On the superconducting transition temperature for metallic nanocrystals

A new approach is proposed for calculating the Debye temperature of a nanocrystal in the form of an n-dimensional rectangular parallelepiped with an arbitrary microstructure and the number of atoms N ranging from 2ⁿ to infinity. The geometric shape of the system is determined by the lateral-to-basal edge ratio of the parallelepiped. The size dependences of the Debye and melting temperatures for a number of materials are calculated using the derived relationship. The theoretical curves thus obtained agree well with the experimental data. The calculated dependences of the superconducting transition temperature T _c on the size d of aluminum, indium, and lead nanocrystals are also in reasonable agreement with the experimental estimates of T _c (d). It is demonstrated that, as the nanocrystal size d decreases, the greater the deviation of the nanocrystal shape from an equilibrium shape (in our case, a cube), the higher the temperature of the superconducting transition T _c (d). The superconducting transition temperature is calculated as a function of the thickness (diameter) of a plate (rod) with an arbitrary length. It is found that a decrease in the thickness (diameter) of the plate (rod) leads to an increase in the temperature T _c (z): the looser the microstructure of the metallic nanocrystal, the higher the temperature T _c (z).     

Superconducting Properties of Indium Nanostructured in Pores of Thin Films of SiO<Subscript>2</Subscript> Microspheres

Samples of a superconducting indium nanocomposite based on a thin-film porous dielectric matrix prepared by the Langmuir–Blodgett method are obtained for the first time, and their low-temperature electrophysical and magnetic properties are studied. Films with thickness b ≤ 5 μm were made from silicon dioxide spheres with diameter D = 200 and 250 nm; indium was introduced into the pores of the films from the melt at a pressure of P ≤ 5 kbar. Thus, a three-dimensional weakly ordered structure of indium nanogranules was created in the pores, forming a continuous current-conducting grid. Measurements of the temperature and magnetic field dependences of the resistance and magnetic moment of the samples showed an increase in the critical parameters of the superconductivity state of nanostructured indium (critical temperature T_c ≤ 3.62 K and critical magnetic field H_c at T = 0 K H_c(0) ≤ 1700 Oe) with respect to the massive material (T_c = 3.41 K, H_c(0) = 280 Oe). In the dependence of the resistance on temperature and the magnetic field, a step transition to the superconductivity state associated with the nanocomposite structure was observed. A pronounced hysteresis M(H) is observed in the dependence of the magnetic moment M of the nanocomposite on the magnetic field at T < T_c, caused by the multiply connected structure of the current-conducting indium grid. The results obtained are interpreted taking into account the dimensional dependence of the superconducting characteristics of the nanocomposite.     

On the effect of heating and cooling rates on the melting and crystallization of metal nanoclusters

The effect of heating and cooling rates on melting (T_m) and crystallization (T_c) temperatures of metal nanoclusters is investigated in terms of the isothermal molecular dynamics. We report on the results obtained for nickel nanoclusters, although analogous results were also obtained for gold and aluminum nanoclusters. It is found that T_m increases, while T_c decreases with increasing heating and cooling rates, both T_m and T_c tending to the same value for heating and cooling rates tending to zero. The results indicate that the hysteresis of melting and crystallization of nanoparticles must be completely due to nonequilibrium conditions of heating and cooling. The transition of Ni nanoclusters to the amorphous state begins at very high cooling rates exceeding 10 TK/s.     

Electron transport,penetration depth,and the upper critical magnetic field in ZrB<Subscript>12</Subscript> and MgB<Subscript>2</Subscript>

We report on the synthesis and measurements of the temperature dependences of the resistivity ρ, the penetration depth λ, and the upper critical magnetic field H_c2, for polycrystalline samples of dodecaboride ZrB₁₂ and diboride MgB₂. We conclude that ZrB₁₂ behaves as a simple metal in the normal state with the usual Bloch-Grüneisen temperature dependence of ρ(T) and with a rather low resistive Debye temperature T_R = 280 K (to be compared to T_R = 900 K for MgB₂). The ρ(T) and λ(T) dependences for these samples reveal a superconducting transition in ZrB₁₂ at T_c = 6.0 K. Although a clear exponential λ(T) dependence in MgB₂ thin films and ceramic pellets was observed at low temperatures, this dependence was almost linear for ZrB₁₂ below T_c/2. These features indicate an s-wave pairing state in MgB₂, whereas a d-wave pairing state is possible in ZrB₁₂. In disagreement with conventional theories, we found a linear temperature dependence, of H_c2(T) for ZrB₁₂ (H_c2(0) = 0.15 T).     

