Superconducting state parameters of metallic glass Mg70Zn30 using linearized screened pseudopotential

A linearized form for the screened form factors of electron-phonon interaction in the metallic glass Mg₇₀Zn₃₀ is applied for the first time to predict the superconducting state parameters viz. electron-phonon coupling strength (λ), Coulomb pseudopotential (μ*), transition temperature (T _c), isotope effect exponent (α) and the interaction strength (N ₀ V). Computed results agree with the experimental data available in the literature.     

Pressure dependence of the superconducting state parameters of a binary Ca<Subscript>70</Subscript>Mg<Subscript>30</Subscript> metallic glass superconductor

Theoretical computation of the pressure dependence of superconducting state parameters of a binary Ca₇₀Mg₃₀ metallic glass has been performed using the model potential formalism. Explicit expressions have been derived for the volume dependence of the electron-phonon coupling strength λ and the Coulomb pseudopotential μ*, considering the variation of the Fermi momentum k _F and Debye temperature θ_D with volume. Well-known Ashcroft’s empty core model pseudopotential and five different types of the local-field correction functions, namely, Hartree, Taylor, Ichimaru-Utsumi, Farid et al. and Sarkar et al. have been used for obtaining pressure dependence of transition temperature T _C and the logarithmic volume derivative Φ of the effective interaction strength N ₀ V for the metallic glass superconductor. It has been obtained that T _C of Ca₇₀Mg₃₀ metallic glass decreases rapidly with increasing pressure up to 60% decrease in the volume, for which the μ* and Φ curves show a linear nature. The superconducting phase disappears at about 60% decrease in the volume.     

Icosahedral medium-range order formed in Mg70Zn30 metallic glass: a larger-scale molecular dynamics simulation

A larger-scale Mg70Zn30 alloy system including 100000 atoms has been simulated by using the molecular dynamics method to investigate the icosahedral medium-range order (IMRO) formed in the Mg70Zn30 metallic glass. It is found that the simulated pair distribution function of Mg70Zn30 metallic glass is in good agreement with the experimental results. The glass transition temperature Tg is near 450 K under the cooling rate of 1×1012 K/s. The icosahedral local structures play a critical role in the formation of metallic glass, and they are the dominant local configurations in the Mg70Zn30 metallic glass. The IMRO in the Mg70Zn30 metallic glass is characterized by certain types of extended icosahedral clusters combined by intercross-sharing atoms in the form of chains or dendrites. The size distributions of these IMRO clusters present a magic number sequence of 19, 23, 25, 27, 29, 31, 33, 35, 37, 39,. . . , and the magic clusters can be classified into three types according to their compactness. The IMRO clusters grow rapidly in a low-dimensional way with cooling, but this growth is limited near Tg.     

Isotope effect in charge transport of LuB12

The galvanomagnetic properties of single-crystal samples with various isotopic boron compositions have been investigated for the first time for the normal state of superconductor LuB₁₂ (T c ≈ 0.44 K). Precision measurements of the resistivity, Hall coefficient, and magnetic susceptibility have been performed over a wide temperature range of 2–300 K in magnetic fields up to 80 kOe. A change of the charge transport regime in this nonmagnetic compound with metallic conduction is shown to occur near T* ≈ 50−70 K. As a result, a sharp peak with significantly different amplitudes for Lu¹⁰B₁₂ and Lu¹¹B₁₂ is recorded in the temperature dependences of the Hall coefficient R _H(T) near T*. A significant (about 10%) difference (in absolute value) of the Hall coefficients R _H for the Lu¹⁰B₁₂ and Lu¹¹B₁₂ compounds at helium and intermediate temperatures has been found and the patterns of behavior of the dependence R _H(H) for T < T* in an external magnetic field H ≤ 80 kOe for Lu¹⁰B₁₂ and Lu¹¹B₁₂ are shown to differ significantly. Analysis of the Curie-Weiss contribution to the magnetic susceptibility χ(T) leads to the conclusion about the formation of magnetic moments μ_eff ≈ (0.13−0.19)μ_B in each unit cell of the fcc structure of LuB₁₂ compounds with various isotopic compositions. The possibility of the realization of an electronic topological 2.5-order transition near T* and the influence of correlation effects in the 5d-band on the formation of a spin polarization near the rare-earth ions in LuB₁₂ is discussed.     

