Superconductor-insulator transition in Coulomb disorder

Superconductor-insulator transition driven by the decreasing concentration of electrons $n$ is studied in the case of the disorder potential created by randomly positioned charged impurities. Electrons and Cooper pairs (formed by an non-Coulomb attraction) nonlinearly screen the random potential of impurities. Both electrons and Cooper pairs can be delocalized or localized in the resulting self-consistent potential. The border separating the superconductor and insulator phases in the plane of the concentration of electrons and the length of the Cooper pair is found. For a strong disorder the central segment of this border follows the BEC-BCS crossover line defined for a clean sample.Comment: 4.5 pages, introduction rewritten, a dozen of references added, 2D case adde

Compensation driven superconductor-insulator transition

The superconductor-insulator transition in the presence of strong compensation of dopants was recently realized in La doped YBCO. The compensation of acceptors by donors makes it possible to change independently the concentration of holes n and the total concentration of charged impurities N. We propose a theory of the superconductor-insulator phase diagram in the (N,n) plane. It exhibits interesting new features in the case of strong coupling superconductivity, where Cooper pairs are compact, non-overlapping bosons. For compact Cooper pairs the transition occurs at a significantly higher density than in the case of spatially overlapping pairs. We establish the superconductor-insulator phase diagram by studying how the potential of randomly positioned charged impurities is screened by holes or by strongly bound Cooper pairs, both in isotropic and layered superconductors. In the resulting self-consistent potential the carriers are either delocalized or localized, which corresponds to the superconducting or insulating phase, respectively

Strong asymptotics for the Pollaczek multiple orthogonal polynomials

The asymptotic properties of multiple orthogonal polynomials with respect to two Pollaczek weights with different parameters are considered. This set of weights is a Nikishin system generated by two measures with unbounded supports; moreover, the second measure is discrete. During the last years, multiple orthogonal polynomials with respect to Nikishin systems of this type have found wide applications in the theory of random matrices. Strong asymptotic formulas for the polynomials under consideration are obtained by means of the matrix Riemann-Hilbert method.The first author acknowledges the support of the Rus sian Science Foundation, project no. 14 -21- 00025. The second author’s research was supported by MTM2012 -36732 -C03 -01 MEC. The third author’s research was supported by MTM2011-28952-C02-01 ERDF, Exc. Grant no. P11- FQM -7276, Res. Group FQM -229, and CEIMAR Universidad de Almeria

Theory of Interaction Effects in N-S Junctions out of Equilibrium

We consider a normal metal - superconductor (N-S) junction in the regime, when electrons in the normal metal are driven out of equilibrium. We show that the non-equilibrium fluctuations of the electron density in the N-layer cause the fluctuations of the phase of the order parameter in the S-layer. As a result, the density of states in the superconductor deviates from the BCS form, most notably the density of states in the gap becomes finite. This effect can be viewed as a result of the time reversal symmetry breaking due to the non-equilibrium, and can be described in terms of a low energy collective mode of the junction, which couples normal currents in N-layer and supercurrents. This mode is analogous to the Schmid-Sch\"{o}n mode. To interpret their measurements of the tunneling current, Pothier {\em et. al} [Phys. Rev. Lett. {\bf 79}, 3490 (1997)] had to assume that the energy relaxation rate in the normal metal is surprisingly high. The broadening of the BCS singularity of the density of states in the S-layer manifest itself similarly to the broadening of the distribution function. Mechanism suggested here can be a possible explanation of this experimental puzzle. We also propose an independent experiment to test our explanation.Comment: 16 pages, 2 .eps figure

"Unusual" metals in two dimensions: one-particle model of the metal-insulator transition at T=0

The conductance of disordered nano-wires at T=0 is calculated in one-particle approximation by reducing the original multi-dimensional problem for an open bounded system to a set of exactly one-dimensional non-Hermitian problems for mode propagators. Regarding two-dimensional conductor as a limiting case of three-dimensional disordered quantum waveguide, the metallic ground state is shown to result from its multi-modeness. On thinning the waveguide (in practice, e. g., by means of the ``pressing'' external electric field) the electron system undergoes a continuous phase transition from metallic to insulating state. The result predicted conform qualitatively to the observed anomalies of the resistance of different planar electron and hole systems.Comment: 7 pages, LATEX-2

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

ОПРЕДЕЛЕНИЕ СООТНОШЕНИЯ ОКСИДОВ ЛИТИЯ И БОРА В БОРАТАХ ЛИТИЯ ПО ИЗМЕРЕНИЯМ РАССЕЯННОГО ИЗЛУЧЕНИЯ РЕНТГЕНОВСКОЙ ТРУБКИ НА РЕНТГЕНОФЛУОРЕСЦЕНТНОМ СПЕКТРОМЕТРЕ

