Majorana stellar representation for mixed-spin (s,12)(s,\frac{1}{2}) systems

By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, Majorana's stellar representation provides an intuitive geometric perspective to comprehend a quantum system with high-dimensional Hilbert space. However, the problem of the representation of a two-spin coupling system on a Bloch sphere has not been solved satisfactorily yet. Here, we present a practical method to resolve the problem for the mixed-spin $(s, 1/2)$ system. The system can be decomposed into two spins: spin-$(s+1/2)$ and spin-$(s-1/2)$ at the coupling bases, which can be regarded as independent spins. Besides, we may write any pure state as a superposition of two orthonormal states with one spin-$(s+1/2)$ state and the other spin-$(s-1/2)$ state. Thus, the whole state can be regarded as a state of a pseudo spin-$1/2$. In this way, the mixed spin decomposes into three spins. Therefore, we can represent the state by $(2s+1)+(2s-1)+1=4s+1$ sets of stars on a Bloch sphere. Finally, to demonstrate our theory, we give some examples that indeed show laconic and symmetric patterns on the Bloch sphere, and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on a Bloch sphere

Tuning Optical Properties of Transparent Conducting Barium Stannate by Dimensional Reduction

We report calculations of the electronic structure and optical properties of doped $n$-type perovskite BaSnO3 and layered perovskites. While doped BaSnO$_3$ retains its transparency for energies below the valence to conduction band onset, the doped layered compounds exhibit below band edge optical conductivity due to transitions from the lowest conduction band. This gives absorption in the visible for Ba2SnO4. Thus it is important to minimize this phase in transparent conducting oxide (TCO) films. Ba3Sn2O7 and Ba4Sn3O10 have strong transitions only in the red and infrared, respectively. Thus there may be opportunities for using these as wavelength filtering TCO

First-principles Study of High-Pressure Phase Stability and Superconductivity of Bi4I4

Bismuth iodide Bi4I4 exhibits intricate crystal structures and topological insulating states that are highly susceptible to influence by environments, making its physical properties highly tunable by external conditions. In this work, we study the evolution of structural and electronic properties of Bi4I4 at high pressure using an advanced structure search method in conjunction with first-principles calculations. Our results indicate that the most stable ambient-pressure monoclinic α−Bi4I4 phase in C2/m symmetry transforms to a trigonal P31c structure (ɛ−Bi4I4) at 8.4 GPa, then to a tetragonal P4/mmm structure (ζ−Bi4I4) above 16.6 GPa. In contrast to the semiconducting nature of ambient-pressure Bi4I4, the two high-pressure phases are metallic, in agreement with reported electrical measurements. The ɛ−Bi4I4 phase exhibits distinct ionic states of Iδ− and (Bi4I3)δ + (δ=0.4123 e), driven by a pressure-induced volume reduction. We show that both ɛ- and ζ−Bi4I4 are superconductors, and the emergence of pressure-induced superconductivity might be intimately linked to the underlying structural phase transitions

Crystal Structure Prediction via Particle Swarm Optimization

We have developed a powerful method for crystal structure prediction from "scratch" through particle swarm optimization (PSO) algorithm within the evolutionary scheme. PSO technique is dramatically different with the genetic algorithm and has apparently avoided the use of evolution operators (e.g., crossover and mutation). The approach is based on a highly efficient global minimization of free energy surfaces merging total-energy calculations via PSO technique and requires only chemical compositions for a given compound to predict stable or metastable structures at given external conditions (e.g., pressure). A particularly devised geometrical structure factor method which allows the elimination of similar structures during structure evolution was implemented to enhance the structure search efficiency. The application of designed variable unit cell size technique has greatly reduced the computational cost. Moreover, the symmetry constraint imposed in the structure generation enables the realization of diverse structures, leads to significantly reduced search space and optimization variables, and thus fastens the global structural convergence. The PSO algorithm has been successfully applied to the prediction of many known systems (e.g., elemental, binary and ternary compounds) with various chemical bonding environments (e.g., metallic, ionic, and covalent bonding). The remarkable success rate demonstrates the reliability of this methodology and illustrates the great promise of PSO as a major technique on crystal structure determination.Comment: 17 pages,3 figures,submitted to PRB(10May10

Metallic Icosahedron Phase of Sodium at Terapascal Pressures

Alkali metals exhibit unexpected structures and electronic behavior at high pressures. Compression of metallic sodium (Na) to 200 GPa leads to the stability of a wide-band-gap insulator with the double hexagonal hP4 structure. Post-hP4 structures remain unexplored, but they are important for addressing the question of the pressure at which Na reverts to a metal. Here we report the reentrant metallicity of Na at the very high pressure of 15.5 terapascal (TPa), predicted using first-principles structure searching simulations. Na is therefore insulating over the large pressure range of 0.2-15.5 TPa. Unusually, Na adopts an oP8 structure at pressures of 117-125 GPa, and the same oP8 structure at 1.75-15.5 TPa. Metallization of Na occurs on formation of a stable and striking body-centered cubic cI24 electride structure consisting of Na12 icosahedra, each housing at its center about one electron which is not associated with any Na ions.Comment: 5 pages, 4 figures, PRL (2015