Bulk Critical Temperature Research Articles

Superconductivity of Metaphosphatecobalt(II) Salt at 173 K

An inorganically template metaphosphate of Co(II) complex has been synthesized and thermal properties have been studied at a low temperature up to 173 K from 298 K by the Differential Scanning Calorimeter (DSC). The specific heat capacity is measured in atmospheric O2 at a heating rate of 283 K min−1 from 298 K and kept constant at 173 K for 4 minutes then reversed to 298 K again. The bulk critical temperature of superconductivity of metaphosphatecobalt(II) salt was found at 173 K.

Tunneling break-junction measurements of the superconducting gap in Y2C3

Tunneling measurements of the electron spectrum in the superconducting state have been carried out in Y2C3 samples with the bulk (resistive and diamagnetic) critical temperature Tc=15–16K. A break-junction technique was crucial to find the intrinsic gap features. The representative gap structure at 4K reveals distinct BCS-like peaks with the gap value of 2Δ(4K)=3–4meV. Assuming local Tc values of 10–13K, the characteristic gap to Tc ratio 2Δ/kBTc (kB is the Boltzmann constant) was found to possess the BCS weak-coupling value 3.5±0.2, appropriate to isotropic s-wave superconductors.

Casimir amplitudes and capillary condensation of near-critical fluids between parallel plates: Renormalized local functional theory

We investigate the critical behavior of a near-critical fluid confined between two parallel plates in contact with a reservoir by calculating the order parameter profile and the Casimir amplitudes (for the force density and for the grand potential). Our results are applicable to one-component fluids and binary mixtures. We assume that the walls absorb one of the fluid components selectively for binary mixtures. We propose a renormalized local functional theory accounting for the fluctuation effects. Analysis is performed in the plane of the temperature T and the order parameter in the reservoir ψ(∞). Our theory is universal if the physical quantities are scaled appropriately. If the component favored by the walls is slightly poor in the reservoir, there appears a line of first-order phase transition of capillary condensation outside the bulk coexistence curve. The excess adsorption changes discontinuously between condensed and noncondensed states at the transition. With increasing T, the transition line ends at a capillary critical point T=T(c) (ca) slightly lower than the bulk critical temperature T(c) for the upper critical solution temperature. The Casimir amplitudes are larger than their critical point values by 10-100 times at off-critical compositions near the capillary condensation line.

Enhancement of the critical temperature in iron pnictide superconductors by finite-size effects

Recent experiments have shown that, in agreement with previous theoretical predictions, superconductivity in metallic nanostructures can be enhanced with respect to the bulk limit. Motivated by these results we study finite size effects (FSE) in an iron-pnictide superconductor. For realistic values of the bulk critical temperature Tc ~ 20-50K, we find that, in the nanoscale region L ~ 10 nm, Tc(L) has a complicated oscillating pattern as a function of the system size L. A substantial enhancement of Tc with respect to the bulk limit is observed for different boundary conditions, geometries and two microscopic models of superconductivity. Thermal fluctuations, which break long range order, are still small in this region. Finally we show that the differential conductance, an experimental observable, is also very sensitive to FSE.

Effect of Pore Size on the Condensation/Evaporation Transition of Confined Water in Equilibrium with Saturated Bulk Water

The effect of pore size on the condensation/evaporation transition of confined water upon varying the strength of the water-surface interaction is studied under conditions of equilibrium with saturated bulk. Monte Carlo simulations in the grand canonical ensemble were used to determine water density in spherical pores of radius R(p) = 9, 12, 15, 20, and 25 Å in the temperature range from T = 270 K to the bulk critical temperature. The critical values of the well depth of the water-surface interaction potential, which mark the limits of the metastability of vapor and liquid phases in pores (U(0)(cond) and U(0)(evap), respectively), were determined. U(0)(cond) strongly depends on temperature, practically does not depend on the pore size, and corresponds to some particular density of water vapor near a surface. In contrast, U(0)(evap) only slightly depends on temperature, depends strongly on pore size, and corresponds to the density in the pore interior by about 2% below the bulk value. The critical water-pore interaction U(0)(c), which separates regimes of capillary condensation and capillary evaporation, is found to be changed from -1.75 to -0.94 kcal/mol when the pore radius R(p) increases from 9 to 25 Å. The size dependence of U(0)(c) is attributed to the change of the contact angle due to the line tension effect. Extrapolation of the dependence U(0)(c)(R(p)) to the flat surface gives the critical value U(0)(c)(∞) ≈ -0.61 kcal/mol.