Crystallization and melting of spin-polarized<Superscript>3</Superscript>He

The melting and growth of³He crystals, spin-polarized by an external magnetic field, are different in nature depending on whether the temperature is higher or lower than the characteristic ordering temperatures in the crystal (the Neel temperatureT _N ) and in the liquid (the superfluid transition temperatureT _c ). In the high-temperature region (T≥T _N ,T _c ) the liquid which appears upon melting has a high nonequilibrium spin density. In the low-temperature region (T?T _N ,T _c ) the melting and growth are accompanied by spin supercurrents both in the liquid and in the crystal in addition to mass supercurrents in the liquid. The crystallization waves at the liquid-solid interface should exist in the low-temperature region. With increasing magnetic field the waves change in nature, because the spin currents begin to play a dominant role. The wave spectrum becomes linear with a velocity inversely proportional to the magnetic field. The attenuation of the waves at low enough temperatures is mainly due to the interaction of the moving crystal-liquid interface with thermal spin waves in the crystal. The waves could be weakly damped at temperatures below a few hundreds microkelvins.     

Effect of phase transitions on the exciton absorption spectrum of Rb<Subscript>x</Subscript>K<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript>4</Subscript>I<Subscript>5</Subscript> superionic conductors

The absorption spectrum of thin films of solid solutions of Rb_xK_1?xAg₄I₅ superionic conductors is investigated in the energy range 3–6 eV at temperatures from 90 to 290 K upon heating and cooling. It is established that the temperature dependences of the spectral position E _m and the half-width Γ of the long-wavelength exciton band are determined by the exciton-phonon interaction and the generation of Frenkel defects at phase transitions to the superionic state. Fluctuations of the composition of solid solutions do not affect the behavior of the dependences E _m (x) and Γ(x) at 90 K, which is indicative of the localization of excitons in the AgI sublattice of these compounds. A difference in the dependences T _c 1(x) and T _c 2(x) (the γ → β and β → α phase transitions, respectively) is revealed: the curve T _c 1(x) has a minimum at x ≈ 0.5, whereas the curve T _c 2(x) shows a weak maximum.     

Electrical and Magnetic Properties of Pb and In Nanofilaments in Asbestos near the Superconducting Transition

Bulk nanocomposites based on superconducting metals Pb and In embedded into matrices of natural chrysotile asbestos with the nanotube internal diameter d ~ 6 nm have been fabricated and studied. The low-temperature electrical and magnetic properties of the nanocomposites demonstrate the superconducting transition with the transition critical temperature T_c ≈ (7.18 ± 0.02) K for the Pb–asbestos nanocomposite (this temperature is close to T_{c bulk} = 7.196 K for bulk Pb). The electrical measurements show that In nanofilaments in asbestos have T_c ~ 3.5–3.6 K that is higher than T_{c bulk} = 3.41 K for bulk In. It is shown that the temperature smearing of the superconducting transition in the temperature dependences of the resistance R(T) ΔT ≈ 0.06 K for the Pb–asbestos and ΔT ≈ 1.8 K for the In–asbestos are adequately described by the fluctuation Aslamazov–Larkin and Langer–Ambegaokar theories. The resistive measurements show that the critical magnetic fields of the nanofilaments extrapolated to T = 0 K are H_c(0) ~ 47 kOe for Pb in asbestos and H_c(0) ~ 1.5 kOe for In in asbestos; these values are significantly higher than the values for the bulk materials (H\(H_{\rm{c}}^{\rm{bulk}}\) = 803 Oe for Pb and \(H_{\rm{c}}^{\rm{bulk}}\) = 285 Oe for In). The results of the electrical measurements for Pb?asbestos and In–asbestos agree with the data for the magnetic-field dependences of the magnetic moment in these nanocomposites.     

Exponential Increase in the Resistivity upon Cooling and Superconductivity in Indium-Doped Pb<Subscript>0.45</Subscript>Sn<Subscript>0.55</Subscript>Te

We have analyzed the temperature and magnetic-field dependences of resistivity ρ(T, H) of semiconducting compound Pb_0.45Sn_0.55Te doped with 5 at % In under a hydrostatic compression at P < 12 kbar. It is found that the temperature dependence ρ(T) at all pressures at T < 100 K is exponential with the activation energy decreasing upon an increase in pressure; this is accompanied with a superconducting transition on the ρ(T) and ρ(H) dependences at P > 4.8 kbar at T > 1 K (T _c = 1.72 K at a level of 0.5ρ _N at P = 6.8 kbar). We consider the model describing the low-temperature “dielectrization” of the semiconducting solid solution and the formation of the superconducting state upon an increase in the hydrostatic compression P > 4 kbar.     

