In this paper we study an s-wave topological superconductor (SC) with a square vortex-lattice. We proposed a topological Majorana lattice model to describe this topological state which was supported by the numerical calculations. We found that the Majorana lattice model is really a "topological SC" on the parent topological SC. Such hierarchy structure becomes a new holographic feature of the topological state. II. THE S-WAVE PAIRING TOPOLOGICAL SUPERCONDUCTOR WITH RASHBA SPIN-ORBITAL COUPLINGAs a starting point, the s-wave pairing SC with Rashba SO coupling is defined on a square lattice[5], which is described bywhere the kinetic term H k , the Rashba spin-orbital (SO) coupling term H so , and the superconducting pairing term

A systematic first-principle study is performed to calculate the lattice parameters, electronic structure, and thermodynamic properties of UN using the local-density approximation (LDA)+U and the generalized gradient approximation (GGA)+U formalisms. To properly describe the strong correlation in the U 5f electrons, we optimized the U parameter in calculating the total energy, lattice parameters, and bulk modulus at the nonmagnetic (NM), ferromagnetic (FM), and antiferromagnetic (AFM) configurations. Our results show that by choosing the Hubbard U around 2 eV within the GGA+U approach, it is promising to correctly and consistently describe the above mentioned properties of UN. The localization behavior of 5f electrons is found to be stronger than that of UC and our electronic analysis indicates that the effective charge of UN can be represented as U 1.71+ N 1.71− . As for the thermodynamic study, the phonon dispersion illustrates the stability of UN and we further predict the lattice vibration energy, thermal expansion, and specific heat by utilizing the quasiharmonic approximation. Our calculated specific heat is well consistent with experiments.

In this paper, the p x + ip y topological superconductor with vortex superlattice is studied. We found that there exist mid-gap energy bands induced by the vortex superlattice and the mid-gap energy bands have nontrivial topological properties including the gapless edge states and non-zero winding number. An topological anisotropic tight-binding Majorana lattice model is proposed to describe the midgap states.

Lattice parameter, electronic structure, mechanical and thermodynamic properties of ThN are systematically studied using the projector-augmented-wave method and the generalized gradient approximation based on the density functional theory. The calculated electronic structure indicates the important contributions of Th 6d and 5f states to the Fermi-level electron occupation. Through Bader analysis it is found that the effective valencies in ThN can be represented as Th +1.82 N −1.82 .Elastic constant calculations shows that ThN is mechanically stable and elastically anisotropic.Furthermore, the melting curve of ThN is presented up to 120 GPa. Based on the phonon dispersion data, our calculated specific heat capacities including both lattice and conduction-electron contributions agree well with experimental results in a wide range of temperature.

34 samples of Ru Guan porcelain body and 50 samples of Jun Guan porcelain body (both kinds being in different body colors) were selected with the purpose of finding out the source of raw materials and their classification relationship so as to search for ways of non-destructive discrimination. Proton induced X-ray emission (PIXE) has been applied to these samples to determine their chemical elements. The data of seven major chemical elements collected from these samples were further studied through fuzzy cluster analysis. Results indicate that the origin of raw materials of Jun Guan porcelain body samples is comparatively more concentrated in certain places, while that of Ru Guan porcelain body samples is scattered about. The places of origin of raw materials of the majority of Ru Guan and Jun Guan porcelain body samples have something in common, but some differences still exist. It might be an important way for non-destructive discrimination among Ru Guan and Jun Guan porcelains by combining PIXE with fuzzy cluster analysis.Keywords: Ru Guan and Jun Guan porcelain, source of porcelain body, PIXE, fuzzy cluster analysis, non-destructive discrimination.