A New Kind of Graded Lie Algebra and Parastatistical Supersymmetry

In this paper the usual $Z_2$ graded Lie algebra is generalized to a new form, which may be called $Z_{2,2}$ graded Lie algebra. It is shown that there exists close connections between the $Z_{2,2}$ graded Lie algebra and parastatistics, so the $Z_{2,2}$ can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems

Critical fluctuations and pseudogap observed in the microwave conductivity of Bi2Sr2CaCu2O8+δ, Bi2Sr2Ca2Cu3O10+δ, and YBa2Cu3O7-δ thin films

Critical fluctuations have been studied in the microwave conductivity of Bi2Sr2CaCu2O8+δ, Bi2Sr2Ca2Cu3O10+δ, and YBa2Cu3O7-δ thin films above T-c. It is found that a consistent analysis of the real and imaginary parts of the fluctuation conductivity can be achieved only if an appropriate wave vector or energy cutoff in the fluctuation spectrum is taken into account. In all of the three underdoped superconducting films one observes strong fluctuations extending far above T-c. The coherence length inferred from the imaginary part of the conductivity exhibits the static critical exponent ν=1 very close to T-c, and a crossover to the region with ν=2/3 at higher temperatures. In parallel, our analysis reveals the absence of the normal conductivity near T-c, i.e., fully opened pseudogap. Following the crossover to the region with ν=2/3, the normal conductivity is gradually recovered, i.e., the closing of the pseudogap is monitored

Berry-Esseen type bounds for the Left Random Walk on GL d (R) under polynomial moment conditions

Let $A_n= \varepsilon_n \cdots \varepsilon_1$, where $(\varepsilon_n)_{n \geq 1}$ is a sequence of independent random matrices taking values in $GL_d(\mathbb R)$, $d \geq 2$, with common distribution $\mu$. In this paper, under standard assumptions on $\mu$ (strong irreducibility and proximality), we prove Berry-Esseen type theorems for $\log ( \Vert A_n \Vert)$ when $\mu$ has a polynomial moment. More precisely, we get the rate $((\log n) / n)^{q/2-1}$ when $\mu$ has a moment of order $q \in ]2,3]$ and the rate $1/ \sqrt{n}$ when $\mu$ has a moment of order $4$, which significantly improves earlier results in this setting

General solution for the complex frequency shift in microwave measurements of thin films

Perturbation of a microwave cavity by a small sample with variable dielectric, magnetic, or conducting properties is considered. The complex frequency shift is derived in terms of a volume integral, or equivalently, in terms of a surface integral. These are used to obtain a general formula for thin films in the microwave electric field maximum. The complex frequency shift depends on the depolarization factor of the film and on its thickness in a nontrivial way. The previously known expressions for the complex frequency shift are shown to be good approximations of the present solution in the low and high conductivity limits. Our formula is applied to calculate the signal shapes in superconducting films of various geometric parameters and conductivities. It is shown that a diversity of signal shapes can result, and experimental support of those shapes is provided. The role of the dielectric substrate on which the thin film is grown is simply reduced to an asymmetry effect

Short-wavelength cutoff effects in the ac fluctuation conductivity of superconductors

The short-wavelength cutoff has been introduced in the calculation of the ac fluctuation conductivity of superconductors. It is shown that a finite cutoff leads to a breakdown of the scaling property in frequency and temperature. Also, it increases the phase φ of the complex conductivity (tanφ=σ2/σ1) beyond π/4 at Tc. Detailed expressions containing all essential parameters are derived for three-dimensional isotropic and anisotropic fluctuation conductivity. In the two-dimensional case we obtain individual expressions for the fluctuation conductivity for each term in the sum over discrete wave vectors perpendicular to the film plane. A comparison of the theory to the experimental microwave fluctuation conductivity is provided

