Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-Order PDEs

Very singular self-similar solutions of semilinear odd-order PDEs are studied on the basis of a Hermitian-type spectral theory for linear rescaled odd-order operators.Comment: 49 pages, 12 Figure

Gap nodes induced by coexistence with antiferromagnetism in iron-based superconductors

We investigate the pairing in iron pnictides in the coexistence phase, which displays both superconducting and antiferromagnetic orders. By solving the pairing problem on the Fermi surface reconstructed by long-range magnetic order, we find that the pairing interaction necessarily becomes angle-dependent, even if it was isotropic in the paramagnetic phase, which results in an angular variation of the superconducting gap along the Fermi surfaces. We find that the gap has no nodes for a small antiferromagnetic order parameter M, but may develop accidental nodes for intermediate values of M, when one pair of the reconstructed Fermi surface pockets disappear. For even larger M, when the other pair of reconstructed Fermi pockets is gapped by long-range magnetic order, superconductivity still exists, but the quasiparticle spectrum becomes nodeless again. We also show that the application of an external magnetic field facilitates the formation of nodes. We argue that this mechanism for a nodeless-nodal-nodeless transition explains recent thermal conductivity measurements of hole-doped Ba_{1-x}K_xFe_2As_2. [J-Ph. Read et.al. arXiv:1105.2232].Comment: 13 pages, 10 figures, submitted to PR

Enhancement of TcT_{c} by disorder in underdoped iron pnictides

We analyze how disorder affects the transition temperature $T_{c}$ of the $s^{+-}$superconducting state in the iron pnictides. The conventional wisdom is that $T_{c}$ should rapidly decrease with increasing inter-band non-magnetic impurity scattering, but we show that this behavior holds only in the overdoped region of the phase diagram. In the underdoped regime, where superconductivity emerges from a pre-existing magnetic state, disorder gives rise to two competing effects: breaking of the Cooper pairs, which tends to reduce $T_{c}$, and suppression of the itinerant magnetic order, which tends to bring $T_{c}$ up. We show that for a wide range of parameters the second effect wins, leading to an increase of $T_{c}$ with disorder in the coexistence state. Our results explain several recent experimental findings and provide another evidence for $s^{+-}$-pairing in the iron pnictides.Comment: 5 pages, 3 figures; revised version accepted in PRB-R

Two-band superconductivity in doped SrTiO3_{3} films and interfaces

We investigate the possibility of multi-band superconductivity in SrTiO$_{3}$ films and interfaces using a two-dimensional two-band model. In the undoped compound, one of the bands is occupied whereas the other is empty. As the chemical potential shifts due to doping by negative charge carriers or application of an electric field, the second band becomes occupied, giving rise to a strong enhancement of the transition temperature and a sharp feature in the gap functions, which is manifested in the local density of states spectrum. By comparing our results with tunneling experiments in Nb-doped SrTiO$_{3}$, we find that intra-band pairing dominates over inter-band pairing, unlike other known multi-band superconductors. Given the similarities with the value of the transition temperature and with the band structure of LaAlO$_{3}$/SrTiO$_{3}$ heterostructures, we speculate that the superconductivity observed in SrTiO$_{3}$ interfaces may be similar in nature to that of bulk SrTiO$_{3}$, involving multiple bands with distinct electronic occupations.Comment: revised expanded versio

Semi-empirical analysis of Sloan Digital Sky Survey galaxies III. How to distinguish AGN hosts

We consider the techniques to distinguish normal star forming (NSF) galaxies and active galactic nuclei (AGN) hosts using optical spectra. The observational data base is a set of 20000 galaxies extracted from the Sloan Digital Sky Survey, for which we have determined the emission line intensities after subtracting the stellar continuum obtained from spectral synthesis. Our analysis is based on photoionization models computed using the stellar ionizing radiation predicted by Starburst 99 and, for the AGNs, a broken power-law spectrum. We explain why, among the four classical emission line diagnostic diagrams, the [OIII]/Hb vs [NII]/Ha one works best. We show however, that none of these diagrams is efficient in detecting AGNs in metal poor galaxies, should such cases exist. We propose a new divisory line between ``pure'' NSF galaxies and AGN hosts. We also show that a classification into NSF and AGN galaxies using only [NII]/Ha is feasible and useful. Finally, we propose a new classification diagram, the DEW diagram, plotting D_n(4000) vs max(EW[OII],EW[NeIII]). This diagram can be used with optical spectra for galaxies with redshifts up to z = 1.3, meaning an important progress over classifications proposed up to now. Since the DEW diagram requires only a small range in wavelength, it can also be used at even larger redshifts in suitable atmospheric windows. It also has the advantage of not requiring stellar synthesis analysis to subtract the stars and of allowing one to see ALL the galaxies in the same diagram, including passive galaxies.Comment: 14 pages, 9 figures, accepted for publication in MNRAS (replaced on august 3, 2006, eqs 6 and 7 corrected