On the Bose-Einstein condensation of free relativistic bosons with or without mass

The Bose-Einstein condensation of free relativistic particles [=(M ² c ⁴ +c ² p ² ) ^1/2 –Mc ² ] is studied rigorously. For massless bosons (=cp), the condensation transition of third (second) order occurs in2 (3) dimensions (D). The molar heat capacity follows the T ² (T ³ ) law below the condensation temperature T_c [k ^B T_c=(2 ² c ² n/1.645) ^1/2 [( ^{2 3} c ³ n/1.202) ^1/3 ], reaches4.38 (10.8) R at T=T_c, and approaches the high-temperature-limit value2 (3) R with no jump (a jump equal to6.75R) in2 (3)D. For finite-mass (M) bosons, the phase transition occurs only in3D with the condensation temperature T_c always smaller than that of the corresponding nonrelativistic bosons [=(2M) ^–1 p ² ]. If the mass M is reduced to zero, the condensation temperature T_c grows monotonically and reaches eventually that of massless relativistic bosons. This mass-dependence of T_c is therefore distinct from the case of nonrelativistic bosons, where T_c grows to infinity as M 0. A brief discussion is given for a possible connection with the normal-to-super transition of the independently moving Cooper pairs (bosons).     

Low temperature self-ion irradiation of pure and granular aluminium-films

Al-films, evaporated at room temperature under different oxygen partial pressures, were irradiated with self-ions (500 keV, Al⁺⁺) at low temperature (<7 K). The observed increase of the resistivity and of the superconducting transition temperatureT _c depends strongly on the oxygen contentc ₀ present in the layers. A qualitative different behaviour of the above quantities was found for different fluence ranges of the bombarding ions. For high fluences in all cases an oxygen stabilized disorder state was obtained with correspondingT _c-increases betweenT _c=0.2 K for the purest films (c ₀0.5 at %) andT _c =1.2 K for films with c ₀=40 at %. The annealing behaviour of the irradiated films is also dependent on the oxygen contentc ₀.     

39K NMR study of the low temperature phase transitions in KLiSO4

The³⁹K NMR spectra, spin-spin (T ₂) and spin-lattice (T ₁) relaxation times of KLiSO₄ have been measured in the temperature range from 300 K to 90 K. The temperature dependence of the³⁹K (I=3/2) NMR spectra demonstrates the occurrence of a first order phase transition atT _c1=217 K which occurs without a change in the K⁺ site symmetry and another first order transition atT _c2=190 K which is connected with a lowering of the K⁺ site symmetry and the formation of three kinds of ferroelastic domains. From the angular dependence of the second order quadrupole shifts of the³⁹K NMR 1/2–1/2 transitions the electric-field gradient (EFG) tensors at the potassium sites were determined at 290 K, 204 K and 180 K. The symmetry of the ferroelastic phase is monoclinic and not orthorhombic as the K⁺ EFG tensors are tilted away from thec-axis belowT _c2. TheT ₁ data further show the freezing in of the slow reorientational motion 10^–8 s with decreasing temperature from 300 to 90 K.On leave from: J. Stefan Institute, E. Kardelj University of Ljubljana, Ljubljana, Yugoslavia     

Ferroelastic phase transition in CaCl2 studied by Raman spectroscopy

CaCl₂ undergoes a second-order proper ferroelastic phase transition from the tetragonal rutile type to the orthorhombic calcium-chloride type structure atT _c 490 K. The transition is of the optical type and induced by an order parameter ofB _1g symmetry. An underdamped soft mode exists above and belowT _c , the frequency and intensity of which have been measured by Raman spectroscopy. Due to a strong coupling to strain the softening is incomplete and a transverse acoustical mode is predicted to become soft. The frequency of the optical soft mode, _s, exhibits a classical Landau behavior in a remarkably large temperature range. The unusual value of the ratio of _s ² / below and aboveT _c of about –6.5 can be accounted for by appropriate terms of the thermodynamical potential. The Raman active hard modes show no significant anomaly atT _c .     

