Exceptional topological insulators

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.

Stability, Structural and Electronic Properties of Indium Phosphide Wurtzite-Diamantane Molecules and Nanocrystals: A Density Functional Theory Study

The density functional theory is applied for examining the electronic structure and spectroscopic properties for InP wurtzite molecules and nanocrystals. In this paper we present calculations of the energy gap, bond lengths, IR and Raman spectrum, reduced mass and force constant. The results of the presented work showing that the InP’s energy gap was fluctuated about to experimental bulk energy gap (1.49 eV). Results of spectroscopic properties including IR and Raman spectrum, reduced mass and force constant as a function of frequency were in accordance with the provided experimental results. In addition, the study of the Gibbs free energy proved the stability phase of InP wurtzoids against transition to InP diamondoids structure.

Quadratic-stretch elasticity

A nonlinear small-strain elastic theory is constructed from a systematic expansion in Biot strains, truncated at quadratic order. The primary motivation is the desire for a clean separation between stretching and bending energies for shells, which appears to arise only from reduction of a bulk energy of this type. An approximation of isotropic invariants, bypassing the solution of a quartic equation or computation of tensor square roots, allows stretches, rotations, stresses, and balance laws to be written in terms of derivatives of position. Two-field formulations are also presented. Extensions to anisotropic theories are briefly discussed.

A regularity result for minimal configurations of a free interface problem

We prove a regularity result for minimal configurations of variational problems involving both bulk and surface energies in some bounded open region $$\varOmega \subseteq {\mathbb {R}}^n$$ Ω ⊆ R n . We will deal with the energy functional $${\mathscr {F}}(v,E):=\int _\varOmega [F(\nabla v)+1_E G(\nabla v)+f_E(x,v)]\,dx+P(E,\varOmega )$$ F ( v , E ) : = ∫ Ω [ F ( ∇ v ) + 1 E G ( ∇ v ) + f E ( x , v ) ] d x + P ( E , Ω ) . The bulk energy depends on a function v and its gradient $$\nabla v$$ ∇ v . It consists in two strongly quasi-convex functions F and G, which have polinomial p-growth and are linked with their p-recession functions by a proximity condition, and a function $$f_E$$ f E , whose absolute valuesatisfies a q-growth condition from above. The surface penalization term is proportional to the perimeter of a subset E in $$\varOmega $$ Ω . The term $$f_E$$ f E is allowed to be negative, but an additional condition on the growth from below is needed to prove the existence of a minimal configuration of the problem associated with $${\mathscr {F}}$$ F . The same condition turns out to be crucial in the proof of the regularity result as well. If (u, A) is a minimal configuration, we prove that u is locally Hölder continuous and A is equivalent to an open set $${\tilde{A}}$$ A ~ . We finally get $$P(A,\varOmega )={\mathscr {H}}^{n-1}(\partial {\tilde{A}}\cap \varOmega $$ P ( A , Ω ) = H n - 1 ( ∂ A ~ ∩ Ω ).

A Primer on Weyl Semimetals: Down the Discovery of Topological Phases

Recently discovered Weyl semimetals (WSM) have found special place in topological condensed matter studies for they represent first example of massless Weyl fermions found in electronic condensed matter systems. A WSM shows gapless bulk energy spectra with Dirac-like point degeneracies, famously called Weyl nodes, which carry with themselves well defined chiralities and topologically protected chiral charges. One finds the Berry curvature of the Bloch bands to become singular, like in a magnetic monopole, at these Weyl nodes. Moreover, these systems feature topological surface states in the form of open Fermi arcs. In this review, we undergo a concise journey from graphene based Dirac physics to Weyl semimetals: the underlying Hamiltonians, their basic features and their unique response to external electric and magnetic fields in order to provide a basic walk-through of how the Weyl physics unfolded with time starting from the discovery of Graphene.

Study of the structure and mechanical properties of samples obtained by the selective laser alloying technology from the Inconel 738 heat-resistant alloy powder

The technology of selective laser melting of heat-resistant alloys is of great interest in the aerospace industry, because it allows you to implement a more complex geometry of parts in comparison with traditional technologies. This paper presents the results of determining the rational technological parameters of scanning a metal powder of a heat-resistant alloy Inconel 738. By statistical processing of experimental data to determine the effect of technological parameters of scanning on the tensile strength of a material, rational technological parameters of scanning are established, namely, the laser radiation power is 325 W, the scanning step is 0,12 mm, scanning speed of 677 mm/s, which corresponds to a bulk energy density of 80 J/mm3. The results of tests of cylindrical samples manufactured at angles of 0°, 30°, 45°, 60° and 90° to the uniaxial tension building platform are presented. A study of the microstructure of the samples was executed.