High-temperature surface superconductivity in topological flat-band systems

We show that the topologically protected flat band emerging on a surface of a nodal fermionic system promotes the surface superconductivity due to an infinitely large density of states associated with the flat band. The critical temperature depends linearly on the pairing interaction and can be thus considerably higher than the exponentially small bulk critical temperature. We discuss an example of surface superconductivity in multilayered graphene with rhombohedral stacking.

Aspect-ratio dependence of thermodynamic Casimir forces

We consider the three-dimensional Ising model in a L(⊥)×L(∥)×L(∥) cuboid geometry with a finite aspect ratio ρ=L(⊥)/L(∥) and periodic boundary conditions along all directions. For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations. The Monte Carlo results compare well with recent field theoretical results for the Ising universality class at temperatures above and slightly below the bulk critical temperature T(c). Furthermore, the excess free energy and Casimir force scaling functions of the two-dimensional Ising model are calculated exactly for arbitrary ρ and compared to the three-dimensional case. We give a general argument that the Casimir force vanishes at the critical point for ρ=1 and becomes repulsive in periodic systems for ρ>1.

Observation of multi-gap superconductivity in GdO(F)FeAs by Andreev spectroscopy

We have studied current-voltage characteristics of Andreev contacts in polycrystalline GdO0.88F0.12FeAs samples with bulk critical temperature T c = (52.5 ± 1) K using break-junction technique. The data obtained can- not be described within the single-gap approach and suggests the existence of a multi-gap superconductivity in this compound. The large and small superconducting gap values estimated at T = 4.2 K are Δ L = 10.5 ± 2 meV and Δ s = 2.3 ± 0.4 meV, respectively.

Static susceptibility in a paraelectric particle

Static dielectric susceptibility for the paraelectric phase of a particle was calculated exactly. Temperature and diameter dependence are described analytically. There are two regimes of the susceptibility: for temperatures above the bulk critical ferroelectric temperature of the particle and below it. The critical transition temperature from the exact calculation is the same as that from the soft mode approach.

Finite-size effects in film geometry with nonperiodic boundary conditions: Gaussian model and renormalization-group theory at fixed dimension

Finite-size effects are investigated in the Gaussian model with isotropic and anisotropic short-range interactions in film geometry with nonperiodic boundary conditions (bc) above, at, and below the bulk critical temperature Tc. We have obtained exact results for the free energy and the Casimir force for antiperiodic, Neumann, Dirichlet, and Neumann-Dirichlet mixed bc in 1<d<4 dimensions. For the Casimir force, finite-size scaling is found to be valid for all bc. For the free energy, finite-size scaling is valid in 1<d<3 and 3<d<4 dimensions for antiperiodic, Neumann, and Dirichlet bc, but logarithmic deviations from finite-size scaling exist in d=3 dimensions for Neumann and Dirichlet bc. This is explained in terms of the borderline dimension d*=3 , where the critical exponent 1-α-ν=(d-3)∕2 of the Gaussian surface energy density vanishes. For Neumann-Dirichlet bc, finite-size scaling is strongly violated above Tc for 1<d<4 because of a cancelation of the leading scaling terms. For antiperiodic, Dirichlet, and Neumann-Dirichlet bc, a finite film critical temperature Tc,film(L)<Tc exists at finite film thickness L . Our results include an exact description of the dimensional crossover between the d -dimensional finite-size critical behavior near bulk Tc and the (d-1) -dimensional critical behavior near Tc,film(L). This dimensional crossover is illustrated for the critical behavior of the specific heat. Particular attention is paid to an appropriate representation of the free energy in the region Tc,film(L)≤T≤Tc. For 2<d<4 , the Gaussian results are renormalized and reformulated as one-loop contributions of the φ4 field theory at fixed dimension d and are then compared with the ε=4-d expansion results at ε=1 as well as with d=3 Monte Carlo data. For d=2 , the Gaussian results for the Casimir force scaling function are compared with those for the Ising model with periodic, antiperiodic, and free bc; unexpected exact relations are found between the Gaussian and Ising scaling functions. For both the d -dimensional Gaussian model and the two-dimensional Ising model it is shown that anisotropic couplings imply nonuniversal scaling functions of the Casimir force that depend explicitly on microscopic couplings. Our Gaussian results provide the basis for the investigation of finite-size effects of the mean spherical model in film geometry with nonperiodic bc above, at, and below the bulk critical temperature.

