Two phase transitions in (d(x2-y2)+is)-wave superconductors

We study numerically the temperature dependencies of specific heat, susceptibility, penetration depth, and thermal conductivity of a coupled (d(x2-y2) + is)-wave Bardeen-Cooper-Schrieffer (BCS) superconductor in the presence of a weak s-wave component (1) on square lattice and (2) on a lattice with orthorhombic distortion. As the temperature is lowered past the critical temperature T-c, a less ordered superconducting phase is created in d(x2-y2) wave, which changes to a more ordered phase in (d(x2-y2) + is) wave at T-c1. This manifests in two second-order phase transitions. The two phase transitions are identified by two jumps in specific heat at T-c and T-c1. The temperature dependencies of the superconducting observables exhibit a change from power-law to exponential behavior as temperature is lowered below T-c1 and confirm the new phase transition. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Numerical solution of the time dependent Ginzburg-Landau equations for mixed (d plus s)-wave superconductors

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Interaction between vortices and impurities in a d-wave superconductor /

High temperature superconductors were discovered in 1986, but despite considerable research efforts, both experimental and theoretical, these materials remain poorly understood. Because their electronic structure is both inhomogeneous and highly correlated, a full understanding will require knowledge of quasiparticle properties both in real space and momentum space. In this thesis, we will present a theoretical analysis of the scanning tunneling microscopy (STM) data in BSCCO. We introduce the Bogoliubov-De Gennes Hamiltonian and solve it numerically on a two-dimensional 20 x 20 lattice under a magnetic field perpendicular to the surface. We consider a vortex at the center of our model. We introduce a Zn impurity in our lattice as a microscopic probe of the physical properties of BSCCO. By direct numerical diagonalization of the lattice BogoliubovDe Gennes Hamiltonian for different positions of the impurity, we can calculate the interaction between the vortex and the impurity in a d-wave superconductor.

Manifestation of the pairing symmetry in the vortex core structure in iron-based superconductors

The superconducting gap is a basic character of a superconductor. While the cuprates and conventional phonon-mediated superconductors are characterized by distinct d- and s-wave pairing symmetries with nodal and nodeless gap distributions respectively, the superconducting gap distributions in iron-based superconductors are rather diversified. While nodeless gap distributions have been directly observed in Ba1–xKxFe2As2, BaFe2–xCoxAs2, LiFeAs, KxFe2–ySe2, and FeTe1–xSex, the signatures of a nodal superconducting gap have been reported in LaOFeP, LiFeP, FeSe, KFe2As2, BaFe2–xRuxAs2, and BaFe2(As1–xPx)2. Due to the multiplicity of the Fermi surface in these compounds s± and d pairing states can be both nodeless and nodal. A nontrivial orbital structure of the order parameter, in particular the presence of the gap nodes, leads to effects in which the disorder is much richer in dx2–y2-wave superconductors than in conventional materials. In contrast to the s-wave case, the Anderson theorem does not work, and nonmagnetic impurities exhibit a strong pair-breaking influence. In addition, a finite concentration of disorder produces a nonzero density of quasiparticle states at zero energy, which results in a considerable modification of the thermodynamic and transport properties at low temperatures. The influence of order parameter symmetry on the vortex core structure in iron-based pnictide and chalcogenide superconductors has been investigated in the framework of quasiclassical Eilenberger equations. The main results of the thesis are as follows. The vortex core characteristics, such as, cutoff parameter, ξh, and core size, ξ2, determined as the distance at which density of the vortex supercurrent reaches its maximum, are calculated in wide temperature, impurity scattering rate, and magnetic field ranges. The cutoff parameter, ξh(B; T; Г), determines the form factor of the flux-line lattice, which can be obtained in _SR, NMR, and SANS experiments. A comparison among the applied pairing symmetries is done. In contrast to s-wave systems, in dx2–y2-wave superconductors, ξh/ξc2 always increases with the scattering rate Г. Field dependence of the cutoff parameter affects strongly on the second moment of the magnetic field distributions, resulting in a significant difference with nonlocal London theory. It is found that normalized ξ2/ξc2(B/Bc2) dependence is increasing with pair-breaking impurity scattering (interband scattering for s±-wave and intraband impurity scattering for d-wave superconductors). Here, ξc2 is the Ginzburg-Landau coherence length determined from the upper critical field Bc2 = Φ0/2πξ2 c2, where Φ0 is a flux quantum. Two types of ξ2/ξc2 magnetic field dependences are obtained for s± superconductors. It has a minimum at low temperatures and small impurity scattering transforming in monotonously decreasing function at strong scattering and high temperatures. The second kind of this dependence has been also found for d-wave superconductors at intermediate and high temperatures. In contrast, impurity scattering results in decreasing of ξ2/ξc2(B/Bc2) dependence in s++ superconductors. A reasonable agreement between calculated ξh/ξc2 values and those obtained experimentally in nonstoichiometric BaFe2–xCoxAs2 (μSR) and stoichiometric LiFeAs (SANS) was found. The values of ξh/ξc2 are much less than one in case of the first compound and much more than one for the other compound. This is explained by different influence of two factors: the value of impurity scattering rate and pairing symmetry.