Extremity of the disordered phase in the Ising model on the Bethe lattice

We prove that the disordered Gibbs distribution in the ferromagnetic Ising model on the Bethe lattice is extreme forTT _c ^SG , whereT _c ^SG is the critical temperature of the spin glass model on the Bethe lattice, and it is not extreme forT _c ^SG .     

Mössbauer study of oxygen-related lattice instabilities in oriented 1-2-3 HTSC

⁵⁷Fe Mössbauer effect measurements as a function of temperature between 78 and 293 K in grain-aligned YBaCuO (T _c=89 K, T _c<2 K) with bothc andc orientations revealed a sequence of anomalies in the recoilless fraction, center shift and linewidth of all⁵⁷Fe quadrupole doublets in the host lattice. These anomalies are believed to arise due to antiferroelectric phase transitions driven by a nonlinear anharmonic vibrational motion of oxygen atoms in a breathing mode configuration. The results obtained are indicative of a possible coexistence of high-T _c superconductivity and antiferroelectricity in 1-2-3 ceramics.     

Far-infrared reflectivity of sintered YBa2Cu3O7 in the normal and superconducting state

We report on a study of the far-infrared reflection for a sintered YBa₂Cu₃O₇ sample that contained a large portion of preferentially oriented crystallites with thea–b plane parallel to the surface and that showed extraordinary high far-infrared reflectivity. From experimental reflection data we determined, by Kramers-Kronig analysis, the dynamical conductivity and extracted the contributions due to free charge carriers and phonons, respectively. We find evidence for an anomalous behavior of the dynamical conductivity at temperatures aboveT _c ; the dynamical conductivity increases strongly for temperatures approachingT _c and is strongly frequency dependent. By use of the Mattis-Bardeen theory we obtain an estimate for the superconducting energy gap of 2/kT _c 4.6 (forTT _c ). We find that the lowest frequency infrared-active phonon mode is less damped in the superconducting state than in the normal state.     

Point-contact measurements of CeB6 and CeCu6 in high magnetic fields

Epitaxial YBa₂Cu₄O₇-thin films with thec-axis oriented perpendicular to the film plane were prepared bydc-sputtering from a single stoichiometric target on (100) SrTiO₃-substrates. Typical values of the inductively measured superconducting transitions were about 90 K with a width less than 0.5 K. Critical current densities were measured on 5 to 10 m wide strips as function of magnetic field and temperature. The temperature dependences ofj _c follow a universal functionj _c(B,T)=j _c ^* (T=0,B)·(1–T/T _c (B)) with =1.5±0.1. ForB=0 andT=77 K we obtainedj _c =4·10⁶ A/cm². The field dependence of the resistive transitions was measured with the magnetic field parallel to thec-axis. The slope of the upper critical fieldB _c2 (T) was determined for different criteria. The carrier concentration evaluated from Hall-effect measurements was found to decrease linearly from one per unit cell at 240 K with decreasing temperature extrapolating nearly through zero forT=0. Highly resolved angular dependent measurements of the critical current density withB perpendicular to the current but tilted from thec-axis show a very strong and sharp enhancement ofj _c for the magnetic field parallel to the (CuO₂)-layers (Bc). Additionally to this phenomenon, which is caused by an intrinsic pinning mechanism due to the layered structure of high-T _c -superconductors the influence of the anisotropy of the upper critical field onj _c (B, T, ) is evident nearT _c .     