Intrinsic inhomogeneities of low-doped lanthanum manganites in the paramagnetic temperature range

The nature of the electrical resistivity for low-doped lanthanum manganites is elucidated. The electrical resistivity is described by the Efros-Shklovskii law (lnρ √ (T ₀/T)^−1/2, where T ₀ √ 1/R _ls) in the temperature range from T* ≈ 300 K ≈ T _C (T _C is the Curie temperature for conducting manganites) to their T _C and is explained by the tunneling of carriers between localized states. The magnetoresistance is explained by a change in the size of localized states R _ls in a magnetic field. The patterns of change in R _ls with temperature and magnetic field strength determined from magnetotransport properties are satisfactorily described in the model of phase separation into small-radius metallic droplets in a paramagnetic matrix. The sizes R _ls and their temperature dependence have been estimated through magnetic measurements. The results confirm the existence of a Griffith phase. The intrinsic inhomogeneities produced by thermodynamic phase separation determine the electrical resistivity and magnetoresistance of lanthanum manganites.     

Superconducting state parameters of CuCZr100-C metallic glasses

The theoretical investigation of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _c, isotope effect exponent α and effective interaction strength N ₀ V of ten Cu _C Zr_100−C metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential. Three local field correction functions proposed by Hartree (H), Taylor (T) and Ichimaru-Utsumi (IU) are used in the current investigation to study the screening influence on the aforesaid properties. It is observed that the electron-phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ*, isotope effect exponent α and effective interaction strength N ₀ V show weak dependences on local field correction functions. The T _c obtained from IU-local field correction function are found an excellent agreement with available theoretical or experimental data. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in metallic glasses.      

Superconducting state parameters of La<Subscript>100-<Emphasis Type="Italic">C</Emphasis></Subscript>Ga<Subscript><Emphasis Type="Italic">C</Emphasis></Subscript> binary metallic glasses

The theoretical investigations of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _C , isotope effect exponent α and effective interaction strength N _O V of six binary La_100-C Ga _C (C = 16, 20, 22, 24, 26 and 28 at. %) metallic glasses have been reported using Ashcroft’s empty core (EMC) model potential for the first time. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. It is observed that the electron-phonon coupling strength λ and the transition temperature T _C are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotential μ*, isotope effect exponent α and effective interaction strength N _O V show weak dependences on the local field correction functions. The T _C obtained from H-local field correction function are found in qualitative agreement with available experimental data and show almost linear nature with the concentration (C) of ‘Ga’ element. A linear T _C equation is proposed by fitting the present outcomes for H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are found to be in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.      

