb interactions are competitive. Moreover, the antiferromagnetic interaction anisotropy only weakly suppresses the superconducting gap and density wave amplitude. Our results show that the t–J–U model with hopping anisotropy is qualitatively consistent with experimental superconducting pair symmetry and charge density waves in the YBa2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}Cu3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document}O7-δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{7-\\delta }$$\\end{document} system.

Evidence for d-wave superconductivity of infinite-layer nickelates from low-energy electrodynamics.

The discovery of superconductivity in infinite-layer nickelates established another category of unconventional superconductors that shares structural and electronic similarities with cuprates. However, key issues of the superconducting pairing symmetry, gap amplitude and superconducting fluctuations are yet to be addressed. Here we utilize static and ultrafast terahertz spectroscopy to address these. We demonstrate that the equilibrium terahertz conductivity and non-equilibrium terahertz responses of an optimally Sr-doped nickelate film (superconducting transition temperature of Tc = 17 K) are in line with the electrodynamics of d-wave superconductivity in the dirty limit. The gap-to-Tc ratio (2Δ/kBTc) is found to be 3.4, indicating that the superconductivity falls in the weak coupling regime. In addition, we observed substantial superconducting fluctuations near Tc that do not extend into the deep normal state as the optimally hole-doped cuprates do. Our results support a d-wave system that closely resembles the electron-doped cuprates.

Parameter optimization of electromagnetic suspension-type maglev train control system based on multi-objective grey wolf non-dominated sorting hybrid algorithm-Ⅱ hybrid algorithm

This paper presents a novel hybrid algorithm based on CMOGWO-ADNSGA-II to solve the vibration stability problem during the operation of a EMS-type maglev train dynamics model subjected to strong non-linear magnetic buoyancy. The proposed algorithm optimizes the control system parameters of EMS-type maglev train suspensions by combining an improved multi-objective chaotic grey wolf algorithm (CMOGWO) with an improved non-dominated Sorting genetic algorithm-II (ADNSGA-II) to enhance the search capability of the algorithm and ensure population diversity. The efficacy of the algorithm is demonstrated by applying it to the EMS-type maglev train suspension frame control system to find the optimal control parameters. Experimental results show that the system with the optimal parameters applied significantly reduces the suspension gap amplitude and the corresponding standard deviation, as well as the vertical acceleration amplitude and the corresponding standard deviation during operation. The proposed algorithm provides a good solution for EMS-type maglev train suspension vibration control, which can improve its performance and safety.

Nonlinear vibration characteristics and bifurcation control of a class of piecewise constrained systems with dynamic clearances

Considering the mass block system under Piecewise nonlinear constraint, the vibration dynamic model of the system is established according to the generalized dissipative Lagrange principle, and the average method is used to solve the amplitude-frequency response of the vibration system. The influence of system parameters on vibration characteristics is analyzed with amplitude-frequency characteristics, phase plane characteristics, frequency characteristics, bifurcation characteristics ,and so on. The results show that: 1) the reverse of the rate of change of Piecewise nonlinear elastic force will destroy the stability of the system and obtain the relationship of the constraint parameters that need to be satisfied when the system is stable at the piecewise critical point. 2) With the increase in the number of nonlinear constraints, the vibration displacement of the system tends to be chaotic, and the frequency composition becomes more complex and variable, prone to resonance behavior. 3) As the static gap decreases and the dynamic gap amplitude and frequency increase, the unstable frequency range of the system will increase, and the vibration behavior will become chaotic and difficult to predict. 4) The design of a differential sliding mode controller can effectively control the bifurcation behavior of the system.