Ultrasonic investigation of phase transitions in K2SnCl6

The velocities and the attenuation of ultrasonic waves have been investigated as a function of temperature (255KT350K) for the cubic phase of K₂SnCl₆ which undergoes a structural transition atT _c1263K. An anomalous decrease of the shear stiffness constantc=1/2(c ₁₁ –c ₁₂) of about 30% between room temperature andT _c1 is found in this cubic high temperature phase whenT _c1 is approached from above. Whereas the softening ofc extends over a substantial temperature range (about 50 K), the other shear constantc ₄₄ shows only a weak decrease, which is an order of magnitude smaller and restricted toT–T _c110 K. NearT _c1, a strong increase occurs in the attenuation of the shear acoustic wave propagated along the [111] direction, while such an anomalous attenuation is not observed for the transverse acoustic wave propagated along [100]. Furthermore, atT _c1 a hysteresis is detected for the longitudinal sound wave velocityv _L[100], which is restricted to the temperature region 262KT263.5 K. In addition, the room-temperature elastic constants of (NH₄)₂SiF₆ and the hydrostatic pressure derivatives of the elastic constants of K₂SnCl₆ and (NH₄)₂SiF₆ at room-temperature are presented and discussed in terms of mode softening behaviour.     

Investigation of the plasma potential oscillations in the range of geodesic acoustic mode frequencies by heavy ion beam probing in tokamaks

Specific oscillations within a range of 20 kHz (20 kHz-mode) were investigated on the T-10 and TEXT tokamaks using Heavy Ion Beam Probe (HIBP) diagnostic. Regimes with ohmic heating on both machines, and with off-axis ECRH in T-10 were studied. It was shown that 20 kHz-modes are mainly the potential oscillations. The power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with a contrast range of (3–5). They are the manifestation of torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. It was shown that in TEXT the radial electric field oscillations exist in a limited radial range of 0.65 > < 0.95. The frequency of 20 kHz-mode is varied in the region of observation; it diminishes to the plasma edge. In T-10, after ECRH switch-on, the frequency increases, correlating with the growth of the electron temperature T _e. In both machines the frequency of the 20 kHz-mode varies with local T _e: f T _e ^1/2 , which is consistent with theoretical scaling for geodesic acoustic modes (GAM): f _GAM c _s/R T _e ^1/2 , where c _s is the speed of sound. The absolute frequencies are close to GAM values within a factor of unity.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Temperature dependence of viscosity near the glass transition

Real glass transitions, where activated processes are included, are analysed near Whitney fold and cusp singularities. In particular the temperature dependence of the viscosity is studied. For sufficiently strongly coupled systems there is close to a fold singularity located atT=T _c , a crossover from an algebraic divergence (T–T _c )^– forT>T _c , to an Arrhenius dependence exp(E/k _B T) forT<T _c . If a parameter vector specifying the system also passes close to a cusp singularity, atT ₀<T _c , there may be a temperature region where the viscosity also shows Fogel-Fulcher like dependence. The results for the viscosity are intimately connected with the dynamics for the so-called -relaxation process, where relaxation occurs via a fractal time process in the delevant time region.     

Variation of electronic properties and evidence for a reversible defect induced metal to semiconductor transition in PbMo6S8 observed by ion irradiation and subsequent annealing of thin films

The influence of lattice disorder varied by low temperature irradiation with 20 MeV³²S-ions and subsequent isochronal thermal annealing on Hall-effectR _H (T), resistivityp(T) and superconducting critical temperatureT _c of thin films of the Chevrel-phase PbMo₆S₈ is reported. It is found that the well known, unusual sensitivity ofT _c is correlated with drastic changes of normal state transport properties e.g.R _H (T) andp(T). In the low fluence regime (6·10¹³ cm^–2,T _c 2 K) annealing leads to a monotonous restoration of the initial properties with the main recovery occurring at temperatures as low as 500 K. Contrary to this, annealing of highly disordered samples (10¹⁵ cm^–2) creates semiconductor-like conduction behavior. This manifests itself by a strong increase of the electrical resistivity with decreasing temperature which becomes more pronounced at higher annealing temperaturesT _A . AfterT _A =800 K the resistivityp(15K) is enhanced by more than a factor of 1000 withp(15K)/p(280 K)=210 compared to as irradiated. Further annealing at 900 K and 1000K results in the reappearance of metallicp(T)-behavior and superconductivity (T _c >10K). The observed effects can be understood by systematic changes of the electronic density of states consistent with an earlier proposed defect model.     

