Universal quadratures for boundary integral equations on two-dimensional domains with corners

We describe the construction of a collection of quadrature formulae suitable for the efficient discretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high-accuracy solution of Dirichlet boundary value problems for Laplace’s equation and the Helmholtz equation on such domains under a mild assumption on the boundary data. Our approach can be adapted to other boundary value problems and certain aspects of our scheme generalize to the case of surfaces with singularities in three dimensions. The performance of the quadrature rules is illustrated with several numerical examples.     

Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys

In this short review, we first discuss the results, which are mainly devoted to the generalizations of the famous Kohn–Luttinger mechanism of superconductivity in purely repulsive fermion systems at low electron densities. In the context of repulsive-U Hubbard model and Shubin–Vonsovsky model we consider briefly the superconducting phase diagrams and the symmetries of the order parameter in novel strongly correlated electron systems including idealized monolayer and bilayer graphene. We stress that purely repulsive fermion systems are mainly the subject of unconventional low-temperature superconductivity. To get the high temperature superconductivity in cuprates (with T_C of the order of 100 K) we should proceed to the t–J model with the van der Waals interaction potential and the competition between short-range repulsion and long-range attraction. Finally we note that to describe superconductivity in metallic hydrogen alloys under pressure (with T_C of the order of 200 K) it is reasonable to reexamine more conventional mechanisms connected with electron–phonon interaction. These mechanisms arise in the attractive-U Hubbard model with static onsite or intersite attractive potential or in more realistic theories (which include retardation effects) such as Migdal–Eliashberg strong coupling theory or even Fermi–Bose mixture theory of Ranninger et al. and its generalizations.     

QCD at finite density and color superconductivity

The paper contains a brief review of recent applications of many-body theory to quark matter. We discuss the progress in theory of dense quark matter during the last two years, especially color superconductivity. We emphasize that there are two basic dynamical reasons for it: short-range forces induced by instantons and long-range ones mediated by exchanges of magnetic gluons. For quark matter which is supposed to be found in neutron stars, both lead to superconducting gaps on the order of 100 MeV. The most surprising facts are the rather impressive richness of different phases and their robustness in respect to variation of the fundamental interaction.     

Coexistence of triplet superconductivity and spin density waves

We discuss the possibility of the coexistence of spin density waves (antiferromagnetism) and triplet superconductivity as a particular example of a broad class of systems where the interplay of magnetism and superconductivity is important. We focus on the case of quasi-one-dimensional metals, where it is known that antiferromagnetism is in close proximity to triplet superconductivity in the pressure versus temperature phase diagram. Over a range of pressures, we propose an intermediate nonuniform phase consisting of antiferromagnetic and triplet superconducting orders. In the coexistence region, we propose a flop transition in the spin density wave order parameter vector, which affects the nature of the superconducting state and leads to the appearance of several new phases.     

On the coexistence of superconductivity and charge density waves

We study a simple tight-binding (Hubbard) model for electrons interacting via a short range attractive potential. We show that on a cubic lattice, for a half-filled band the ground state may feature both superconductivity and a charge density wave. We examine the response of such a ground state to an external magnetic field and describe the effect of the charge density wave on the Meissner effect.     

Tunneling density of states for the two-band model of superconductivity

In the presence of interband scattering of quasiparticles by impurities only a single gap in the excitation spectrum is found. The dependence of this gap and the two order parameters on interband coupling and impurity content is discussed. Graphical representations of the density of states for several sets of parameters are given. For certain ranges of parameters our calculated density of states is qualitatively similar to the experimental results.     

Coexistence of superconductivity and density wave orders in a one-dimensional correlated system

By the field theory approach, we investigate a one-dimensional correlated electronic system modelled by the extended Hubbard Hamiltonian including a nearest-neighbor and a next-nearest-neighbor spin-exchange interactions with easy-axis anisotropy. At half filling, we obtain weak-coupling phase diagram. In addition to two insulating phases with transverse and longitudinal spin-density-wave orders, two metallic phases, characterized by the coexistence of singlet superconductivity and charge-density-wave orders and by the coexistence of triplet superconductivity and spin-density-wave orders, are realized in the ground state. Away from half filling, the degeneracy is split and the superconducting orders are favored.     

Dyson-Schwinger approach to color superconductivity at finite temperature and density

We investigate the phases of dense QCD matter at finite temperature with Dyson-Schwinger equations for the quark propagator for N _f = 2 + 1 flavors. For the gluon propagator we take a fit to quenched lattice data and add quark-loop effects perturbatively in a hard-thermal-loop-hard-dense-loop approximation. We consider 2SC and CFL-like pairing with chiral up and down quarks and massive strange quarks and present results for the condensates and the phase diagram. We find a dominant CFL phase at chemical potentials larger than 500-600MeV. At lower values of the chemical potential we find a 2SC phase, which also exists in a small band at higher temperatures for larger chemical potentials. With values of 20–30 MeV, the critical temperatures to the normal phase turn out to be quite small.     