Meissner response of a bulk superconductor with an embedded sheet of reduced penetration depth

We calculate the change in susceptibility resulting from a thin sheet with reduced penetration depth embedded perpendicular to the surface of an isotropic superconductor, in a geometry applicable to scanning Superconducting QUantum Interference Device (SQUID) microscopy, by numerically solving Maxwell's and London's equations using the finite element method. The predicted stripes in susceptibility agree well in shape with the observations of Kalisky et al. of enhanced susceptibility above twin planes in the underdoped pnictide superconductor Ba(Fe1-xCox)2As2 (Ba-122). By comparing the predicted stripe amplitudes with experiment and using the London relation between penetration depth and superfluid density, we estimate the enhanced Cooper pair density on the twin planes, and the barrier force for a vortex to cross a twin plane. Fits to the observed temperature dependence of the stripe amplitude suggest that the twin planes have a higher critical temperature than the bulk, although stripes are not observed above the bulk critical temperature.

Properties of the solvation force of a two-dimensional Ising strip in scaling regimes

We consider the d = 2 Ising strip with surface fields acting on boundary spins. Using the properties of the transfer matrix spectrum we identify two pseudotransition temperatures and show that they satisfy similar scaling relations as expected for real transition temperatures in strips with d>2. The solvation force between the boundaries of the strip is analysed as a function of temperature, surface fields and the width of the strip. For large widths, the solvation force can be described by scaling functions in three different regimes: in the vicinity of the critical wetting temperature of the 2D semi-infinite system, in the vicinity of the bulk critical temperature and in the regime of weak surface fields, where the critical wetting temperature tends towards the bulk critical temperature. The properties of the relevant scaling functions are discussed.

Extended defects in the Potts-percolation model of a solid: Renormalization group and Monte Carlo analysis

We extend the model of a 2d solid to include a line of defects. Neighboring atoms on the defect line are connected by springs of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the three- and four-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.

Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations

Effective Casimir forces induced by thermal fluctuations in the vicinity of bulk critical points are studied by means of Monte Carlo simulations in three-dimensional systems for film geometries and within the experimentally relevant Ising and XY universality classes. Several surface universality classes of the confining surfaces are considered, some of which are relevant for recent experiments. An approach introduced previously [O. Vasilyev, EPL 80, 60009 (2007)], based inter alia on an integration scheme of free-energy differences, is utilized to compute the universal scaling functions of the critical Casimir forces in the critical range of temperatures above and below the bulk critical temperature. The resulting predictions are compared with corresponding experimental data for wetting films of fluids and with available theoretical results.

Casimir force inO(n)systems with a diffuse interface

We study the behavior of the Casimir force in O(n) systems with a diffuse interface and slab geometry infinity;{d-1}xL , where 2<d<4 is the dimensionality of the system. We consider a system with nearest-neighbor anisotropic interaction constants J_{ parallel} parallel to the film and J_{ perpendicular} across it. We argue that in such an anisotropic system the Casimir force, the free energy, and the helicity modulus will differ from those of the corresponding isotropic system, even at the bulk critical temperature, despite that these systems both belong to the same universality class. We suggest a relation between the scaling functions pertinent to the both systems. Explicit exact analytical results for the scaling functions, as a function of the temperature T , of the free energy density, Casimir force, and the helicity modulus are derived for the n-->infinity limit of O(n) models with antiperiodic boundary conditions applied along the finite dimension L of the film. We observe that the Casimir amplitude Delta_{Casimir}(dmid R:J_{ perpendicular},J_{ parallel}) of the anisotropic d -dimensional system is related to that of the isotropic system Delta_{Casimir}(d) via Delta_{Casimir}(dmid R:J_{ perpendicular},J_{ parallel})=(J_{ perpendicular}J_{ parallel});{(d-1)2}Delta_{Casimir}(d) . For d=3 we derive the exact Casimir amplitude Delta_{Casimir}(3,mid R:J_{ perpendicular},J_{ parallel})=[Cl_{2}(pi3)3-zeta(3)(6pi)](J_{ perpendicular}J_{ parallel}) , as well as the exact scaling functions of the Casimir force and of the helicity modulus Upsilon(T,L) . We obtain that beta_{c}Upsilon(T_{c},L)=(2pi;{2})[Cl_{2}(pi3)3+7zeta(3)(30pi)](J_{ perpendicular}J_{ parallel})L;{-1} , where T_{c} is the critical temperature of the bulk system. We find that the contributions in the excess free energy due to the existence of a diffuse interface result in a repulsive Casimir force in the whole temperature region.