Cyclic behavior of channel-encased braces incorporating round HSS

Bracings made with cold-formed round hollow structural shapes (HSS) are commonly utilized in ductile concentrically braced frames (CBFs) in seismic regions for their efficiency in terms of high load-bearing capacity and ease of construction. Bracings are expected to sustain a ductility demand that ranges between 10 and 20 without fracture when ductile CBFs subject to severe earthquake ground motions. However, the experimental findings accentuate that ductile braces, even those with round HSS that possess impractically small diameter-to-wall thickness ratios (D/t), are prone to premature fracture. Thus, developing a simple and cost-effective performance-enhancing system for existing conventional CBFs incorporating round HSS could be imperative to mitigate the potential seismic risk. For this purpose, an existing round HSS is encased in two channels to form a buckling-controlling mechanism that is expected to improve the seismic hysteretic behavior, consequently, the energy dissipation capacity of ductile braces. Experimental and parametric numerical studies have been conducted to comprehend the level of improvement in the cyclic behavior and the impact of geometric parameters (i.e., slenderness and D/t ratios). The overarching results indicate that channel-encased bracing improves the seismic hysteretic behavior, yielding a stable and symmetric cyclic response. In addition, the results suggest that the optimal design parameters, including gap amplitude and encasing thickness, play a critical role in achieving desired ductility level.

A model for critical current effects in point-contact Andreev-reflection spectroscopy

It is well known that point-contact Andreev-reflection spectroscopy provides reliable measurements of the energy gap(s) in a superconductor when the contact is in the ballistic or diffusive regime. However, especially when the mean free path of the material under study is small, obtaining ballistic contacts can be a major challenge. One of the signatures of a Maxwell contribution to the contact resistance R is the presence of “dips” in the differential conductance, associated with the sudden appearance of a Maxwell term, in turn, due to the attainment of the critical current of the material in the contact region. Here we show that using a proper model for the R(I) of the material under study, it is possible to fit the experimental curves (without the need of normalization) obtaining the correct values of the gap amplitudes even in the presence of such dips, as well as the temperature dependence of the critical current in the contact. We present a test of the procedure in the case of Andreev-reflection spectra in Mg0.85Al0.15B2 single crystals.

Fluid-structure interaction and band gap analysis of periodic composite liquid-filled pipe

This paper studies the vibration band gap characteristics of a liquid-filled composite pipeline. The transfer matrix method is used to create a one-dimensional fluid–structure interaction model of the composite pipeline from the constitutive equation, physical equations, and boundary conditions of the anisotropic material. A phononic crystal pipeline is designed with a periodic arrangement on the axial pipe wall. The method used to analyze the fluid–structure interaction of liquid-filled composite and phononic crystal pipelines is verified by comparing responses with finite-element method results. The results’ agreement demonstrates the method’s and calculation code’s correctness. Furthermore, the band gaps for an empty composite phononic crystal pipe, water hammer, and a liquid-filled pipe are calculated by Bloch vector theory, and the effects of fluid–structure interaction and the composite parameters on the three band gap characteristics are analyzed. The numerical results show that Poisson’s coupling affects the band gap at some frequency points, while the laying angle and fiber volume fraction in the composite pipe influence the band gap length and amplitude change. The research results of this paper provide a reference for the design and vibration control of liquid-filled composite pipelines.

Thermodynamic evidence for a field-angle-dependent Majorana gap in a Kitaev spin liquid

The exactly-solvable Kitaev model of two-dimensional honeycomb magnet leads to a quantum spin liquid (QSL) characterized by Majorana fermions, relevant for fault-tolerant topological quantum computations. In the high-field paramagnetic state of $\alpha$-RuCl3, half-integer quantization of thermal Hall conductivity has been reported as a signature of edge current, but the bulk nature of this state remains elusive. Here, from high-resolution heat capacity measurements under in-plane field rotation, we find strongly angle-dependent low-energy excitations in bulk $\alpha$-RuCl3. The excitation gap has a sextuple node structure, and the gap amplitude increases with field, exactly as expected for itinerant Majorana fermions in the Kitaev model. Our thermodynamic results are fully linked with the transport quantization properties, providing the first demonstration of the bulk-edge correspondence in a Kitaev QSL. Moreover, at higher fields where the quantum thermal Hall effect vanishes, we find the possible emergence of a novel nematic QSL state with two-fold rotational symmetry.