A method for determining the composition of anhydrous lithium borates, based on measuring the scattered characteristic radiation of an X-ray tube using the X-ray fluorescence spectrometer, is proposed. The method is based on the approach previously described in the literature (Van Sprang H. A., e. a., 1998; Kalinin B.D. e. a., 2011) for determining the elements with atomic number less than 6 in borosilicate glasses and organic compounds. As a calibration parameter, the ratio (R) of coherent (Rayleigh) to incoherent (Compton) X-ray intensities of RhKα tube anode line primary scattering radiation is used, which, to a first approximation, is determined by the average atomic number of the substance. For the anhydrous lithium borates (stoichiometric compounds or amorphous glass), the average atomic number is determined by the ratio of lithium and boron oxides which can be approximated by the following dependence: (Li2O / B2O3) = a + bR. The parameters of this calibration equation are determined from the measurements of scattered radiation by lithium metaborate, lithium tetraborate, their mixtures, as well as pure boron oxide. The powdered samples are pressed with a synthetic wax as a binder. The calibration function is constructed using the stoichiometric lithium borates and boron oxide in the 0 - 0.42 range of the (Li2O / B2O3) ratio and is characterized by the standard deviation equal to 0.03. The boron content in the anhydrous lithium borates is calculated from the (Li2O / B2O3) ratio. The standard deviation of boron content in the range of 22-31% wt. is 0.6% wt. The accuracy of the boron determination is about 1% wt. and less than the accuracy of the chemical analysis, but the proposed method can be used for a quick evaluation of the anhydrous lithium borates composition.Keywords: X-ray spectrometry, lithium borates, scattered radiation.DOI: http://dx.doi.org/10.15826/analitika.2020.24.1.005  А.L. Finkelshtein1, A.A. Dergin1, A.I. Nepomnyaschikh1, A.G.Konovalova2 1Vinogradov Institute of Geochemistry SB RAS, 1A, Favorsky St, Irkutsk, 664033, Russian Federation 2Irkutsk State University, 1, Karl Marx St, Irkutsk, 664033, Russian FederationПредложен способ определения состава безводных боратов лития, основанный на измерении интенсивности рассеянного характеристического излучения рентгеновской трубки на рентгенофлуоресцентном спектрометре. В основу способа положен подход, описанный ранее в литературе (Van Sprang H. A. и др., 1998; Калинин Б.Д., и др., 2011), для определения элементов с атомным номером менее 6 в борсиликатных стеклах и органических соединениях. Параметром градуировочного уравнения служит отношение (R) интенсивности когерентно и некогерентно рассеянного на образце первичного излучения  RhKα-линии анода трубки, которое в первом приближении определяется средним атомным номером рассеивающего вещества. Для безводных боратов лития (стехиометрических соединений или аморфного стекла) средний атомный номер определяется соотношением оксидов лития и бора и отношение содержаний оксидов может быть аппроксимировано зависимостью  (Li2O/B2O3) = a + bR . Параметры этого градуировочного уравнения определены по измерениям рассеянного излучения от образцов метабората, тетрабората лития, их смесей, а также чистого оксида бора. Образцы представляли собой таблетки, спрессованные из порошков со связующим веществом (синтетическим воском). Стандартное отклонение градуировочной функции для отношения содержания (Li2O/B2O3) в диапазоне 0 - 0.42 составило 0.03, и соответствующая оценка погрешности определения бора, содержание которого рассчитывается из отношения содержаний (Li2O/B2O3), равна 0.6 % мас. в диапазоне содержания бора 22-31 % мас. в стехиометрических боратах лития и оксиде бора. Точность определения бора составляет приблизительно 1 % мас. и уступает точности химического анализа, однако предлагаемый способ может быть использован для быстрой оценки состава безводных боратов лития.Ключевые слова: рентгеноспектральный анализ, бораты лития, рассеянное излучениеDOI: http://dx.doi.org/10.15826/analitika.2020.24.1.00

A novel superconducting glass state in disordered thin films in Clogston limit

A theory of mesoscopic fluctuations in disordered thin superconducting films in a parallel magnetic field is developed. At zero temperature, the superconducting state undergoes a phase transition into a state characterized by superfluid densities of random signs, instead of a spin polarized disordered Fermi liquid phase. Consequently, the ground state belongs to the same universality class as the 2D XY spin glass. As the magnetic field increases further, mesoscopic pairing states are nucleated in an otherwise homogeneous spin polarized disordered Fermi liquid. The statistics of these pairing states is universal depending on the sheet conductance of the 2D film.Comment: Latex, 39 pages, 2 figures included; to appear in Int. J. Mod. Phys.

Strong asymptotics for Jacobi polynomials with varying nonstandard parameters

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$\lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B,$$ with $A$ and $B$ satisfying $A > -1$, $B>-1$, $A+B < -1$. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived. We show that in a generic case the zeros distribute on the set of critical trajectories $\Gamma$ of a certain quadratic differential according to the equilibrium measure on $\Gamma$ in an external field. However, when either $\alpha_n$, $\beta_n$ or $\alpha_n+\beta_n$ are geometrically close to $\Z$, part of the zeros accumulate along a different trajectory of the same quadratic differential.Comment: 31 pages, 12 figures. Some references added. To appear in Journal D'Analyse Mathematiqu