Three Dimensional Dirac Semimetals

We extend the physics of graphene to three dimensional systems by showing that Dirac points can exist on the Fermi surface of realistic materials in three dimensions. Many of the exotic electronic properties of graphene can be ascribed to the pseudorelativistic behavior of its charge carriers due to two dimensional Dirac points on the Fermi surface. We show that certain nonsymmorphic spacegroups exhibit Dirac points among the irreducible representations of the appropriate little group at high symmetry points on the surface of the Brillouin zone. We provide a list of all Brillouin zone momenta in the 230 spacegroups that can host Dirac points. We describe microscopic considerations necessary to design materials in one of the candidate spacegroups such that the Dirac point appears at the Fermi energy without any additional non-Dirac-like Fermi pockets. We use density functional theory based methods to propose six new Dirac semimetals: BiO2 and SbO2 in the β-cristobalite lattice (spacegroup 227), and BiCaSiO4, BiMgSiO4, BiAlInO4, and BiZnSiO4 in the distorted spinels lattice (spacegroup 74). Additionally we derive effective Dirac Hamiltonians given group representative operators as well as tight binding models incorporating spin-orbit coupling. Finally we study the Fermi surface of zincblende (spacegroup 216) HgTe which is effectively point-like at Γ in the Brillouin zone and exhibits accidental degeneracies along a threefold rotation axis. Whereas compressive strain gaps the band structure into a topological insulator, tensile strain shifts the accidental degeneracies away from Γ and enlarges the Fermi surface. States on the Fermi surface exhibit nontrivial spin texture marked by winding of spins around the threefold rotation axis and by spin vortices indicating a change in the winding number. This is confirmed by microscopic calculations performed in tensile strained HgTe and Hg0.5Zn0.5 Te as well as k.p theory. We conclude with a summary of recent work on the physics of Dirac semimetals especially after the observation of the topological Dirac semimetals Cd3As2 and Na3Bi and outline topics for future research. Symmetry protected Dirac semimetals, on the other hand, have yet to be observed experimentally

The interior Casimir problem

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2009.Includes bibliographical references (leaves 51-52).We study the electromagnetic Casimir interaction of a metallic compact object with a compact and bounded metallic surface in which it is contained. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the external conductor is a sphere and much larger than the internal conductor, the Casimir force can be expressed in terms of the static electric and magnetic multi-pole polarizabilities of the inner object, which is the interior analog of the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is universal. Additionally, we compute the exact Casimir force between two metallic spheres contained one inside the other for arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the first order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.by Saad Zaheer.S.B

Casimir interactions of an object inside a spherical metal shell

We investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration.Comment: 4 pages, 3 figure

Do Mobile Technology in the Classroom Really Improve Learning Outcomes?

This article aims to outline different pedagogical strategies with applications (apps) in the classroom. Every year the use of mobile devices like tablets and smartphones increases. At the same time, applications are being developed to meet this demand. It is therefore essential that educators investigate their use as an motivational technological medium that can possibly be used in the classroom. Apps can be used both as a source of information as well as a tool for creating material. Thus, this article will present the results of a study applying teaching strategies in different contexts. It therefore highlights the importance of mobile learning as a viable alternative in the classroom. In order to do so, there was a multiple case study in the undergraduate pedagogy program and a digital inclusion course for seniors, both offered in the first semester of 2017 at the Federal University of Rio Grande do Sul (UFRGS). Educational applications and examples of teaching strategies using apps were created in these classes. Educational applications offer the possibility to bring innovations to teaching practices, as well as new forms of communication, interaction and authorship, thus contributing to the process of teaching and learning

Spin texture on the Fermi surface of tensile strained HgTe

We present ab initio and k.p calculations of the spin texture on the Fermi surface of tensile strained HgTe, which is obtained by stretching the zincblende lattice along the (111) axis. Tensile strained HgTe is a semimetal with pointlike accidental degeneracies between a mirror symmetry protected twofold degenerate band and two nondegenerate bands near the Fermi level. The Fermi surface consists of two ellipsoids which contact at the point where the Fermi level crosses the twofold degenerate band along the (111) axis. However, the spin texture of occupied states indicates that neither ellipsoid carries a compensating Chern number. Consequently, the spin texture is locked in the plane perpendicular to the (111) axis, exhibits a nonzero winding number in that plane, and changes winding number from one end of the Fermi ellipsoids to the other. The change in the winding of the spin texture suggests the existence of singular points. An ordered alloy of HgTe with ZnTe has the same effect as stretching the zincblende lattice in the (111) direction. We present ab initio calculations of ordered Hg_xZn_1-xTe that confirm the existence of a spin texture locked in a 2D plane on the Fermi surface with different winding numbers on either end.Comment: 8 pages, 8 figure