Glass: Kohlrausch exponent,fragility, anharmonicity

The thermodynamical and mechanical properties of (fragile and strong) glass are modeled based on a generalised activation energy relationship log _τ = ΔG _β /RTn(T′) process of glass-forming liquids. This cooperative process involves 1/n(T′) elementary β motions of activation Gibbs energy ΔG _β dependent on the equivalent temperature T′, the temperature of the liquid in equilibrium having the volume of the glass, function of temperature and aging conditions. From this modified VFT law the relaxation of any properties (V , H , stress, creep) can be calculated and approximated by the Kohlrausch function. This model predicts consistency relationships for: a) the temperature (and aging time) variation of the Kohlrausch exponent; b) the temperature dependence of the stabilisation time domain of strong and fragile glass; c) the linear relation between the activation parameters (E ^* energy, S ^* entropy, V ^* volume) of the α and β transition. The Lawson and Keyes (LK) relations are recalled and it is shown that these relations (somewhat equivalant to the compensation law or Meyer-Neldel rule) are observed generally in glass. Morever the (macroscopic) ratios ΔH/ΔV observed during aging or after a temperature jump and the (microscopic) ratio E ^*/V ^* are found equal to κγ (κ compressibily, γ Grüneisen parameter), in agreement with the LK predictions. From various experiments and in agreement with predictions of this model we conclude that the Grüneisen parameter γ _B (pressure derivative of the bulk modulus) and the Mean Square Displacement (MSD) characterising the anharmonicity of solids (and liquids) are the main parameters which govern the relaxation properties of the glass state. Linear relations between the parameters γ _B , the fragility m, and the Kohlrausch exponent n _g at T _g are explained. These correlations underscore a strong relationship between the fragilty of glass formers and the extent of the anharmonicity in the interatomic interactions.     

Critical evolution of the local order parameters related to the nanopolar domains in Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> ceramics

In the present paper, Pb(Mg_1/3Nb_2/3)O₃ (PMN) ceramics prepared by the columbite method were investigated. The dielectric study indicates typical relaxor properties, with a frequency dispersion in the range of 200–350 K. The relaxor-to-paraelectric phase transition was evidenced by the continuous decrease of the local order parameter derived from the permittivity-temperature data. As a result of the critical behavior, the main Raman modes show anomalies at: (i) ∼150 K; (ii) ∼220 K (i.e. close to the critical temperature reported for the field-induced ferroelectric state in PMN single crystal); (iii) ∼260 K (i.e. the temperature of the permittivity maximum); (iv) ∼350 K (the temperature for initiation of the cluster freezing process T ^*); (v) ∼620 K (Burns temperature). The frequency split of the doublet at ∼605 and ∼500 cm⁻¹ presents a critical behavior related to the local symmetry lowering and to the structure ordering due to a phase transformation which takes place below T ^*. The tunability in the paraelectric state was interpreted in terms of reorientation of the non-interacting nanopolar clusters in a double-well potential. The temperature dependence of the nanopolar domain size also shows anomalies in the range of T ^*. The size and dynamics of the polar nanodomains is essential in determining the functional properties of the Pb(Mg_1/3Nb_2/3)O₃ relaxor.     

Electronic thermal capacity in one-dimensional mesoscopic rings

Summary We have investigated the Aharonov-Bohm (AB) effects of electronic thermal capacityC _v in a one-dimensional normal ring using the free-electron model. The results show that the thermal capacity is an oscillation function of external magnetic flux with periods ϕ₀=hc/e, ϕ₀/2, ϕ₀/3,... The amplitude of the capacity fluctuation decreases when temperature increases forT>3T ^* (T ^*=ħ V _F/(K _BπL)). We suggest an appropriate temperatureT∼3T ^* to observe in experiment the capacity-flux characteristic for metallic rings. The authors of this paper have agreed to not receive the proofs for correction.     

Superconducting state parameters of binary metallic glasses

Ashcroft’s empty core (EMC) model potential is used to study the superconducting state parameters (SSPs) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _C , isotope effect exponent αand effective interaction strength N _O V of some binary metallic glasses based on the superconducting (S), conditional superconducting (S’) and non-superconducting (NS) elements of the periodic table. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used for the first time with EMC potential in the present investigation to study the screening influence on the aforesaid properties. The T _C obtained from the H-local field correction function are in excellent agreement with available theoretical or experimental data. In the present computation, the use of the pseudo-alloy-atom model (PAA) was proposed and found successful. Present work results are in qualitative agreement with such earlier reported experimental values which confirm the superconducting phase in all metallic glasses. A strong dependency of the SSPs of the metallic glasses on the valence ‘Z’ is identified.      

