Tri-Dirac Surface Modes in Topological Superconductors

We propose a new type of topological surface modes having cubic dispersion in three-dimensional topological superconductors. Lower order dispersions are prohibited by the threefold rotational symmetry and time-reversal symmetry. Cooper pairing in the bulk changes sign under improper rotations, akin to$^{3}$He-B. The surface manifestations are a divergent surface density of states at the Fermi level and isospins that rotate three times as they circle the origin in momentum space. We propose that Heusler alloys with band inversion are candidate materials to harbor the novel topological superconductivity.Comment: Five-page main text plus five-page supplementary materials; three figure

Entanglement Spectrum Classification of CnC_n-invariant Noninteracting Topological Insulators in Two Dimensions

We study the single particle entanglement spectrum in 2D topological insulators which possess $n$-fold rotation symmetry. By defining a series of special choices of subsystems on which the entanglement is calculated, or real space cuts, we find that the number of protected in-gap states for each type of these real space cuts is a quantum number indexing (if any) non-trivial topology in these insulators. We explicitly show the number of protected in-gap states is determined by a $Z^n$-index, $(z_1,...,z_n)$, where $z_m$ is the number of occupied states that transform according to $m$-th one-dimensional representation of the $C_n$ point group. We find that the entanglement spectrum contains in-gap states pinned in an interval of entanglement eigenvalues $[1/n,1-1/n]$. We determine the number of such in-gap states for an exhaustive variety of cuts, in terms of the $Z_m$ quantum numbers. Furthermore, we show that in a homogeneous system, the $Z^n$ index can be determined through an evaluation of the eigenvalues of point group symmetry operators at all high-symmetry points in the Brillouin zone. When disordered $n$-fold rotationally symmetric systems are considered, we find that the number of protected in-gap states is identical to that in the clean limit as long as the disorder preserves the underlying point group symmetry and does not close the bulk insulating gap.Comment: 14.2 pages for main text, 4.8 pages for Appendices, four figures and two table

Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators

Quantum anomalous Hall (QAH) insulators are two-dimensional (2D) insulating states exhibiting properties similar to those of quantum Hall states but without external magnetic field. They have quantized Hall conductance $\sigma^H=Ce^2/h$, where integer $C$ is called the Chern number, and represents the number of gapless edge modes. Recent experiments demonstrated that chromium doped thin-film (Bi,Sb)$_2$Te$_3$ is a QAH insulator with Chern number $C=\pm1$. Here we theoretically predict that thin-film topological crystalline insulators (TCI) can host various QAH phases, when doped by ferromagnetically ordered dopants. Any Chern number between $\pm4$ can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through proximity effect and (c) the thickness of the thin film. The tunable Chern numbers found in TCI possess significant potential for ultra-low power information processing applications.Comment: References update

New class of topological superconductors protected by magnetic group symmetries

We study a new type of three-dimensional topological superconductors that exhibit Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time-reversal. This new symmetry enhances the noninteracting topological classification of a superconducting vortex from $Z_2$ to $Z$, indicating that multiple MZMs can coexist at the end of one magnetic vortex of unit flux. Specially, we show that a vortex binding two MZMs can be realized on the $(001)$-surface of a topological crystalline insulator SnTe with proximity induced BCS Cooper pairing, or in bulk superconductor In$_x$Sn$_{1-x}$Te.Comment: Accepted version to appear in PRL: 4-page text plus 4-page supplementary materials, two figure

Fir-Flower Petals on a Wet Black Bough: Constructing New Poetry through Asian Aesthetics in Early Modernist Poets

Critics often credit Ezra Pound and his Imagist movement for the development of American poetics. Pound’s interest in international arts and minimalist aesthetics of cross-cultural poetry gained the attention of prominent writers throughout Modernist and Post-Modern periods. From writers like Wallace Stevens and Gertrude Stein to later poets like Jack Kerouac and Gary Snyder, image and precise language has shaped American literature. Few critics have praised Eastern cultures or the Imagist poets who adopted an East-Western form of poetics: Amy Lowell and William Carlos Williams. Studying traditional Eastern painting and short-form poetry and interactions with personal connections to the East, Lowell and Williams adapt then progress aesthetic fusions Pound began and abandoned through his interpretation of Eastern art. Like Pound, Lowell and Williams illustrate a mix of form, free-verse language, and modernized poetics to not only imitate Eastern art but to create poetics of international discourse which shape American Modernism

Adaptive Element-Free Galerkin method applied to the limit analysis of plates

The implementation of an h-adaptive Element-Free Galerkin (EFG) method in the framework of limit analysis is described. The naturally conforming property of mesh- free approximations (with no nodal connectivity required) facilitates the implementation of h-adaptivity. Nodes may be moved, discarded or introduced without the need for complex manipulation of the data structures involved. With the use of the Taylor expansion technique, the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy. A stabilized conforming nodal integration scheme is extended to error estimators and results in an efficient and truly meshfree adaptive method. To demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions