Condensation Energy Research Articles

General Properties of Conventional and High-Temperature Superconductors

In our review, we analyze the scaling of the condensation energy EΔ divided by γ, EΔ/γ≃N(0)Δ12/γ, and quasiparticles of both conventional and unconventional superconductors, where N(0) is the density of states at zero temperature T=0, Δ1 is the maximum value of the superconducting gap, and γ is the Sommerfeld coefficient. It is shown that Bogoliubov quasiparticles act in superconducting states of unconventional and conventional superconductors. At the same time, quasiparticles are also present in the normal state of unconventional superconductors. We briefly describe the difference between unconventional superconductors and conventional ones, such as the resistivity in normal states and the difference in superfluid density in superconducting states. For the first time, we theoretically show that the universal scaling of EΔ/γ∝Tc2 applies equally to both conventional and unconventional superconductors. Our consideration is based on two experimental facts: Bogoliubov quasiparticles act in conventional and non-conventional superconductors and the corresponding flat band is deformed by the non-conventional superconducting state. As a result, our theoretical observations based on the theory of fermion condensation agree well with the experimental facts.

Spectral condensation and bidirectional energy transfer in quasi-geostrophic turbulence above small-scale topography

Spectral condensation and bidirectional energy transfer in quasi-geostrophic turbulence above small-scale topography

Enhanced contribution of the pairing gap to the QCD equation of state at large isospin chemical potential

In this paper QCD at large isospin density is studied, which is known to be in the superfluid state with Cooper pairs carrying the same quantum number as pions. The gap equation derived from the perturbation theory up to the next-to-leading-order corrections is solved. The pairing gap at large isospin chemical potential is found to be enhanced compared to the color-superconducting gap at large baryon chemical potential due to the 2 difference in the exponent arising from the stronger attraction in one-gluon exchange in the singlet channel. Then, using the gap function, the contribution of the condensation energy of the superfluid state to the QCD equation of state is evaluated. At isospin chemical potential of a few GeV, where the lattice QCD and the perturbative QCD can be both applied, the effect of the condensation energy becomes dominant even compared to the next-to-leading order corrections to the pressure in the perturbation theory. It resolves the discrepancy between the recent lattice QCD results and the perturbative QCD result. Published by the American Physical Society 2024

The impact of the distribution of the condensation energy adsorbed in the water pool on the DCC efficiency at sub-atmospheric pressure

The safety of a fusion reactor like ITER relies on the reliability of the pressure suppression system (for keeping pressure below 0.15 MPa during accidental scenarios), and, in turn, on the efficiency of Direct Contact Condensation (DCC).In this study, the role played by the distribution of the condensation energy in the water is analysed considering the experimental results of temperature and pressure recorded during steam condensation tests in a closed volume at sub-atmospheric conditions.The investigation of the mechanisms involved in the condensation at the water-steam interface is fundamental to verify that the subcooled water mass fully participates into the steam condensation for all the foreseen condensation regimes. Particularly, the paper analyses the distribution of the condensation energy in a water pool for different test conditions and with reference to the large-scale facility under operation at the DICI-University of Pisa.The subcooled water volume of the condensation tank in this system was assumed subdivided in 104 annular discrete volumes corresponding to the location of temperature and pressure sensors (testing monitoring points). Moreover, this discretization was used to implement a model to visualize the experimental data and in particular the accumulation of the condensation energy in the different part of the water pool and of the vacuum space.The experimental results showed that most of the tests had a participating fraction of water mass greater than 50%. Nevertheless, the non-uniformity and stratification of the temperature in the water pool requires a greater water mass for condensing a given steam mass. The analyses of steady state pure steam condensation tests determined that it needs to increase 1.39 times the water mass respect to the case of full participation of the water at the steam condensation.

Charge stripes in the graphene-based materials

We present an analytical model of the charge density wave instability in graphene sheets within the intercalated graphite CaC6 compound. The instability yields the experimentally observed uniaxial charge stripes of periodically modulated electron density, coupled to the softest phonon mode of the superlattice consisting of the Ca atoms intercalated between graphene planes. The Fermi surface of the chemically doped graphene undergoes the novel type of instability driven by the mechanism that gains the condensation energy of the stripe state by the topological reconstruction of the Fermi surface. This mechanism appears to be entirely different from the one based on the Fermi surface nesting, which has been considered a paradigm in the present literature concerning the onset of charge density waves.

Correlation between phase stiffness and condensation energy across the non-Fermi to Fermi-liquid crossover in the Yukawa-Sachdev-Ye-Kitaev model on a lattice

Correlation between phase stiffness and condensation energy across the non-Fermi to Fermi-liquid crossover in the Yukawa-Sachdev-Ye-Kitaev model on a lattice

Statistics of the cuprate pairon states on a square lattice

In this paper the fundamental parameters of high-Tc superconductivity are shown to be connected to the statistics of pairons (hole pairs in their antiferromagnetic (AF) environment) on a square lattice. In particular, we study the density fluctuations and the distribution of the area surrounding each pairon on the scale of the AF correlation length , for the complete range of hole concentration. We show that the key parameters of the phase diagram, the Tc dome, and the pseudogap (PG) temperature , emerge from the statistical properties of the pairon disordered state. In this approach, the superconducting and the PG states appear as inseparable phenomena. The condensation energy, which fixes the critical temperature, is directly proportional to the correlation energy between pairons and not to the energy gap, contrary to conventional superconductors. When the correlation energy between pairons is suppressed by fluctuations, either thermally, by disorder, or in the vortex core, the PG state of disordered pairons is obtained. We attribute the unique features of cuprate superconductivity to this order–disorder transition in real space, which clearly differs from the Bardeen–Cooper–Schrieffer mechanism. Our predictions are in quantitative agreement with low-temperature tunneling and photoemission spectroscopy experiments.

Holographic superfluid with gauge–axion coupling

We have constructed a holographic superfluid with gauge–axion coupling. Depending on whether the coupling is positive or negative, the system displays metallic or insulating behavior in its normal state. A significant feature of the system is the appearance of a mid-IR peak in the alternating current (AC) conductivity in a certain range of parameters. This peak arises due to competition between explicit symmetry breaking (ESB) and spontaneous symmetry breaking (SSB), which results in the presence of a pseudo-Goldstone mode. Moreover, a dip in low-frequency AC conductivity is observed, stemming from the excitation of the SSB Goldstone mode. In the superfluid phase, the effect of gauge–axion coupling on the condensation or superfluid energy gap is only amplified in the presence of strong momentum dissipation. Notably, for the case with negative gauge–axion coupling, a hard-gap-like behavior at low frequency and a pronounced peak at intermediate frequency are observed, indicating that the evolution of the superfluid component is distinct from that of positive coupling.

Equilibrium magnetic properties of the Fe-doped HTSC YBaCuO

For the polycrystalline high-temperature superconductor Y1 –xFexBa2Cu3Oy (0 ≤ x ≤ 0.05), where a significant increase in the intragrain critical current density has recently been found, the effect of iron doping on the equilibrium magnetic characteristics is studied. The field dependences of the magnetization are measured in the temperature range of 40–85 K and in the field range up to 60 kOe with increasing and decreasing fields. The temperature dependences of the London penetration depth λab, the superconducting carrier density ns, and the thermodynamic critical field Hc are determined from an analysis of the middle lines of the magnetic hysteresis loop. It is shown that the thermodynamic properties of Fe substituted samples do not change at x ≤ 0.03. At a higher Fe content, a slight decrease in Hc and the superconducting transition temperature is observed. However, changes in the condensation energy turn out to be much smaller than values expected due to an increase in the density of effective pinning centres created by substitutional atoms in both the yttrium and copper sublattices. It is concluded that the pinning regions in chain CuO planes near substituted Cu sites are two-dimensional in nature and do not affect the superconducting pairing in CuO2 planes. Another possible pinning mechanism, which does not affect Hc, is the interaction of vortices with the magnetic moments of Fe3+ ions.

A new biomass-based hybrid energy system integrated with a flue gas condensation process and energy storage option: An effort to mitigate environmental hazards

The development of biomass-fueled cogeneration plants can be fruitful to achieve the sustainable development goals, due to the crises of fossil energy-fueled ones. Additionally, biomass fuels can offer higher reliability and more sustainable energy compared to the two more well-known renewables (i.e., solar and wind energies) due to the no dependence on environmental and weather conditions. The present article provides a comprehensive assessment (thermodynamic-design, exergoeconomic and environmental) and optimization of a new biomass-driven cogeneration plant cascaded with a heat recovery unit. The planned plant is based on a biomass gasification process, some thermodynamic power generation cycles based on steam and gas turbines (i.e., Rankine cycle, Brayton cycle, and organic Rankine cycle (ORC)), and flue gas condensation process. Besides, a compressed air energy storage system (CAESS) as an energy storage process is integrated with the considered plant to establish a balance between production and demand and reduce electricity costs. To achieve optimal performance, a multi-objective optimization (based on a genetic algorithm) is applied. The findings showed that by considering the multi-objective optimization techniques, the plant's exergy efficiency could improve by about 15%. At the same time, the exergy cost rate is reduced by almost 17.3%. Avoiding the payment of carbon tax and the high electricity production level in the on-peak consumption period are unique and competitive features of the proposed biomass-driven power plant. It was also found that the LCOE and the payback period were 13.27 USD/GJ and 2.03 years, respectively, therefore, the proposed power plant exhibits reasonable economic feasibility.

Higgs response and pair condensation energy in superfluid nuclei

Abstract The pairing correlation in nuclei causes a characteristic excitation, known as the pair vibration, which is populated by the pair transfer reactions. Here we introduce a new method of characterizing the pair vibration by employing an analogy to the Higgs mode, which emerges in infinite superconducting/superfluid systems as a collective vibrational mode associated with the amplitude oscillation of the Cooper pair condensate. The idea is formulated by defining a pair-transfer probe, the Higgs operator, and then describing the linear response and the strength function to this probe. We will show that the pair condensation energy in nuclei can be extracted with use of the strength sum and the static polarizability of the Higgs response. In order to demonstrate and validate the method, we perform numerical analysis for Sn isotopes based on the quasi-particle random phase approximation to the Skyrme–Hartree–Fock–Bogoliubov model. We discuss the possibility of applying this new scheme to pair-transfer experiments.

Theoretical Study of Some Properties of High‐Temperature Two‐Band Model Iron‐Based Superconductor Ba1−xRbxFe2As2

This work focuses on the theoretical investigations of some properties of high‐temperature two‐band model iron‐based superconductor Ba1−xRbxFe2As2. The mathematical expressions of superconducting parameters are treated by the temperature‐dependent Green's function formalism. The superconducting order parameters of the material for electron, hole bands and for the interband are plotted as a function of temperature. The parameters decrease with increasing temperature and vanish at the superconducting transition temperature (Tc) of Ba1−xRbxFe2As2. The values of the superconducting order parameters and coupling strength in electron intraband, hole intraband, and the electron–hole interband are computed quantitatively. It is found that the pairing potential of Ba1−xRbxFe2As2 increases as a function of temperature. The phase diagrams of temperature‐dependent electron and hole intrabands and density of states versus excitation energy are plotted and it is observed that both decrease as the excitation energy increases. The impacts of temperature, pairing potential, and transitional temperature on condensation energy are also investigated and the results show that condensation energy decreases with the increase of temperature and pairing potential and vanishes at Tc of Ba1−xRbxFe2As2. Furthermore, the density of states is plotted for electron and hole‐intrabands at different temperatures versus excitation energy, and it is perceived that the density of states decreased gradually as the excitation energy increases and vanished at low‐temperature values. The current results are compatible with previous findings.

Development and modified implementation of Lee model for condensation simulation

Numerical oscillation is a non-physical phenomenon in which the interface temperature fluctuates around the saturation temperature. The simulation for condensation is more susceptible to the numerical oscillation caused by the phase change model. To suppress the numerical oscillation and reduce interface temperature deviation in condensation simulation, a developed model modified the Lee model is presented in this study. In the present model, the mass source terms and the energy source terms are added in the governing equations to calculate the condensate within the cell and the allocation of condensation energy between the interface cells. The mass and energy source transfer model is firstly compared with the original Lee model to simulate one-dimensional Stefan problem. Indicating that with the similar accuracy the developed model could increase computational efficiency by 40 times. Then the Nusselt condensation problem is verified with a reasonable selection of model parameters, and the average error of the film thickness was controlled below 2%, as the interfacial temperature deviation within 3%. Finally, verification is also attained on the forced convective condensation of R134a and the interfacial temperature deviation is below 0.1 K. Simulation results validate the feasibility of using this model to predict heat and mass transfer in condensation. The numerical oscillations are also significantly suppressed in the simulations.

Generalization of interlayer tunneling models to cuprate superconductors with charge density waves

At the beginning of cuprate superconductors, the interlayer tunneling (ILT) and Lawrence-Doniach (L-D) models, which connect the CuO planes by Josephson coupling were considered the leading theoretical proposals for these materials. However, measurements of the interlayer magnetic penetration depth $\lambda_{c}$ yielded larger values than required by the ILT model. After the discovery of planar stripes and incommensurate charge ordering, it was also possible to consider Josephson coupling between these mesoscopic charge domains or blocks. We show that the average intralayer is larger than the interlayer coupling and comparable with the condensation energy, leading to a superconducting transition by long-range phase order. Another consequence is that the ratio $[\lambda_{c}/\lambda_{ab}]^2$ is directly proportional resistivity ratio $\rho_c/ \rho_{ab}$ near the superconducting transition temperature in agreement with several measurements.

Electromagnetic response of cuprate superconductors with coexisting electronic nematicity

ABSTRACT The electronically nematic order has emerged as a key feature of cuprate superconductors, however, its correlation with the fundamental properties such as the electromagnetic response remains unclear. Here the nematic-order state strength dependence of the electromagnetic response in cuprate superconductors is investigated within the framework of the kinetic-energy-driven superconductivity. It is shown that a significant anisotropy of the electromagnetic response is caused by the electronic nematicity. In particular, in addition to the pure d-wave component of the superconducting gap, the pure s-wave component of the superconducting gap is generated by the electronic nematicity, therefore there is a coexistence and competition of the d-wave component and the s-wave component. This coexistence and competition leads to that the maximal condensation energy appears at around the optimal strength of the electronic nematicity, and then decreases in both the weak and strong strength regions, which in turn induces the enhancement of superconductivity, and gives rise to the dome-like shape of the nematic-order state strength dependence of the superfluid density.

Interrelations among zero-field critical current density, irreversibility field and pseudogap in hole doped high-Tc cuprates

Critical current density and the irreversibility magnetic fields are two parameters which control most of the applications of high-temperature superconductors. In this brief communications we have investigated the intrinsic effects that determine the magnitudes of these two parameters. The roles of hole concentration in the CuO2 plane (p) and oxygen deficiency (δ) in the CuO1-δ chains on the zero-field low-temperature critical current density, Jc0, were studied for a series of Y1-xCaxBa2Cu3O7-δ (x = 0.00, 0.05, 0.10, and 0.20) thin films. Jc0 above the optimum hole concentration were found to be high. The magnitude of Jc0 were largely determined by the hole concentration, maximizing at p ∼ 0.185 ± 0.005, regardless of the values of x and δ. This implied that oxygen deficiency/disorder plays a secondary role and the intrinsic Jc0 is governed largely by the number of doped holes in the CuO2 planes of Y1-xCaxBa2Cu3O7-δ. Further support in favor of this finding was garnered from the analysis of the in-plane resistive transitions of thin films of YBa2Cu3O7-δ (YBCO) with magnetic fields (H) applied along the crystallographic c-direction. The characteristic magnetic field (H0), linked to the vortex activation energy and the irreversibility field, exhibits similar p-dependence as shown by Jc0(p). We have explained these observations in terms of the doping dependent pseudogap (PG) energy/temperature scale in the low-energy electronic energy density of states observed in high-Tc cuprates. Both the intrinsic critical current density and the irreversibility field depend directly on the superconducting condensation energy, which in turn is primarily determined by the magnitude of the hole concentration dependent PG in the quasiparticle spectral density.

Theoretical Investigation of the Superconducting and Thermodynamic Properties of Two-Band Model High-Temperature Iron-Based Superconductor Ba1–xNaxFe2As2

This work presents the theoretical investigation of the superconducting and thermodynamic properties of the two-band model high-temperature iron-based superconductor Ba1-xNaxFe2As2. By developing a model Hamiltonian and by employing the well-knownvdouble-time temperature-dependent Green’s function formalism, we have computed the superconducting orderbparameters for the electron and hole intra- and inter-band transitions, superconducting transition temperature, densitiesbof states, and condensation energies. Furthermore, the electronic specific heat and the entropy for electron and hole intra-band transitions have been determined. By using appropriate experimental data and some credible approximations of the parameters in the computed expressions, we have found the phase diagrams of superconducting order parameters versus the temperature, superconducting critical temperature versus the inter-band interaction potential, temperature dependences of the electronic specific heat and entropy for electron and hole intra-band transitions, and densities of states for the electron and hole intra-band transitions as functions of the excitation energy at different values of the temperature. Finally, the phase diagrams of the condensation energy versus the temperature, inter-band pairing potential at T = 0 K versus the condensation energy, and condensation energy versus the superconducting transition temperature (TC) have been drawn. In some of the phase diagrams, the comparison between theoretical and experimental values has been made. The results are in a good agreement with previous findings.