CrAs——第一个Cr 基化合物超导体的发现

非常规超导体自发现以来便引起了凝聚态物理学家的广泛兴趣,诸如重费米子超导体,铜基高温超导体和铁基高温超导体等。这类超导体的一个基本特征是,当长程反铁磁序被抑制时会出现超导现象。而要破坏长程磁有序,除了掺杂不同元素以引入电荷载流子或者化学压力外,物理加压也是一种有效的调控手段。文章将介绍第一个Cr基化合物超导体——CrAs单晶通过物理加压首次实现超导电性的过程。当压力为8 kbar 时,超导临界温度出现在2 K,这时发生在常压下265 K的一级反铁磁相变被完全压制。在CrAs体系中,超导与反铁磁序之间的竞争关系说明CrAs是非常规超导体。CrAs的超导也为发现新型超导体打开了一扇大门。     

Surface superconductivity and twinning-plane superconductivity in aluminum

The critical supercooling field H _sc is measured in aluminum single crystals and twinned bicrystals in a temperature range slightly below T _c0 (T _c0 ? 0.055 K < T < T _c0), where T _c0 is the critical superconducting transition temperature. It is found that, even in this small temperature range, the H _sc(H _c) dependence, which is considered to be identical to the H _c3(H _c) dependence for single crystals, is substantially nonlinear. The H _sc(H _c) dependences of the twinned bicrystals and single crystals are shown to be significantly different. The qualitative features of the phase diagram of the twinned aluminum bicrystals coincide with those of the phase diagram of twinning-plane superconductivity obtained earlier for tin in [1]. These findings allow the conclusion that the phenomenon of twinning-plane superconductivity also exists in face-centered cubic crystal lattices.     

Quark condensation, induced symmetry breaking and color superconductivity at high density

The phase structure of hadronic matter at high density relevant to the physics of compact stars and relativistic heavy-ion collisions is studied in a low-energy effective quark theory. The relevant phases that figure are (1) chiral condensation, (2) diquark color condensation (color superconductivity) and (3) induced Lorentz-symmetry breaking (“ISB”). For a reasonable strength for the effective four-Fermi current–current interaction implied by the low-energy effective quark theory for systems with a Fermi surface we find that the “ISB” phase sets in together with chiral symmetry restoration (with the vanishing quark condensate) at a moderate density while color superconductivity associated with scalar diquark condensation is pushed up to an asymptotic density. Consequently, color superconductivity seems rather unlikely in heavy-ion collisions although it may play a role in compact stars. Lack of confinement in the model makes the result of this analysis only qualitative but the hierarchy of the transitions we find seems to be quite robust.     

Charge-orbital density wave and superconductivity in the strong spin-orbit coupled IrTe2:Pd

Using transmission electron microscopy, the anomalies in resistivity and magnetic susceptibility at ~262 K in IrTe2 are found to accompany the superlattice peaks with q[over q=(1/5,0,-1/5). The wave vector is consistent with our theoretical calculation for the Fermi surface nesting vector, indicating that the ~262 K transition is of the charge-orbital density wave (DW) type. We also discovered that both Pd intercalation and substitution induce bulk superconductivity with T(c) up to ~3 K, which competes with DW in a quantum critical pointlike manner.     

The coexistence of superconductivity and antiferromagnetism

It is shown that the exchange interaction in an ensemble of itinerant electrons gives rise to a super-conducting phase and a mixed phase in which the Cooper instability occurs in the presence of the long-range antiferromagnetic order. A phase diagram determining the regions of existence of the phases mentioned above is constructed.     

The Lorentz force and superconductivity

To change the velocity of an electron requires that a Lorentz force acts on it, through an electric or a magnetic field. We point out that within the conventional understanding of superconductivity electrons appear to change their velocity in the absence of Lorentz forces. This indicates a fundamental problem with the conventional theory of superconductivity. A hypothesis is proposed to resolve this difficulty. This hypothesis is consistent with the theory of hole superconductivity.     

晶格常数与掺杂YBCO体系超导电性的关系

依据现有的YBCO掺杂实验,对掺杂YBCO体系超导电性与其晶格常数进行了研究,发现它们之间具有较好的规律性。因此提出用晶格常数作为掺杂YBCO超导电性的一个判断标准,这对探索超导机制及对今后实验工作掺杂元素和掺杂比例的选取有很好的指导意义。     

Prediction of superconductivity of Ta2AlC: in situ Raman spectrometry and density functional investigations

In this paper, in situ Raman spectra of Ta₂AlC are measured in the temperature range of 80–500 K at ambient pressure. The frequencies of the Raman modes decrease with increasing temperature, which have been explained by the anharmonic and thermal expansion effects. The line‐width of E_2g (ω₃) mode increases at elevated temperatures, which is found to be due to the anharmonic phonon–phonon scatterings. On the other hand, the line‐widths of E_2g (ω₁) and A_1g (ω₄) modes decrease continuously with increasing temperature, which is explained by the electron–phonon couplings of these two phonon modes with the Ta 5d electrons. The electron–phonon coupling strengths are obtained both in experiments and density functional calculations. Finally, Ta₂AlC is predicted to be a new superconductive MAX phase. Copyright © 2014 John Wiley & Sons, Ltd.     

Correlation of superconductivity with material properties

A simple model is used to study the trends of the electron-phonon interaction parameter γ.