Dynamic critical behavior of modelAin films: Zero-mode boundary conditions and expansion near four dimensions

The critical dynamics of relaxational stochastic models with nonconserved $n$-component order parameter $\ensuremath{\phi}$ and no coupling to other slow variables (``model $A$'') is investigated in film geometries for the cases of periodic and free boundary conditions. The Hamiltonian $\mathcal{H}$ governing the stationary equilibrium distribution is taken to be $O(n)$ symmetric and to involve, in the case of free boundary conditions, the boundary terms ${\ensuremath{\int}}_{{\mathfrak{B}}_{j}}{\stackrel{\r{}}{c}}_{j}{\ensuremath{\phi}}^{2}/2$ associated with the two confining surface planes ${\mathfrak{B}}_{j}$, $j=1,2$, at $z=0$ and $z=L$. Both enhancement variables ${\stackrel{\r{}}{c}}_{j}$ are presumed to be subcritical or critical, so that no long-range surface order can occur above the bulk critical temperature ${T}_{c,\ensuremath{\infty}}$. A field-theoretic renormalization-group study of the dynamic critical behavior at $d=4\ensuremath{-}ϵ$ bulk dimensions is presented, with special attention paid to the cases where the classical theories involve zero modes at ${T}_{c,\ensuremath{\infty}}$. This applies when either both ${\stackrel{\r{}}{c}}_{j}$ take the critical value ${\stackrel{\r{}}{c}}_{\text{sp}}$ associated with the special surface transition or else periodic boundary conditions are imposed. Owing to the zero modes, the $ϵ$ expansion becomes ill-defined at ${T}_{c,\ensuremath{\infty}}$. Analogously to the static case, the field theory can be reorganized to obtain a well-defined small-$ϵ$ expansion involving half-integer powers of $ϵ$, modulated by powers of $\text{ln}\text{ }ϵ$. This is achieved through the construction of an effective $(d\ensuremath{-}1)$-dimensional action for the zero-mode component of the order parameter by integrating out its orthogonal component via renormalization-group improved perturbation theory. Explicit results for the scaling functions of temperature-dependent finite-size susceptibilities at temperatures $T\ensuremath{\ge}{T}_{c,\ensuremath{\infty}}$ and of layer and surface susceptibilities at the bulk critical point are given to orders $ϵ$ and ${ϵ}^{3/2}$, respectively. They show that $L$ dependent shifts of the multicritical special point occur along the temperature and enhancement axes. For the case of periodic boundary conditions, the consistency of the expansions to $O({ϵ}^{3/2})$ with exact large-$n$ results is shown. We also discuss briefly the effects of weak anisotropy, relating theories whose Hamiltonian involves a generalized square gradient term ${B}^{kl}{\ensuremath{\partial}}_{k}\mathbf{\ensuremath{\phi}}\ensuremath{\cdot}{\ensuremath{\partial}}_{l}\mathbf{\ensuremath{\phi}}$ to those with a conventional ${(\ensuremath{\nabla}\mathbf{\ensuremath{\phi}})}^{2}$ term.

Finite-size effects in the spherical model of finite thickness

A detailed analysis of the finite-size effects on the bulk critical behaviour of the d-dimensional mean spherical model confined to a film geometry with finite thickness L is reported. Along the finite direction different kinds of boundary conditions are applied: periodic (p), antiperiodic (a) and free surfaces with Dirichlet (D), Neumann (N) and a combination of Neumann and Dirichlet (ND) on both surfaces. A systematic method for the evaluation of the finite-size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary d. It is found, for 2 < d < 4, that the singular part of the free energy has the required finite-size scaling form at the bulk critical temperature only for (p) and (a). For the remaining boundary conditions the standard finite-size scaling hypothesis is not valid. At d = 3, the critical amplitude of the singular part of the free energy (related to the so-called Casimir amplitude) is estimated. We obtain Δ(p) = −2ζ(3)/(5π) = −0.153 051…, Δ(a) = 0.274 543… and Δ(ND) = 0.019 22…, implying a fluctuation-induced attraction between the surfaces for (p) and repulsion in the other two cases. For (D) and (N) we find a logarithmic dependence on L.