Casimir potential of a compact object enclosed by a spherical cavity

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects' scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object's electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading order correction to the Proximity Force Approximation for two metallic spheres both outside and within one another.Comment: 12 pages, 6 figure

Casimir spring and compass: Stable levitation and alignment of compact objects

We investigate a stable Casimir force configuration consisting of an object contained inside a spherical or spheroidal cavity filled with a dielectric medium. The spring constant for displacements from the center of the cavity and the dependence of the energy on the relative orientations of the inner object and the cavity walls are computed. We find that the stability of the force equilibrium can be predicted based on the sign of the force, but the torque cannot be.Comment: 5 pages, 4 figure

ARHITEKTONSKE SLOŽENOSTI I MORFOLOŠKE VARIJACIJE SEDIMENTNIH VALOVA PLIO-PLEISTOCENSKIH KANALA U DELTI INDA

The architecture of the turbidity current sediment waves exhibits intricate morphologies and patterns on the Indus Fan channel levee backslope. The sediment waves are present on the channel levee of Plio-Pleistocene age and are absent in the deeper sections of the study area. The architecture of channel levee backslope on the Indus Fan is poorly understood. We used seismic interpretation techniques and modelling by utilizing high-resolution seismic data to approach this problem. The morphological variations in wavelength, crest dimensions and potential wave formation patterns suggest the autogenic and allogenic processes associated with wave development. Wavelengths reach up to 1473 m with an average of 486.84 m and the height of the levee ranges between 10 m and 60 m (average 30 m). The angle of the channel levee and dimension of the sediment wave here are independent of each other. Low angle levees have accommodated high dimension sediment waves and vice versa at multiple points downslope. Characteristically, the waves have formed on the outer levee (usually left) of the channels marked by steep margins suggesting that flow overspill caused the development of the waves. Generally, the younger sediment waves followed the patterns of older sediment waves, but the varying trends are often observed in the study area. The patterns of the sediment waves towards the younger sections of the levee indicate the modified and varying architectural style of growth. Sediment waves are generated by downslope turbidity currents. However, the deformation features have also possibly triggered the development of sediment waves.Arhitektura sedimentnih valova nastalih uslijed turbiditnih struja pokazuje zamršenu morfologiju i obrasce unutar kanala i njihovih rubova u prostoru deltne lepeze Inda. Tragovi taloženja energijom valova prisutni su u plio-pleistocenskim kanalima i oko njih, no izostaju u dubljim dijelovima istraživanoga područja. Arhitektura rubova kanala u delti Inda do sada nije bila detaljno opisana. U istraživanju ovoga problema korištene su seizmičke metode i modeliranje podataka visoke razlučivosti. Morfološke varijacije u duljinama valova, dimenzijama kresta i potencijalnim obrascima stvaranja valova upućuju na autogene i alogene procese povezane s razvojem valova. Dujine valova dosežu do 1473 m s prosjekom od 486,84 m, a visina se kreće između 10 m i 60 m (prosječno 30 m). Kut rubova kanala i dimenzija vala u ovome slučaju bili su neovisni jedno o drugome. Mali kut omogućio je na nekoliko točaka u nižim dijelovima akomodiranje valova velikih dimenzija i obrnuto. Karakteristični valovi nastajali su na vanjskome dijelu nasipa kanala (obično lijevome) sa strmim rubovima, što upućuje na to da je njihovo prelijevanje utjecalo na energiju. Općenito, mlađi valni sedimenti slijedili su obrasce starijih, ali se ponekad može uočiti i promjena trenda. Obrasci valnih taložina u mlađim naslagama rubova upućuju na promjenu, pa i inverziju oblika. Općenito su valni sedimenti posljedica aktivnosti turbiditnih struja u podnožju rubova kanala, a i njihov nastanak vrlo je usko povezan s deformacijskim strukturama