Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Epitaxial graphene on SiC(0001): More than just honeycombs

The potential of graphene to impact the development of the next generation of electronics has renewed interest in its growth and structure. The graphitization of hexagonal SiC surfaces provides a viable alternative for the synthesis of graphene, with wafer-size epitaxial graphene on SiC(0001) now possible. Despite this recent progress, the exact nature of the graphene-SiC interface and whether the graphene even has a semiconducting gap remain controversial. Using scanning tunneling microscopy with functionalized tips and density functional theory calculations, here we show that the interface is a warped carbon sheet consisting of three-fold hexagon-pentagon-heptagon complexes periodically inserted into the honeycomb lattice. These defects relieve the strain between the graphene layer and the SiC substrate, while still retaining the three-fold coordination for each carbon atom. Moreover, these defects break the six-fold symmetry of the honeycomb, thereby naturally inducing a gap: the calculated band structure of the interface is semiconducting and there are two localized states near K below the Fermi level, explaining the photoemission and carbon core-level data. Nonlinear dispersion and a 33 meV gap are found at the Dirac point for the next layer of graphene, providing insights into the debate over the origin of the gap in epitaxial graphene on SiC(0001). These results indicate that the interface of the epitaxial graphene on SiC(0001) is more than a dead buffer layer, but actively impacts the physical and electronic properties of the subsequent graphene layers

Transport properties and anisotropy in rare earth doped CaFe2As2 single crystals with Tc above 40 K

In this paper we report the superconductivity above 40 K in the electron doping single crystal Ca1-xRexFe2As2 (Re = La, Ce, Pr). The x-ray diffraction patterns indicate high crystalline quality and c-axis orientation. the resistivity anomaly in the parent compound CaFe2As2 is completely suppressed by partial replacement of Ca by rare earth and a superconducting transition reaches as high as 43 K, which is higher than the value in electron doping FeAs-122 compounds by substituting Fe ions with transition metal, even surpasses the highest values observed in hole doping systems with a transition temperature up to 38 K. The upper critical field has been determined with the magnetic field along ab-plane and c-axis, yielding the anisotropy of 2~3. Hall-effect measurements indicate that the conduction in this material is dominated by electron like charge carriers. Our results explicitly demonstrate the feasibility of inducing superconductivity in Ca122 compounds via electron doping using aliovalent rare earth substitution into the alkaline earth site, which should add more ingredients to the underlying physics of the iron-based superconductors.Comment: 21 pages, 7 figure

Valley dependent many-body effects in 2D semiconductors

We calculate the valley degeneracy ($g_v$) dependence of the many-body renormalization of quasiparticle properties in multivalley 2D semiconductor structures due to the Coulomb interaction between the carriers. Quite unexpectedly, the $g_v$ dependence of many-body effects is nontrivial and non-generic, and depends qualitatively on the specific Fermi liquid property under consideration. While the interacting 2D compressibility manifests monotonically increasing many-body renormalization with increasing $g_v$, the 2D spin susceptibility exhibits an interesting non-monotonic $g_v$ dependence with the susceptibility increasing (decreasing) with $g_v$ for smaller (larger) values of $g_v$ with the renormalization effect peaking around $g_v\sim 1-2$. Our theoretical results provide a clear conceptual understanding of recent valley-dependent 2D susceptibility measurements in AlAs quantum wells.Comment: 5 pages, 3 figure

An external potential dynamic study on the formation of interface in polydisperse polymer blends

The formation of interface from an initial sharp interface in polydisperse A/B blends is studied using the external potential dynamic method. The present model is a nonlocal coupling model as we take into account the correlation between segments in a single chain. The correlation is approximately expressed by Debye function and the diffusion dynamics are based on the Rouse chain model. The chain length distribution is described by the continuous Schulz distribution. Our numerical calculation indicates that the broadening of interface with respect to time obeys a power law at early times, and the power law indexes are the same for both monodisperse and polydisperse blend. The power law index is larger than that in the local coupling model. However there is not a unified scaling form of the broadening of the interface width if only the interfacial width at equilibrium is taken into account as the characteristic length of the system, because the correlation makes an extra characteristic length in the system, and the polydispersity is related to this length.Comment: 15 pages, 5 figure