On negative effective mass and negative group velocity in anharmonic seismic metamaterials

In this work, an anharmonic mass-in-mass system that can be employed as a nonlinear seismic metamaterial is represented as an equivalent anharmonic mass-spring system via an effective medium approach. The dispersion relation and the behavior of the effective mass as a function of the angular frequency obtained in the regime of weak anharmonicity deviate from those of the corresponding linear system because of the effect of the fourth-order potential anharmonicity. In the presence of anharmonic soft springs it is found a range of wave vectors close to the Brillouin border zone at which the group velocity of the acoustic and optical modes is negative, namely it is opposite to the phase velocity, and a wider band gap at the border of the first Brillouin zone with respect to that of the linear case. Both effects can be tuned by varying the anharmonicity strength. The huge band gap amplitude together with the strong reduction of the frequency of the acoustic mode could be exploited for the design of nonlinear seismic metamaterials at the basis of composite foundations operating in the stop band frequencies.

Vocal Fold Vibration Characteristics during SOVTE using a Vibration Simulator and Digital Kymography

Objectives: The purpose of this study is to investigate the characteristics of vocal fold vibration during sustained vowel /a/ phonation and various semi-occluded vocal tract exercise (SOVTEs) using a vibration simulator and digital kymography (DKG).Methods: A total of 12 normal young speakers (6 males, 6 females) aged 20-30 years participated in the study. They phonated a sustained /a/ vowel and performed SOVTE. The vocal fold vibration characteristics were measured according to the number of vibration sources (single vs. double), and vocal tract occlusion degree using a vibration simulator and DKG. Glottal gap quotient (GQ, %), speed quotient (SQ, %) and amplitude (pixel) were estimated quantitatively from the DKG image.Results: The results showed that significantly higher GQ (p = .000) and SQ (p = .000) were observed in the humming and bilabial fricative /β/ compared to open vowels. The amplitude was significantly higher in the open vowel /a/ than in humming (p = .018) and bilabial fricative /β/ (p = .003). Also, when comparing the vocal fold vibration parameters according to vibration type (single source: straw phonation vs. double source: straw phonation with water), the double source presented a significantly higher GQ (p = .000) as well as SQ (p = .008) in comparison with a single source.Conclusion: SOVTE showed a glottal gap that is different from the opened vowel /a/. It also had a longer opening of the vocal fold and a smaller amplitude than the vowel. This suggests that SOVTE may be helpful for facilitating vocal fold vibration and good voice quality in clinical practice. The current study can be meaningful in providing theoretical and clinical evidence for SOVTE.

Influence of the gap size on the response of a single-degree-of-freedom vibro-impact system with two-sided constraints: Experimental tests and numerical modeling

The large displacements caused by strong earthquakes in base-isolated structures (buildings, bridges, strategic facilities, equipment, ⋯) can excessively deform or damage the isolation system or lead to pounding with surrounding moat walls or adjacent structures, if the available seismic gap is not sufficient. The acceleration spikes caused by the impact can damage the structure itself as well as sensitive equipment housed in it. A possible mitigation measure consists in the interposition of deformable shock absorbers (bumpers). In this paper, the influence of the gap amplitude on the experimental response of a single-degree-of-freedom oscillator, excited by a harmonic base acceleration and symmetrically constrained by two unilateral deformable and dissipative bumpers, is investigated. The parametric investigation considered both positive, null, and negative gaps. Particular attention is paid to the study of the effect, on the system response, of the transition from positive to small negative gaps and of excessive negative gaps. Secondary resonances in the low frequency range, associated with the occurrence of multiple impacts, were experimentally observed for small positive gaps. Finally, the experimental results were reproduced, in a sufficiently accurate manner, using a suitable numerical model, whose parameters were identified based on the experimental data.