Universal behavior of CePd<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Rh<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> ferromagnet at the quantum critical point

The heavy-fermion metal CePd_1−x Rh _x can be tuned from ferromagnetism at x = 0 to the nonmagnetic state at some critical concentration x _c . The non-Fermi liquid behavior (NFL) at x ≃ x _c is recognized by the power-law dependence of the specific heat C(T) given by the electronic contribution susceptibility X(T) and volume expansion coefficient α(T) at low temperatures: C/T ∝ X(T) ∝ α(T)/T∝ 1/ √T. We also demonstrate that the behavior of the normalized effective mass M _N ^* observed in CePd_1−x Rh _x at x ≃ 0.8 agrees with that of M _N ^* observed in paramagnetic CeRu₂Si₂ and conclude that these alloys exhibit the universal NFL thermodynamic behavior at their quantum critical points. We show that the NFL behavior of CePd_1−x Rh _x can be accounted for within the frameworks of the quasiparticle picture and fermion condensation quantum phase transition, while this alloy exhibits a universal thermodynamic NFL behavior that is independent of the characteristic features of the given alloy such as its lattice structure, magnetic ground state, dimension, etc. The text was submitted by the authors in English.     

The 2<Superscript>1/3</Superscript> rule for magnetic susceptibility of gadolinium

The dependences of the magnetization M and the magnetic susceptibility χ = ∂M/∂H of pure gadolinium (the concentration of foreign impurities is lower than 0.1 wt %) on the temperature T and the magnetic field H have been measured using a Quantum Design MPMS-5XL SQUID magnetometer. In this material, inhomogeneities of the atomic structure should not lead to a nonuniform distribution of the magnetic characteristics (including the Curie temperature T _C) over the volume of the sample. The obtained dependences of M and χ have been used to investigate the possibility of suppressing magnetic inhomogeneities of other types by magnetic fields with a strength of up to 50 kOe. It has been assumed that these inhomogeneities are suppressed when the specific relationship, namely, the 2^1/3 rule is fulfilled. The rule relates the portions of the dependence χ(T, H) which at the temperature T = T _C and at the maximum in the curve χ(T) (T = T _m ) depend on H in accordance with the H ^2/3 law. It has been shown that the portions separated from the experimental curves χ(T _C, H) and χ(T _m , H) obey the 2^1/3 rule.     

Current-voltage characteristics of YBa2Cu3O7−x single crystals and Kosterlitz-Thouless transition

The nonlinear I-V characteristic (V(I)) of YBa₂Cu₃O_7−x single crystal was investigated near the transition from the resistive to the superconducting state in the absence of a magnetic field. A modulation Fourier analysis at temperature T* (the maximum of the amplitudes of the higher (n>1) harmonics of the response voltage) was used to determine an analytic dependence V(I) which accurately describes the experimental results (direct measurements and harmonics) in the range of currents I<30 mA (j<310 A/cm²). It is shown that at T* the power approximation of the I-V characteristic V∼I ³ is only found in the low current density limit (j≪j ₀=140 A/cm²). The results are interpreted in terms of the Kosterlitz-Thouless (KT) transition model. It is established that T* corresponds to the temperature of the KT transition T _KT, which means that T _KT can be determined directly. The deviation of V(I) from a power dependence is caused by the nonlogarithmic variation of the vortex interaction energy as a function of the distance between them. Fiz. Tverd. Tela (St. Petersburg) 40, 202–204 (February 1998)     

Screening dependence superconducting state parameters of La100−CGaC binary metallic glasses

The screening dependence theoretical investigations of the superconducting state parameters (SSP) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ^*, transition temperature T_C, isotope effect exponent α and effective interaction strength N₀V of six binary La_100−CGa_C (C=16, 20, 22, 24, 26 and 28 at.%) metallic glasses have been reported using Ashcroft's empty core (EMC) model potential for the first time. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used in the present investigation to study the screening influence on the aforesaid properties. The T_C obtained from H-local field correction function is found in qualitative agreement with available experimental data and show almost linear nature with the concentration (C) of ‘Ga’ element. A linear T_C equation is proposed by fitting the present outcomes for H-local field correction function, which is in conformity with other results for the experimental data. Also, the present results are found in qualitative agreement with other such earlier reported data, which confirms the superconducting phase in the metallic glasses.     