DC Transport and Magnetotransport Properties of the 2D Isotropic Metallic System with the Fermi Surface Reconstructed by the Charge Density Wave

We report the ground state stabilization and corresponding electrical transport and magnetotransport properties of a 2D metallic system with an isotropic Fermi surface reconstructed by a charge density wave. The onset of the charge density wave is a spontaneous process, stabilized by the condensation energy gain due to the self-consistent mechanism of topological reconstruction of the Fermi surface and opening of the pseudo-gap around it. We address the signature of the uni-axial reconstruction in terms of the measurable quantities, such as the intra-band transport properties, including the one-particle density of states, the total and effective concentration of electrons, and the Hall coefficient. Additionally, we analyze the magnetotransport properties of the system reconstructed by the bi-axial, checkerboard-like charge density wave, under conditions of magnetic breakdown. It manifests huge quantum oscillations in diagonal components of magnetoconductivity, while the Hall conductivity changes sign, varying the external magnetic field with a finite region of vanishing Hall coefficient in between.

Superconductivity out of a non-Fermi liquid: Free energy analysis

In this paper, we present in-depth analysis of the condensation energy $E_c$ for a superconductor in a situation when superconductivity emerges out of a non-Fermi liquid due to pairing mediated by a massless boson. This is the case for electronic-mediated pairing near a quantum-critical point in a metal, for pairing in SYK-type models, and for phonon-mediated pairing in the properly defined limit, when the dressed Debye frequency vanishes. We consider a subset of these quantum-critical models, in which the pairing in a channel with a proper spatial symmetry is described by an effective $0+1$ dimensional model with the effective dynamical interaction $V(\Omega_m) = {\bar g}^\gamma/|\Omega_m|^\gamma$, where $\gamma$ is model-specific (the $\gamma$-model). In previous papers, we argued that the pairing in the $\gamma$ model is qualitatively different from that in a Fermi liquid, and the gap equation at $T=0$ has an infinite number of topologically distinct solutions, $\Delta_n (\omega_m)$, where an integer $n$, running between $0$ and infinity, is the number of zeros of $\Delta_n (\omega_m)$ on the positive Matsubara axis. This gives rise to the set of extrema of $E_c$ at $E_{c,n}$, of which $E_{c,0}$ is the global minimum. The spectrum $E_{c,n}$ is discrete for a generic $\gamma <2$, but becomes continuous at $\gamma = 2-0$. Here, we discuss in more detail the profile of the condensation energy near each $E_{c,n}$ and the transformation from a discrete to a continuous spectrum at $\gamma \to 2$. We also discuss the free energy and the specific heat of the $\gamma$-model in the normal state.

Influence of shock wave/boundary layer interaction on condensation flow and energy recovery in supersonic nozzle

Shock train phenomenon occurs when the Mach number increases during the process of energy recovery in the nozzle. However, the reduction of wet natural gas purification efficiency and the increase in energy loss can be caused by shock wave in the supersonic separator. This study focused on the condensation characteristics and pressure energy recovery efficiency under the shock train in the Laval nozzle. A mathematical model was developed for the process of methane-water vapour supersonic condensation and verified by condensation experiments. The results demonstrate that the length of the boundary layer separation interval can be reduced by 0.142 m with a decrease of 0.909 upstream Mach number from 2.367 to 1.458. Multiple nucleation of vapour occurs under the effect of shock train. The droplet growth interval increases from 0 to 0.0859 m and the liquid mass fraction enhances from 0 to 0.12% as the pressure energy recovery efficiency decreasing from 80% to 30%. This indicates that the suitable pressure energy recovery efficiency from 40% to 60% can effectively control the location of the shock train and organize its structure in the nozzle to reduce the separation length of boundary layer and improve the nozzle liquefaction efficiency.