Quantum transport in flat bands and supermetallicity

Quantum physics in flat-band (FB) systems embodies a variety of exotic phenomenon and even counter intuitive features. The quantum transport in several graphene based compounds that exhibit a flat band and a tunable gap is investigated. Despite the localized nature of the FB states and a zero group velocity, a super-metallic (SM) phase at the FB energy is revealed. The SM phase is robust against the inelastic scattering strength and controlled only by the inter-band transitions between the FB and the dispersive bands. The SM phase appears insensitive and quasi independent of the gap amplitude and nature of the lattice (disordered or nano-patterned). The universal nature of the unconventional FB transport is illustrated with the case of electrons in the Lieb lattice.

Nematic superconductivity in LiFeAs

The role of nematic order for the mechanism of high-temperature superconductivity is highly debated. In most iron-based superconductors (IBS) the tetragonal symmetry is broken already in the normal state, resulting in orthorhombic lattice distortions, static stripe magnetic order, or both. Superconductivity then emerges, at least at weak doping, already from the state with broken $C_4$ rotational symmetry. One of the few stoichiometric IBS, lithium iron arsenide, superconducts below 18 K and does not display either structural or magnetic transition in the normal state. Here we demonstrate, using angle-resolved photoemission, that even superconducting state in LiFeAs is also a nematic one. We observe spontaneous breaking of the rotational symmetry in the gap amplitude on all Fermi surfaces, as well as unidirectional distortion of the Fermi pockets. Remarkably, these deformations disappear above superconducting $T_c$. Our results demonstrate the realization of a novel phenomenon of superconductivity-induced nematicity in IBS, emphasizing the intimate relation between them. We suggest a theoretical explanation based on the emergence of a secondary instability inside the superconducting state, which leads to the nematic order and s-d mixing in the gap function.

The role of mechanical stimulation in the enhancement of bone healing.

The biomechanical environment plays a dominant role in the process of fracture repair. Mechanical signals control biological activities at the fracture site, regulate the formation and proliferation of different cell types, and are responsible for the formation of connective tissues and the consolidation of the fractured bone. The mechanobiology at the fracture site can be easily manipulated by the design and configuration of the fracture fixation construct and by the loading of the extremity (weight-bearing prescription). Depending on the choice of fracture fixation, the healing response can be directed towards direct healing or towards indirect healing through callus formation. This manuscript summarizes the evidence from experimental studies and clinical observations on the effect of mechanical manipulation on the healing response. Parameters like fracture gap size, interfragmentary movement, interfragmentary strain, and axial and shear deformation will be explored with respect to their respective effects on fracture repair. Also, the role of externally applied movement on the potential enhancement on the fracture repair process will be explored. Factors like fracture gap size, type and amplitude of the mechanical deformation as well as the loading history and its timing will be discussed.

Atomic structures and nanoscale electronic states on the surface of MgB2 superconductor observed by scanning tunneling microscopy and spectroscopy

The systematic study of the nanoscale local electronic states on the MgB2 surface was performed using the low-temperature scanning tunnel microscopy/spectroscopy (STM/STS). The STM topography shows the atomic image of the hexagonal lattice with the constant parameter a’ = 0.31 nm, which is identified as mainly the Mg site occupancy. The temperature-dependent STS measurements were analyzed assuming the existence of two energy gaps. As a result, the fitting gap amplitudes Δfit ≃ 10.2 meV and 4.8 meV were found at T = 4.9 K. The scanned conductance (dI/dV) maps in the area of 4 × 2 nm2 show homogenous distributions of the gaps associated with the π-band. In addition, the conductance peaks at zero-bias voltage were observed through defined lines with lengths about ∼0.8 nm, which is much smaller than the superconducting coherence length ξab∼40nm of MgB2. The form of the zero-bias peaks looks like that in the case of the Andreev-Saint-James reflection at the tip-sample contact.