Note on the interfacial tension of phase-separated polymer solutions

Earlier theoretical calculations of the interfacial tension of phase-separated polymer solutions as a function of the degree of polymerizationN and the temperatureT, based partly on the mean-field approximation, had led toN ^–1/4(1–T/T _c )^3/2 for fixedN1 andT approaching the critical solution temperatureT _c It is here remarked that the scaling procedure of de Gennes then modifies this toN ^–0.37(1–T/T _c )^1.26, which is in close accord with the experimentalN ^–0.44(1–T/T _c )^1.26. The simplest mean-field picture yieldsN ^–1/2(1–T/T _c )^3/2.     

Thermal expansion,sound velocities,specific heat and pressure derivative ofT c in YBa2Cu3O7

We report measurements, between helium and room temperature, of the thermal expansion (T), sound velocitiesv _L (T) andv _T (v) and specific heatC(T) of YBa₂Cu₃O₇ samples, all cut from the same sintered pellet. A linear term in (T) is resolved at low temperatures. It is compared with a corresponding term in the low temperature specific heat and, using the bulk modulus from our sound propagation measurements, a Grüneisen parameter of usual size (1.2±0.4) is derived-in conformity with the possible existence of non-superconducting carriers well belowT _c . Longtime drift effects in the length of the sample between 30 K and 60 K point to the vicinity of a structural instability. The Debye temperature derived fromC(T) amounts to about 450 K atT=T _c =91 K and forT0 approaches 350 K, in agreement with the value deduced fromv _L (T) andv _T (T). The superconducting transition is indicated by anomalies with idealized discontinuities and C. A thermodynamic relation between and C yields the relative pressure derivative ofT _c ,t _p =T _c ^–1 (T _c /p) _p0=+(0.7±0.2)·10^–7 kbar^–1.     

Low temperature properties of (La,Nd)Sn3 alloys

Dilute (La_1–x Nd _x )Sn₃ alloys with 0.01<x<0.15 are characterized by determination of the superconducting transition temperatureT _c as well as low temperature measurements of the specific heat and inelastic neutron scattering. As an important result of these experiments we found that the Nd impurities in LaSn₃ exist as stable trivalent ions, in contrast to all other light rare earths. In addition, specific heat and neutron scattering results revealed the scheme of crystal field (CF) levels of Nd³⁺.Using this level scheme, the concentration dependence of the superconducting transition temperature,T _c (x), could be quantitatively fitted up tox9 at % by the theory of Keller and Fulde [J. Low. Temp. Phys.4, 289 (1971)]. From the relatively high initial slope ofT _c (x) we inferred that — besides isotropic spin exchange — other pair-breaking processes are important.In contrast toT _c (x), the reduced specific heat jumpsC/C ₀ as a function ofT _c /T _c0 (whereT _c0 andC ₀ refer to LaSn₃) were found to lie considerably below the theoretical curve for isolated Nd³⁺ ions. This is explained by Nd—Nd interactions resulting in a mean Zeeman splitting (<k _B T _c ) of the CF ground state, which could be directly observed in the form of broadened Schottky humps in the normal state specific heats.     

The ferromagnetic order and the critical exponentγ of Gd monolayers and thin films on W(110)

The new application of electron-spin resonance to paramagnetic monolayers on well characterized surfaces (LEED, AES) in UHV is described. The high sensitivity of ESR is demonstrated for 10^–2 monolayers NO₂ adsorbed on Xe/Ag(111), corresponding to 10¹² detectable molecules. For monolayers of Gd(0001) on W(110) the critical exponent of the susceptibility and the ordering temperatureT _c are determined by analysing the ESR intensity and resonance field forTT _c ⁺ . Both determinations independently give a monolayerT _c of app. 271 K. The critical exponent changes from 2D to 3D Ising-values for monolayers to thicker films.     