Phase transitions and vortex structure evolution in two-level high-temperature granular superconductor YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 – δ</Subscript> under temperature and magnetic field

Temperature dependences of the resistivity ρ(T) of samples of granular high-temperature superconductor YBa₂Cu₃O_{7 – δ} are measured at various transverse external magnetic fields at 0 < H _ext < 1900 Оe in the temperature range from the upper Josephson critical temperature of “weak bonds” T _c2J to temperatures slightly exceeding the superconducting transition temperature T _c . Based on the data obtained, the behavior of the field dependences of the critical temperatures of superconducting grains and “weak bonds,” and temperature and field dependences of the magnetic contribution to the resistivity \(\left[ {\Delta \rho \left( {T,H} \right) = \rho {{\left( T \right)}_{{H_{ext}} = const}} - \rho {{\left( T \right)}_{{H_{ext}} = 0}}} \right]\). It is shown that the behavior of the magnetic contribution to the resistivity Δρ along the line of the phase transition related to the onset of the magnetic field penetration in the form of Abrikosov vortices into the subsystem of superconducting grains T _c1g (H _ext) is anomalous. The concepts on the magnetic flux redistribution between both subsystems of two-level HTSC near in the vicinity of T _c1g : the Josephson vortex decreases, and the Abrikosov vortex density increases.     

Mechanism of carrier generation and the origin of the pseudogap and 60 K phases in YBCO

The mechanism of hole carrier generation is considered in the framework of a model assuming the formation of negative U centers (NUCs) in HTSC materials under doping. The calculated dependences of carrier concentration on the doping level and temperature are in quantitative agreement with experiment. An explanation is proposed for the pseudogap and 60 K phases in YBa₂Cu₃O_6+δ. It is assumed that a pseudogap is of superconducting origin and arises at temperature T* > T_c∞ > T_c in small nonpercolating clusters as a result of strong fluctuations in the occupancy of NUCs (T_c∞ and T_c are the superconducting transition temperatures of an infinitely large and finite NUC clusters, respectively). The T*(δ) and T_c(δ) dependences calculated for YBa₂Cu₃O_6+δ correlate with experimental dependences. In accordance with the model, the region between T*(δ) and T_c(δ) is the range of fluctuations in which finite nonpercolation clusters fluctuate between the superconducting and normal states due to NUC occupancy fluctuations.     

Effect of the magnetic anisotropy energy distribution of MnSb clusters on spontaneous magnetization reversal of GaMnSb thin films

Temperature m(T) and time m(t) dependences of the magnetic moment of GaMnSb thin films with MnSb clusters have been measured. The m(t) dependences are straightened in semilogarithmic coordinates m(lnt). The temperature dependences of magnetic viscosity S(T) corresponding to the slope of straight lines m(lnt) have been studied. It have been demonstrated that the behavior of dependences S(T) is governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters. It have been found that the behavior of dependences m(T) measured after the films were cooled in zero magnetic field and in magnetic field H = 10 kOe is also governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters.     

Size Dependences of the Magnetic Properties of Superconducting Lead–Porous Glass Nanostructures

Superconducting structures Pb–PG formed by filling a porous glass matrix with the lead from melt under pressure have been investigated. Samples with characteristic pore structure diameters of d ≈ 7, 3, and 2 nm have been studied. It has been found that the critical temperature of the superconducting transition in the samples under study is similar to the corresponding value T_c ≈ 7.2 K for bulk lead. At the same time, it has been observed that the critical magnetic field of the nanocomposites, which attains H_c(T = 0 K) ≈ 165 kOe for Pb–PG (3 nm), exceeds several times the value H_c(0) = 803 Oe for bulk lead. The low-temperature magnetic- field dependences of magnetic moment M(H) contain quasi-periodic flux jumps, which vanish with a decrease in the lead nanostructure diameter. A qualitative model of the observed effects is considered.     