S-, P- and D-wave resonances in positronium-sodium and positronium-potassium scattering

Scattering of positronium (Ps) by sodium and potassium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(ls,2s,2p) states using a time-reversal-symmetric regularized electron-exchange model potential fitted to reproduce accurate theoretical results for PsNa and PsK binding energies. We find a narrow S-wave singlet resonance at 4.58 eV of width 0.002 eV in the Ps-Na system and at 4.77 eV of width 0.003 eV in the Ps-K system. Singlet P-wave resonances in both systems are found at 5.07 eV of width 0.3 eV. Singlet D-wave structures are found at 5.3 eV in both systems. We also report results for elastic and Ps-excitation cross sections for Ps scattering by Na and K.

S-, P-, and D-wave resonances in positronium-lithium-atom scattering

We investigate ortho-positronium-lithium-atom (Ps-Li) scattering using static-exchange and three-Ps-state coupled-channel calculations. The present three-PS-state scheme, while closely agreeing with the resonance and binding energies in the Ps-H system, predicts S-, P-, and D-wave resonances at 4.25 eV, 4.9 eV, and, 5.25 eV. respectively, in the electronic spin-singlet channel of Ps-Li scattering. The present calculation also yields a Ps-Li binding in this attractive singlet channel with an approximate binding energy of 0.218 eV, which is in adherence with the recent findings of a chemically stable PsLi system using stocastic variational and quantum Monte Carlo calculations. We further report elastic, Ps(2s)-, and Ps(2p)-excitation cross sections at low to medium energies (0.068-30 eV).

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Strong electronic correlations in superconducting organic charge transfer salts

We review the role of strong electronic correlations in quasi-two-dimensional organic charge transfer salts such as (BEDT-TTF)(2)X, (BETS)(2)Y, and beta'-[Pd(dmit)(2)](2)Z. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerized and is described by a half-filled Hubbard model; the second class is not strongly dimerized and is described by a quarter-filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-filled quasi-two-dimensional organic charge transfer salts, focusing on the metallic and superconducting phases. We review work showing that the metallic phase, which has both Fermi liquid and 'bad metal' regimes, is described both quantitatively and qualitatively by dynamical mean field theory (DMFT). The phenomenology of the superconducting state is still a matter of contention. We critically review the experimental situation, focusing on the key experimental results that may distinguish between rival theories of superconductivity, particularly probes of the pairing symmetry and measurements of the superfluid stiffness. We then discuss some strongly correlated theories of superconductivity, in particular the resonating valence bond (RVB) theory of superconductivity. We conclude by discussing some of the major challenges currently facing the field. These include parameterizing minimal models, the evidence for a pseudogap from nuclear magnetic resonance (NMR) experiments, superconductors with low critical temperatures and extremely small superfluid stiffnesses, the possible spin- liquid states in kappa-(ET)(2)Cu-2(CN)(3) and beta'-[Pd(dmit)(2)](2)Z, and the need for high quality large single crystals.

Phase transition from a d(x(2)-y(2)) to d(x(2)-y(2))+id(xy) superconductor

The temperature dependencies of specific heat and spin susceptibility of a coupled dx2-y2 + idxy superconductor in the presence of a weak dxy component are investigated in the tight-binding model (1) on square lattice and (2) on a lattice with orthorhombic distortion. As the temperature is lowered past the critical temperature Tc, first a less ordered dx2-y2 superconductor is created, which changes to a more ordered dx2-y2 + idxy superconductor at Tcl(< Tc). This manifests in two second order phase transitions identified by two jumps in specific heat at Tc and Tc1. The temperature dependencies of the superconducting observables exhibit a change from power-law to exponential behavior as temperature is lowered below Tc1 and confirm the new phase transition. © 1998 Published by Elsevier Science B.V. All rights reserved.