Note on the quantum displacement of the critical point

The quantum corrections to the law of corresponding states are studied by calculating the critical pressure, temperature, and density to first order in Planck's constanth on an exactly soluble model. The ratio of the critical parameters to the corresponding classical values are found to be (p _c/p _c ⁰)^1/2=_c/_c ⁰ = T_c/T_c ⁰ = 1–0.67, with=h _c ^1/3(mkT _c)^–1/2. The critical ratio is independent ofh to first order. The results are compared with critical data for noble gases and hydrogen isotopes.     

Quantum BRST charge for quadratically nonlinear Lie algebras

We consider the construction of a nilpotent BRST charge for extensions of the Virasoro algebra of the form {T _a ,T _b }=f _ab ^c T _c +V _ab ^cd T _c T _d , (classical algebras in terms of Poisson brackets) and [T _a ,T _b ]=h _ab I+f _ab ^c T _c +V _ab ^cd (T _c T _d )(quantum algebras in terms of commutator brackets; normal ordering of the product (T _c T _d ) is understood). In both cases we assume that the set of generators {T _a } splits into a set {H _i } generating an ordinary Lie algebra and remaining generators {S }, such that only theV _ij are nonvanishing. In the classical case a nilpotent BRST charge can always be constructed; for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent BRST charge. Non-trivial examples are the spin-3 algebra with central chargec=100 and theso(N)-extended superconformal algebras with levelS=–2(N–3).     

Acoustic properties of amorphous SiO2 and PdSiCu,and of crystalline Ag,NbTi and Ta at very low temperatures

With the vibrating reed and vibrating wire techniques we have investigated the acoustic properties of vitreous silica (SiO₂, Suprasil I) and of amorphous PdSiCu as well as of polycrystalline Ag, NbTi and Ta at frequencies of 100 Hz/2<6 kHz and at temperatures of 0.1 mKT1 K. The relative change of sound velocity v/v of SiO₂ shows saturation effects, strain amplitude dependence, as well as an unexpected temperature dependence below its maximum atT<50 mK. For PdSiCu we observe that below a certain temperature, which depends on the applied strain, the temperature dependence of the sound velocityv deviates from the logarithmic behavior observed at higher temperatures and reaches an almost constant value atT<1 mK. In the same temperature rangeQ ^–1 does not remain constant but steadily decreases. The acoustic properties of the two amorphous materials at finite strain show substantial deviations from the standard tunneling model. Some of the observed anomalies can be explained taking into account the change of population of the tunneling systems energy states and a nonlinear relaxation absorption. For polycrystalline Ag we find v/v lnT andQ ^–1T ^1/3 over three decades inT atT<100 mK; it shows low-temperature acoustic properties which are strikingly similar to those of amorphous materials. The temperature and strain dependencies of the acoustic properties of polycrystalline superconducting NbTi and Ta resemble those obtained for SiO₂. These results indicate that there are basically no differences in the low-temperature acoustic properties of polycrystals and amorphous materials.     

Dependence ofT c on doping in oxygen-hole induced Jahn-Teller mediated superconductors

A bipolaronic model of high-T _c superconductivity, that is based upon the idea that a doped oxygenhole reduces the separation between the and levels of the neighbouring Cu-ion and hence causes a Jahn-Teller mixing between the two levels, is suggested. Within the BCS scheme, the bipolaron Hamiltonian is investigated for the superconducting order parameter and the critical temperatureT _c as a function of hole-doping. Under suitable approximation for the bipolaronic kinetic energy, the hole-doping dependence ofT _c shows a universal behaviour. For temperatures close toT _c and forT _c 1, obeys the BCS type of relation with pre-factor of (1–T/T _c )² related to the range of superconducting-phase against the doping axis.