Heat capacity of the Pb<Subscript>5</Subscript>(Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>x</Subscript>)<Subscript>3</Subscript>O<Subscript>11</Subscript> ferroelectric system

The temperature dependences of the molar heat capacity at constant pressure, C_p, of Pb₅(Ge_1?xSi_x)₃O₁₁ crystals with x=0, 0.39, and 0.45 in the range 5–300 K, as well as of their permittivity, dielectric losses, and the pyroelectric effect, have been measured. Experimental data on the temperature behavior of the heat capacity are presented in the form of a sum of two Debye and one Einstein terms, C_p(T)=0.405C_D1(Θ_D1=160 K, T)+0.53C_D2(Θ_D2=750 K, T)+0.046C_E(Θ_E=47 K, T). Besides a peak in the region of the ferroelectric Curie point T_c=450 K for crystals with x=0, the temperature dependences of the heat capacity did not reveal any other pronounced anomalies.     

Field Confinement Energy at a Nonlinear Interface between Nonlinear Defocusing Media

The dependences of the resistance of the layered quasi-one-dimensional semiconductor TiS₃ on the direction and magnitude of the magnetic field B have been measured. The anisotropy and angular dependences of the magnetoresistance indicate the two-dimensional character of the conductivity at T < 100 K. Below T₀ ≈ 50 K, the magnetoresistance for the directions of the field in the plane of the layers (ab plane) increases sharply, whereas the transverse magnetoresistance (B ∥ c) becomes negative. The results confirm the possibility of an electron phase transition to a collective state at T₀. The negative magnetoresistance (at B ∥ c) below T₀ is explained by the magnetic-field-induced suppression of two-dimensional weak localization. The positive magnetoresistance (at B ∥ ab) is explained by the effect of the magnetic field on the spectrum of electronic states.     

A new critical point in the non-linear conductivity due to variable range hopping in Si

A critical point in the non-linear conductivity has been observed in epitaxial silicon in the variable range hopping regime, due to a negative differential resistance with a dc bias currentI _dc. This gives thermal breakdown via the electron-phonon coupling and circuit-limited oscillations with a frequencyf∝I _dc, below a critical temperatureT _c. This critical behaviour is intrinsic, and forR(T)=R ₀ exp(T ₀ /T)^1/2 we show thatT _c=0.00512T ₀.     

Josephson vortex lattice melting in Bi-2212 probed by commensurate oscillations of Josephson flux-flow

We studied the commensurate semifluxon oscillations of Josephson flux-flow in Bi-2212 stacked structures near T_c as a probe of melting of a Josephson vortex lattice. We found that oscillations exist above 0.5 T. The amplitude of the oscillations is found to decrease gradually with the temperature and to turn to zero without any jump at T = T₀ (3.5 K below the resistive transition temperature T_c), thus, indicating a phase transition of the second order. This characteristic temperature T₀ is identified as the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, T_BKT, in the elementary superconducting layers of Bi-2212 at zero magnetic field. On the basis of these facts, we infer that melting of a triangular Josephson vortex lattice occurs via the BKT phase with formation of characteristic flux loops containing pancake vortices and antivortices. The B-T phase diagram of the BKT phase found from our experiment is consistent with theoretical predictions.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Hall coefficient in heavy fermion metals

Experimental studies of the antiferromagnetic (AF) heavy fermion metal YbRh₂Si₂ in a magnetic field B indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at B ≥ B_c0 and induces the jump even though the change of the magnetic field at B = B_c0 is infinitesimal. We investigated this by using the model of heavy electron liquid with the fermion condensate. Within this model, the jump takes place when the magnetic field reaches the critical value B_c0 at which the ordering temperature T_N(B = B_c0) of the AF transition vanishes. We show that at B → B_c0, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At T → 0 and B = B_c0 the Grüneisen ratio as a function of the temperature T diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy \(S(T) \propto S_0 + a\sqrt T + bT\) with S₀; a and b are temperature independent constants.     

Magnetic Resonance in Gadolinium Nanoparticles near the Curie Point

The Influence of temperature in the range from 275 to 320 K on ESR spectra and magnetization m of ensembles of spherical gadolinium nanoparticles with the diameter from 89 to 18 nm was studied. The particles with d = 18 nm had a cubic face centered structure and no magnetic transition. At T > T_C all particles were paramagnetic, and their g factors were g = 1.98 ± 0.02 irrespective of their size and structure. At T = T_C the particles having 28 to 89 nm in size experienced a magnetic and orientation transition; at T < T_C their m(H) dependences were described by the Langevin function, and the FMR lines broadened and shifted towards H = 0. FMR lines of the Gd particle ensembles showed a hysteresis behavior during magnetization reversal, which did not correlate with the coercivity of the particles. Dependences of the Gd nanoparticles FMR linewidth ΔH(T) changed proportionally to |T–T_C|.