Rational material design of mixed-valent high Tc_c superconductors

We design, from first principles calculations, a novel family of thallium halide-based compounds as candidates for new high temperature superconductors, whose superconductivity is mediated by the recently proposed mechanism of non-local correlation-enhanced strong electron-phonon coupling. Two prototype compounds namely CsTlF$_3$ and CsTlCl$_3$ are studied with various hole doping levels and volumes. The critical superconducting temperature T$_c$ are predicted to be about 30 K and 20 K with $\sim$0.35/f.u. hole doping and require only modest pressures ($\sim$10 and $\sim$2 GPa), respectively. Our procedure of designing this class of superconductors is quite general and can be used to search for other "other high temperature superconductors".Comment: 6- ages, EPL 101, 27002 (2013

Correlation-enhanced electron-phonon coupling: Applications of GW and screened hybrid functional to bismuthates, chloronitrides, and other high Tc superconductors

We show that the electron-phonon coupling (EPC) in many materials can be significantly underestimated by the standard density functional theory (DFT) in the local density approximation (LDA) due to large non-local correlation effects. We present a simple yet efficient methodology to evaluate the realistic EPC going beyond LDA by using more advanced and accurate GW and screened hybrid functional DFT approaches. The corrections we propose explain the extraordinarily high superconducting temperatures that are observed in two distinct classes of compounds-the bismuthates and the transition metal chloronitrides, thus solving a thirty-year-old puzzle. Our work calls for the critically reevaluation of the EPC of certain phonon modes in many other materials such as cuprates and iron-based superconductors. The proposed methodology can be used to design new correlation-enhanced high temperature superconductors and other functional materials involving electron-phonon interaction.Comment: Substantilly extended version of the previous manuscript, 19 pages, 10 figures, accepted for publication in Phys. Rev.

The Role of Crystal Symmetry in the Magnetic Instabilities of β\beta-YbAlB4_4 and α\alpha-YbAlB4_4

Density functional theory methods are applied to investigate the properties of the new superconductor $\beta$-YbAlB$_4$ and its polymorph $\alpha$-YbAlB$_4$. We utilize the generalized gradient approximation + Hubbard U (GGA+U) approach with spin-orbit(SO) coupling to approximate the effects of the strong correlations due to the open $4f$ shell of Yb. We examine closely the differences in crystal bonding and symmetry of $\beta$-YbAlB$_4$ and $\alpha$-YbAlB$_4$. The in-plane bonding structure amongst the dominant itinerant electrons in the boron sheets is shown to differ significantly. Our calculations indicate that, in both polymorphs, the localized 4$f$ electrons hybridize strongly with the conduction sea when compared to the related materials YbRh$_{2}$Si$_{2}$ and YbB$_{2}$. Comparing $\beta$-YbAlB$_4$ to the electronic structure of related crystal structures indicates a key role of the 7-member boron coordination of the Yb ion in $\beta$-YbAlB$_4$ in producing its enhanced Kondo scale and superconductivity. The Kondo scale is shown to depend strongly on the angle between the B neighbors and the Yb ion, relative to the $x-y$ plane, which relates some of the physical behavior to structural characteristics.Comment: 9 pages, 9 figures, 2 table

A numerical approach to optimal dividend policies with capital injections and transaction costs

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Optimal debt ratio and dividend payment strategies with reinsurance

This paper derives the optimal debt ratio and dividend payment strategies for an insurance company. Taking into account the impact of reinsurance policies and claims from the credit derivatives, the surplus process is stochastic that is jointly determined by the reinsurance strategies, debt levels, and unanticipated shocks. The objective is to maximize the total expected discounted utility of dividend payment until financial ruin. Using dynamic programming principle, the value function is the solution of a second-order nonlinear Hamilton–Jacobi–Bellman equation. The subsolution–supersolution method is used to verify the existence of classical solutions of the Hamilton–Jacobi–Bellman equation. The explicit solution of the value function is derived and the corresponding optimal debt ratio and dividend payment strategies are obtained in some special cases. An example is provided to illustrate the methodologies and some interesting economic insights.postprin