Operational methods in the study of Sobolev-Jacobi polynomials

Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the so-called umbral image technique. Besides providing a class of new formulae for generalized hypergeometric functions and an implementation of series manipulations for computing lacunary generating functions, our main application of these techniques is the study of Sobolev-Jacobi polynomials. Motivated by applications to theoretical chemistry, we moreover present a deep link between generalized normal-ordering techniques introduced by Gurappa and Panigrahi, two-variable Hermite polynomials and our integral-based series transforms. Notably, we thus calculate all K-tuple L-shifted lacunary exponential generating functions for a certain family of Sobolev-Jacobi (SJ) polynomials explicitly

Electronic properties of LaO1-xFxFeAs in the normal state probed by nmr/nqr

We report 139La, 57Fe and 75As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements on powders of the new LaO1−xFxFeAs superconductor for x=0 and 0.1 at temperatures up to 480 K, and compare our measured NQR spectra with local density approximation (LDA) calculations. For all three nuclei in the x=0.1 material, it is found that the local Knight shift increases monotonically with an increase in temperature, and scales with the macroscopic susceptibility, suggesting a single magnetic degree of freedom. Surprisingly, the spin lattice relaxation rates for all nuclei also scale with one another, despite the fact that the form factors for each site sample different regions of q-space. This result suggests a lack of any q-space structure in the dynamical spin susceptibility that might be expected in the presence of antiferromagnetic correlations. Rather, our results are more compatible with simple quasi-particle scattering. Furthermore, we find that the increase in the electric field gradient at the As cannot be accounted for by LDA calculations, suggesting that structural changes, in particular the position of the As in the unit cell, dominate the NQR response

New insight into the physics of iron pnictides from optical and penetration depth data

We report theoretical values for the unscreened plasma frequencies Omega_p of several Fe pnictides obtained from DFT based calculations within the LDA and compare them with experimental plasma frequencies obtained from reflectivity data. The sizable renormalization observed for all considered compounds points to the presence of many-body effects beyond the LDA. From the large empirical background dielectric constant of about 12-15, we estimate a large arsenic polarizability of about 9.5 +- 1.2 Angstroem^3 where the details depend on the polarizabilities of the remaining ions taken from the literature. This large polarizability can significantly reduce the value of the Coulomb repulsion U_d about 4 eV on iron known from iron oxides to a level of 2 eV or below. In general, this result points to rather strong polaronic effects as suggested by G.A. Sawatzky et al., in Refs. arXiv:0808.1390 and arXiv:0811.0214 (Berciu et al.). Possible consequences for the conditions of a formation of bipolarons are discussed, too. From the extrapolated muon spin rotation penetration depth data at T= 0 and the experimental Omega_p we estimate the total coupling constant lambda_tot for the el-boson interaction within the Eliashberg-theory adopting a single band approximation. For LaFeAsO_0.9F_0.1 a weak to intermediately strong coupling regime and a quasi-clean limit behaviour are found. For a pronounced multiband case we obtain a constraint for various intraband coupling constants which in principle allows for a sizable strong coupling in bands with either slow electrons or holes.Comment: 34 pages, 10 figures, submitted to New Journal of Physics (30.01.2009

Magnetic behavior of single crystalline Ho2_2PdSi3_3

The magnetic behavior of single-crystal Ho$_2$PdSi$_3$, crystallizing in an AlB$_2$-derived hexagonal structure, is investigated by magnetic susceptibility ($\chi$) and electrical resistivity ($\rho$) measurements along two directions. There is no dramatic anisotropy in the high temperature Curie-Weiss parameter or in the $\rho$ and isothermal magnetization data, though there is a noticeable anisotropy in the magnitude of $\rho$ between two perpendicular orientations. The degree of anisotropy is overall less prominent than in the Gd (which is an S-state ion!) and Tb analogues. A point of emphasis is that this compound undergoes long range magnetic ordering below 8 K as in the case of analogous Gd and Dy compounds. Considering this fact for these compounds with well-localised f-orbital, the spin glass freezing noted for isomorphous U compounds in the recent literature could be attributed to the role of the f-ligand hybridization, rather than just Pd-Si disorder.Comment: Physical Review B, in pres

Evidence for Pauli-limiting behaviour at high fields and enhanced upper critical fields near T_c in several disordered FeAs based Superconductors

We report resistivity and upper critical field B_c2(T) data for disordered (As deficient) LaO_0.9F_0.1FeAs_1-delta in a wide temperature and high field range up to 60 T. These samples exhibit a slightly enhanced superconducting transition at T_c = 28.5 K and a significantly enlarged slope dB_c2/dT = -5.4 T/K near T_c which contrasts with a flattening of B_c2(T) starting near 23 K above 30 T. The latter evidences Pauli limiting behaviour (PLB) with B_c2(0) approximately 63 T. We compare our results with B_c2(T)-data from the literature for clean and disordered samples. Whereas clean samples show almost no PLB for fields below 60 to 70 T, the hitherto unexplained pronounced flattening of B_c2(T) for applied fields H II ab observed for several disordered closely related systems is interpreted also as a manifestation of PLB. Consequences are discussed in terms of disorder effects within the frames of (un)conventional superconductivity, respectively.Comment: 2 pages, 3 figures, submitted to M2S Tokyo 0

Electronic properties of LaOFFeAs in the normal state probed by NMR/NQR

We report 139La, 57Fe and 75As nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements on powders of the new LaO1-xFxFeAs superconductor for x = 0 and x = 0.1 at temperatures up to 480 K, and compare our measured NQR spectra with local density approximation (LDA) calculations. For all three nuclei in the x = 0.1 material, it is found that the local Knight shift increases monotonically with an increase in temperature, and scales with the macroscopic susceptibility, suggesting a single magnetic degree of freedom. Surprisingly, the spin lattice relaxation rates for all nuclei also scale with one another, despite the fact that the form factors for each site sample different regions of q-space. This result suggests a lack of any q-space structure in the dynamical spin susceptibility that might be expected in the presence of antiferromagnetic correlations. Rather, our results are more compatible with simple quasi-particle scattering. Furthermore, we find that the increase in the electric field gradient at the As cannot be accounted for by LDA calculations, suggesting that structural changes, in particular the position of the As in the unit cell, dominate the NQR response.Comment: 17 pages, 6 figure

Nanoscale Electronic Order in Iron Pnictides

The charge distribution in RFeAs (R=La, Sm) iron pnictides is probed using As NQR. Whereas undoped and optimally-doped/overdoped compounds feature a single charge environment, two charge environments are detected in the underdoped region. Spin- lattice relaxation measurements show their coexistence at the nanoscale. Together with the quantitative variations of the spectra with doping, they point at a local electronic order in the iron layers, where low- and high-doping-like regions would coexist. Implications for the interplay of static magnetism and superconductivity are discussed