A pseudopotential approach to the superconducting state parameters of (Ni33Zr67)1? x M x (M=Ti, V, Co, Cu) ternary metallic glasses

Superconductivity in ternary metallic glasses has been investigated using the model pseudopotential approach, which has been found quite successful in explaining superconductivity in metals, binary alloys and binary glasses. It is observed that this simple methodology successfully explains superconducting behaviour of ternary glasses without requiring the solution of Dirac equation for a many body problem or estimation of various interactions as required in ab-initio pseudopotential theory. In the present work superconducting state parameters of fourteen metallic glasses of (Ni-Zr)-M system (M=Ti, V, Co, Cu) have been determined in the BCS-Eliashberg-McMillan framework. It is observed that addition of V, Co, and Cu as the third element (M) to a binary metallic glass (Ni₃₃ Zr₆₇) causes the parameters λ,T _c, α, andN ₀ V to decrease, and Coulomb pseudopotential (μ*) to increase with concentration of M, showing that the presence of third element (M) causes suppression of superconducting behaviour of the alloy. The decrease inT _c with increasing concentration of third element (M) may be attributed to the modifications in density of states at the Fermi levelN(E _F), and probable changes in the band structure of the alloy due to addition of the third element (M). Slight difference is noticed when Ti is added to the Ni₃₃ Zr₆₇ alloy. In this caseT _c rises initially and then decreases with concentration of M, showing a peak at aboutx=0.05. This indicates that on addition of Ti, 3d states grow near the Fermi level and hence contribute substantially toN(E _F), favouring superconducting behaviour in this case. The present results forT _c show an excellent agreement with the experimental data. QuadraticT _c equations have been proposed, which provide successfully theT _c values of ternary metallic glasses under consideration. Paper presented at National Conference on Current Trends in Condensed Matter Research, Warangal, India, September 20–22, 2004.     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

Microscopic theory of a strongly correlated two-dimensional electron gas

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T _⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T _*, appears through a crossover at temperatures T ∼ T _* > T _⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T ^−α with the exponent α }~ 2/3.     

Effect of pressure on the behavior of nontransition metallic superconductors

An explicit expression has been derived for the volume dependence of electron-phonon coupling strength () by using a recently proposed quadratic form of the screened pseudopotential and by considering the variation of Fermi momentum with volume. Variation of Coulomb pseudopotential ( ^*) has also been explicitly considered by varying the Fermi momentum. Dependence of transition temperatureT _c and the logarithm of the effective interaction strength (N ₀ V) on the volume has been studied for eight nontransition metallic superconductors. A linear drop inT _c for small values of (–/ ₀) as well as the calculated values of= InN ₀ V/ In, exhibits better matching with the experimental data, as compared to the earlier theoretical results.     

Noncommutative electromagnetism as a large <Emphasis Type="Italic">N</Emphasis> gauge theory

We map noncommutative (NC) U(1) gauge theory on ℝ _C ^d ×ℝ _NC ²ⁿ to U(N→∞) Yang–Mills theory on ℝ _C ^d , where ℝ _C ^d is a d-dimensional commutative spacetime while ℝ _NC ²ⁿ is a 2n-dimensional NC space. The resulting U(N) Yang–Mills theory on ℝ _C ^d is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang–Mills theory onto ℝ _C ^d . We show that the gauge-Higgs system (A _μ ,Φ ^a ) in the U(N→∞) Yang–Mills theory on ℝ _C ^d leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4{\mathcal{N}}=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A _μ ,Φ ^a ) in half-BPS configurations describes self-dual Einstein gravity.