Critical dynamics in confined systems with quenched random impurities

We study the critical dynamics of a system confined to a hypercubic geometry with periodic boundary conditions in the presence of quenched short-range correlated impurities. By using the random ${T}_{c}$ model with purely relaxational dynamics (model A) and the renormalization group method in the vicinity of the upper critical dimension ${d}_{u}=4$, we derive to first order in $ϵ=4\ensuremath{-}d$ the expression for the relaxation time. Its scaling behavior is discussed in detail both analytically and numerically when the system is quenched from the high-temperature phase toward its bulk critical temperature.

Thermodynamic Casimir effects involving interacting field theories with zero modes

Systems with an $O(n)$ symmetrical Hamiltonian are considered in a $d$-dimensional slab geometry of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$. The effective forces induced by thermal fluctuations at and above the bulk critical temperature ${T}_{c,\ensuremath{\infty}}$ (thermodynamic Casimir effect) are investigated below the upper critical dimension ${d}^{*}=4$ by means of field-theoretic renormalization-group methods for the case of periodic and special-special boundary conditions, where the latter correspond to the critical enhancement of the surface interactions on both boundary planes. As shown previously [Europhys. Lett. 75, 241 (2006)], the zero modes that are present in Landau theory at ${T}_{c,\ensuremath{\infty}}$ make conventional renormalization-group-improved perturbation theory in $4\ensuremath{-}ϵ$ dimensions ill-defined. The revised expansion introduced there is utilized to compute the scaling functions of the excess free energy and the Casimir force for temperatures $T\ensuremath{\geqslant}{T}_{c,\ensuremath{\infty}}$ as functions of $\mathsf{L}\ensuremath{\equiv}L∕{\ensuremath{\xi}}_{\ensuremath{\infty}}$, where ${\ensuremath{\xi}}_{\ensuremath{\infty}}$ is the bulk correlation length. Scaling functions of the $L$-dependent residual free energy per area are obtained, whose $\mathsf{L}\ensuremath{\rightarrow}0$ limits are in conformity with previous results for the Casimir amplitudes ${\ensuremath{\Delta}}_{C}$ to $O({ϵ}^{3∕2})$ and display a more reasonable small-$\mathsf{L}$ behavior inasmuch as they approach the critical value ${\ensuremath{\Delta}}_{C}$ monotonically as $\mathsf{L}\ensuremath{\rightarrow}0$. Extrapolations to $d=3$ for the Ising case $n=1$ with periodic boundary conditions are in fair agreement with Monte Carlo results. In the case of special-special boundary conditions, extrapolations to $d=3$ are hampered by the fact that the one-loop result for the inverse finite-size susceptibility becomes negative for some values of $\mathsf{L}$ when $ϵ\ensuremath{\gtrsim}0.83$.

Phase transitions and interface fluctuations in double wedges and bi-pyramids with competing surface fields

The interplay between surface and interface effects on binary AB mixtures that are confined in unconventional geometries is investigated by Monte Carlo simulations and phenomenological considerations. Both double-wedge and bi-pyramid confinements are considered and competing surface fields are applied at the two opposing halves of the system. Below the bulk critical temperature, domains of opposite order parameter are stabilized at the corresponding corners and an interface runs across the middle of the bi-partite geometry. Upon decreasing the temperature further one encounters a phase transition at which the AB symmetry is broken. The interface is localized in one of the two wedges or pyramids, respectively, and the order parameter is finite. In both cases, the transition becomes discontinuous in the thermodynamic limit but it is not a first-order phase transition. In an antisymmetric double wedge geometry the transition is closely related to the wedge-filling transition. Choosing the ratio of the cross-section L × L of the wedge and its length L y according to L y /L 3 = const., simulations and phenomenological consideration show that the new type of phase transition is characterized by critical exponents α = 3/4, β = 0, and γ = 5/4 for the specific heat, order parameter, and susceptibility, respectively. In an antisymmetric bi-pyramid the transition occurs at the cone-filling transition of a single pyramid. The important critical fluctuations are associated with the uniform translation of the interface and they can be described by a Landau-type free energy. Monte Carlo results provide evidence that the coefficients of this Landau-type free energy exhibit a system-size dependence, which gives rise to critical amplitudes that diverge with system size and result in a transition that becomes discontinuous in the thermodynamic limit.