Magnetotransport of lanthanum doped RuSr2GdCu2O8 - the role of gadolinium

Strongly underdoped RuSr_1.9La_0.1GdCu_2O_8 has been comprehensively studied by dc magnetization, microwave measurements, magnetoresistivity and Hall resistivity in fields up to 9 T and temperatures down to 1.75 K. Electron doping by La reduces the hole concentration in the CuO2 planes and completely suppresses superconductivity. Microwave absorption, dc resistivity and ordinary Hall effect data indicate that the carrier concentration is reduced and a semiconductor-like temperature dependence is observed. Two magnetic ordering transitions are observed. The ruthenium sublattice orders antiferromagnetically at 155 K for low applied magnetic field and the gadolinium sublattice antiferromagnetically orders at 2.8 K. The magnetoresistivity exhibits a complicated temperature dependence due to the combination of the two magnetic orderings and spin fluctuations. It is shown that the ruthenium magnetism influences the conductivity in the RuO2 layers while the gadolinium magnetism influences the conductivity in the CuO2 layers. The magnetoresistivity is isotropic above 4 K, but it becomes anisotropic when gadolinium orders antiferromagnetically.Comment: 7 pages, 9 figures, submitted to European Physical Journal

Coherence lengths and anisotropy in MgB2 superconductor

Field and temperature microwave measurements have been carried out on MgB2 thin film grown on Al2O3 substrate. The analysis reveals the mean field coherence length xi_{MF} in the mixed state and a temperature independent anisotropy ratio gamma_{MF} = xi_{MF}^{ab} / xi_{MF}^c approximately 2. At the superconducting transition, the scaling of the fluctuation conductivity yields the Ginzburg-Landau coherence length with a different anisotropy ratio gamma_{GL} = 2.8, also temperature independent.Comment: submitted to PR

Correlation gap in the heavy-fermion antiferromagnet UPd_2Al_3

The optical properties of the heavy-fermion compound UPd$_2$Al$_3$ have been measured in the frequency range from 0.04 meV to 5 meV (0.3 to 40 cm$^{-1}$) at temperatures $2 {\rm K}<T< 300$ K. Below the coherence temperature $T^*\approx 50$ K, the hybridization gap opens around 10 meV. As the temperature decreases further ($T\leq 20$ K), a well pronounced pseudogap of approximately 0.2 meV develops in the optical response; we relate this to the antiferromagnetic ordering which occurs below $T_N\approx 14$ K. The frequency dependent mass and scattering rate give evidence that the enhancement of the effective mass mainly occurs below the energy which is associated to the magnetic correlations between the itinerant and localized 5f electrons. In addition to this correlation gap, we observe a narrow zero-frequency conductivity peak which at 2 K is less than 0.1 meV wide, and which contains only a fraction of the delocalized carriers. The analysis of the spectral weight infers a loss of kinetic energy associated with the superconducting transition.Comment: RevTex, 15 pages, 7 figure

A Transport and Microwave Study of Superconducting and Magnetic RuSr2EuCu2O8

We have performed susceptibility, thermopower, dc resistance and microwave measurements on RuSr2EuCu2O8. This compound has recently been shown to display the coexistence of both superconducting and magnetic order. We find clear evidence of changes in the dc and microwave resistance near the magnetic ordering temperature (132 K). The intergranular effects were separated from the intragranular effects by performing microwave measurements on a sintered ceramic sample as well as on a powder sample dispersed in an epoxy resin. We show that the data can be interpreted in terms of the normal-state resistivity being dominated by the CuO2 layers with exchange coupling to the Ru moments in the RuO2 layers. Furthermore, most of the normal-state semiconductor-like upturn in the microwave resistance is found to arise from intergranular transport. The data in the superconducting state can be consistently interpreted in terms of intergranular weak-links and an intragranular spontaneous vortex phase due to the ferromagnetic component of the magnetization arising from the RuO2 planes.Comment: 20 pages including 6 figures in pdf format. To be published in Phys. Rev.