Mixed order parameters, accidental nodes and broken time reversal symmetry in organic superconductors: a group theoretical analysis

We present a group theoretical analysis of several classes of organic superconductor. We predict that highly frustrated organic superconductors, such as K-(ET)(2)Cu-2(CN)(3) (where ET is BEDT-TTF, bis(ethylenedithio) tetrathiafulvalene) and beta'-[Pd(dmit)(2)](2)X, undergo two superconducting phase transitions, the first from the normal state to a d-wave superconductor and the second to a d + id state. We show that the monoclinic distortion of K-(ET)(2)Cu(NCS)(2) means that the symmetry of its superconducting order parameter is different from that of orthorhombic-K-(ET)(2)Cu[N(CN)(2)] Br. We propose that beta'' and theta phase organic superconductors have d(xy) + s order parameters.

s-wave charmed baryon resonances from a coupled-channel approach with heavy quark symmetry

We study charmed baryon resonances that are generated dynamically within a unitary meson-baryon coupled-channel model that treats the heavy pseudoscalar and vector mesons on equal footing as required by heavy-quark symmetry. It is an extension of recent SU(4) models with t-channel vector-meson exchanges to an SU(8) spin-flavor scheme, but differs considerably from the SU(4) approach in how the strong breaking of the flavor symmetry is implemented. Some of our dynamically generated states can be readily assigned to recently observed baryon resonances, while others do not have a straightforward identification and require the compilation of more data as well as an extension of the model to d-wave meson-baryon interactions and p-wave coupling in the neglected s- and u-channel diagrams. Of several novelties, we find that the Delta c(2595), which emerged as a ND quasibound state within the SU(4) approaches, becomes predominantly a ND* quasibound state in the present SU(8) scheme.

Two phase transitions in (s+id)-wave Bardeen-Cooper-Schrieffer superconductivity

We establish universal behaviour in the temperature dependencies of some observables in (s + id)-wave BCS superconductivity in the presence of a weak a wave. We find also a second second-order phase transition. As temperature is lowered-past the usual critical temperature T-c, a less ordered superconducting phase is created in the d wave, which changes to a more ordered phase in a (s + id) wave at T-c1 (

BCS superconductivity in the van Hove scenario in s and d waves

The effect of including a van Hove singularity in the density of state of a renormalized BCS equation in s and d waves and its appropriateness in describing some properties of high-Tc cuprates in the weak-coupling region are studied in two space dimensions. The specific heat and knight shift as a function of temperature exhibit scaling below the critical temperature in d wave. We also study the jump in the specific heat at the critical temperature Tc in s and d waves, which can have values significantly higher than the standard BCS values and which increases with Tc, as experimentally observed in many d-wave high-Tc materials. The experimental results on the specific heat and knight shift of the Y-123 system are compared with the theoretical predictions.

Temperatur- und ortsabhängige Zustandsdichte des organischen Supraleiters Kappa-(BEDT-TTF) 2 Cu[N(CN) 2]Br

Im Rahmen dieser Arbeit wurde die temperatur- und ortsabhängige Zustandsdichte des organischen Supraleiters kappa-(BEDT-TTF)2Cu[N(CN)2]Br mit Rastertunnelspektroskopie bei tiefen Temperaturen untersucht.rnZusätzlich zur bereits bekannten supraleitenden Energielücke wird dabei eine logarithmische Unterdrückung der Zustandsdichte an der Fermikante beobachtet, die auch oberhalb der kritischen Temperatur erhalten bleibt. In der vorliegenden Arbeit wird gezeigt, dass sich dieses Verhalten durch ein für ungeordnete elektronische Systeme entwickeltes Modell unter Berücksichtigung von Coulomb-Wechselwirkungen beschreiben lässt. Die daraus resultierenden Fluktuationen der elektronischen Struktur führen zu einer Verbreiterung der gemessenen supraleitenden Energielücke, die sich durch sehr kleine Kohärenzmaxima im entsprechenden Quasiteilchenanregungsspektrum äußert. Dieses Verhalten wurde bereits beobachtet, konnte jedoch bisher nicht erklärt werden. Die theoretische Beschreibung der logarithmischen Unterdrückung trägt somit zusätzlich zum Verständnis des supraleitenden Beitrags bei, sodass die gesamte Zustandsdichte vollständig beschrieben werden kann. Die Analyse der gemessenen supraleitenden Energielücke wurde für verschiedene Symmetrien des Ordnungsparameters durchgeführt, wobei die beste Übereinstimmung für die Annahme einer d-wellenartigen Symmetrie mit zwei unterschiedlich stark ausgeprägten Energielücken gefunden wurde. Der Paarbildungsmechanismus, der zur Bindung zweier Elektronen zu einem Cooper-Paar führt, kann mit einer $d$-wellenartigen Symmetrie nicht durch die in konventionellen Supraleitern gefundene Elektron-Phonon-Kopplung erklärt werden. Stattdessen wird in Analogie zur Hochtemperatur-Supraleitung eine durch antiferromagnetische Spin-Wechselwirkungen induzierte Kopplung der Elektronen vermutet. Dies wird zum einen durch die oberhalb der kritischen Temperatur auftretende, zweite Energielücke und zum anderen durch die zwischen 4,66 und 5,28 liegende Kopplungsstärke 2Delta/(kB Tc) unterstützt, die deutlich größer als für konventionelle Supraleiter mit Elektron-Phonon-Kopplung ist.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.