Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial preserving rec
overy technique . Our new algorithms compare favorably with some existing methods and enjoy superconvergence property.
We report a systematic investigation on c-axis point-contact Andreev reflection (PCAR) in BaFe$_{2-x}$Ni$_x$As$_2$ superconducting single crystals from underdoped to overdoped regions (0.075 $leq xleq 0.15$). At optimal doping ($x=0.1$) the PCAR spec
trum feature the structures of two superconducting gap and electron-boson coupling mode. In the $spm$ scenario, quantitative analysis using a generalized Blonder-Tinkham-Klapwijk (BTK) formalism with two gaps: one isotropic and another angle dependent, suggest a nodeless state in strong-coupling limit with gap minima on the Fermi surfaces. Upon crossing above the optimal doping ($x > 0.1$), the PCAR spectrum show an in-gap sharp narrow peak at low bias, in contrast to the case of underdoped samples ($x < 0.1$), signaling the onset of deepened gap minima or nodes in the superconducting gap. This result provides evidence of the modulation of the gap amplitude with doping concentration, consistent with the calculations for the orbital dependent pair interaction mediated by the antiferromagnetic spin fluctuations.
Using the analytic extension method, we study Hawking radiation of an $(n + 4)$-dimensional Schwarzschild-de Sitter black hole. Under the condition that the total energy is conserved, taking the reaction of the radiation of particles to the spacetime
into consideration and considering the relation between the black hole event horizon and cosmological horizon, we obtain the radiation spectrum of de Sitter spacetime. This radiation spectrum is no longer a strictly pure thermal spectrum. It is related to the change of the Bekenstein-Hawking(B-H) entropy corresponding the black hole event horizon and cosmological horizon. The result satisfies the unitary principle. At the same time, we also testify that the entropy of de Sitter spacetime is the sum of the entropy of black hole event horizon and the one of cosmological horizon.
We report a detailed investigation on the lower critical field $H_{c1}$ of the superconducting Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ (FeAs-122) single crystals. A pronounced kink is observed on the $H_{c1}(T)$ curve, which is attributed to the existence of
two superconducting gaps. By fitting the data $H_{c1}(T)$ to the two-gap BCS model in full temperature region, a small gap of $Delta_a(0)=2.0pm 0.3$ meV and a large gap of $Delta_b(0)=8.9pm 0.4$ meV are obtained. The in-plane penetration depth $lambda_{ab}(0)$ is estimated to be 105 nm corresponding to a rather large superfluid density, which points to the breakdown of the Uemura plot in FeAs-122 superconductors.
We present the first experimental results of the lower critical field $H_{c1}$ of the newly discovered F-doped superconductor LaO$_{0.9}$F$_{0.1}$FeAs (F-LaOFeAs) by global and local magnetization measurements. It is found that $H_{c1}$ showed an cle
ar linear-$T$ dependence down to a temperature of 2 K, indicative of an unconventional pairing symmetry with a nodal gap function. Based on the d-wave model, we estimated a maximum gap value $Delta_0=4.0 pm 0.6$ meV, in consistent with the recent specific heat and point-contact tunneling measurements. Taking the demagnetization factor into account, the absolute value of $H_{c1}(0)$ is determined to be about 54 Oe, manifesting a low superfluid density for LaO$_{0.9}$F$_{0.1}$FeAs.
