Quick iterative scheme for the calculation of transfer matrices: application to Mo (100)
TL;DR: In this article, the Slater-Koster algorithm is used for the calculation of tight-binding parameters with a basis of nine orbitals per atom (4d, 5s, 5p).
Abstract: The transfer matrix of a solid described by the stacking of principal layers is obtained by an iterative procedure which takes into account 2 layers after n iterations, in contrast to usual schemes where each iteration includes just one more layer. The Green function and density of states at the surface of the corresponding semi-infinite crystal are then given by well known formulae in terms of the transfer matrix. This method, especially convenient near singularities, is applied to the calculation of the spectral as well as the total densities of states for the (100) face of molybdenum. The Slater-Koster algorithm for the calculation of tight-binding parameters is used with a basis of nine orbitals per atom (4d, 5s, 5p). Surface states and resonances are first identified and then analysed into orbital components to find their dominant symmetry. Their evolution along the main symmetry lines of the two-dimensional Brillouin zone is given explicitly. The surface-state peak just below the Fermi level (Swanson hump) is not obtained. This is traced to the difficulty in placing an appropriate boundary condition at the surface with the tight-binding parameterisation scheme.
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TL;DR: In this article, first-principles electronic structure calculations of the layered, stoichiometric crystals Sb2Te3, Bi2Se3, SbSe3 and BiSe3 were performed.
Abstract: Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap of such systems are protected by time-reversal symmetry. The study of such states was originally inspired by the robustness to scattering of conducting edge states in quantum Hall systems. Recently, such analogies have resulted in the discovery of topologically protected states in two-dimensional and three-dimensional band insulators with large spin–orbit coupling. So far, the only known three-dimensional topological insulator is BixSb1−x, which is an alloy with complex surface states. Here, we present the results of first-principles electronic structure calculations of the layered, stoichiometric crystals Sb2Te3, Sb2Se3, Bi2Te3 and Bi2Se3. Our calculations predict that Sb2Te3, Bi2Te3 and Bi2Se3 are topological insulators, whereas Sb2Se3 is not. These topological insulators have robust and simple surface states consisting of a single Dirac cone at the Γ point. In addition, we predict that Bi2Se3 has a topologically non-trivial energy gap of 0.3 eV, which is larger than the energy scale of room temperature. We further present a simple and unified continuum model that captures the salient topological features of this class of materials. First-principles calculations predict that Bi2Se3, Bi2Te3 and Sb2Te3 are topological insulators—three-dimensional semiconductors with unusual surface states generated by spin–orbit coupling—whose surface states are described by a single gapless Dirac cone. The calculations further predict that Bi2Se3 has a non-trivial energy gap larger than the energy scale kBT at room temperature.
4,982 citations
TL;DR: In this paper, the authors present a survey of the use of Wannier functions in the context of electronic-structure theory, including their applications in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization.
Abstract: The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.
2,217 citations
TL;DR: In this article, the surface and bulk densities of states of a solid described by stacking of principal layers are obtained by means of an iterative procedure which allows the inclusion of 2n layers after n iterations, and simultaneous calculation of the Green functions for both the 'right' and 'left' surfaces as well as for the bulk (or central) principal layer, and the use of imaginary parts eta as small as one wishes in the energy without any large increase in computing time.
Abstract: The surface and bulk densities of states of a solid described by the stacking of principal layers are obtained by means of an iterative procedure which allows (i) the inclusion of 2n layers after n iterations, (ii) the simultaneous calculation of the Green functions for both the 'right' and 'left' surfaces as well as for the bulk (or central) principal layer, and (iii) the use of imaginary parts eta as small as one wishes in the energy without any large increase in computing time, so that the limit eta to 0 can really be obtained. As a by-product the authors obtain (i) the 'right' and 'left' transfer matrices of the 'effective field' or continuous fraction approach and (ii) a factorisation theorem which relates the Green functions of both surfaces to the Green functions of both surfaces to the Green functions of the bulk and the free metal atom.
1,628 citations
TL;DR: This code works in the tight-binding framework, which can be generated by another software package Wannier90 Mostofi et al. (2008), and can help to classify the topological phase of a given materials by calculating the Wilson loop, and get the surface state spectrum.
1,566 citations
TL;DR: In this paper, the electronic and transport properties of carbon nanotubes are reviewed, and the fundamental aspects of conduction regimes and transport length scales are presented using simple models of disorder, with the derivation of a few analytic results concerning specific situations of short and long-range static perturbations.
Abstract: This article reviews the electronic and transport properties of carbon nanotubes. The focus is mainly theoretical, but when appropriate the relation with experimental results is mentioned. While simple band-folding arguments will be invoked to rationalize how the metallic or semiconducting character of nanotubes is inferred from their topological structure, more sophisticated tight-binding and ab initio treatments will be introduced to discuss more subtle physical effects, such as those induced by curvature, tube-tube interactions, or topological defects. The same approach will be followed for transport properties. The fundamental aspects of conduction regimes and transport length scales will be presented using simple models of disorder, with the derivation of a few analytic results concerning specific situations of shortand long-range static perturbations. Further, the latest developments in semiempirical or ab initio simulations aimed at exploring the effect of realistic static scatterers chemical impurities, adsorbed molecules, etc. or inelastic electron-phonon interactions will be emphasized. Finally, specific issues, going beyond the noninteracting electron model, will be addressed, including excitonic effects in optical experiments, the Coulomb-blockade regime, and the Luttinger liquid, charge density waves, or superconducting transition.
1,249 citations
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...López-Sancho et al., 1984"....
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References
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TL;DR: In this paper, the LCAO interpolation method was used as an interpolation technique in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods.
Abstract: The LCAO, or Bloch, or tight binding, approximation for solids is discussed as an interpolation method, to be used in connection with more accurate calculations made by the cellular or orthogonalized plane-wave methods. It is proposed that the various integrals be obtained as disposable constants, so that the tight binding method will agree with accurate calculations at symmetry points in the Brillouin zone for which these calculations have been made, and that the LCAO method then be used for making calculations throughout the Brillouin zone. A general discussion of the method is given, including tables of matrix components of energy for simple cubic, face-centered and body-centered cubic, and diamond structures. Applications are given to the results of Fletcher and Wohlfarth on Ni, and Howarth on Cu, as illustrations of the fcc case. In discussing the bcc case, the splitting of the energy bands in chromium by an antiferromagnetic alternating potential is worked out, as well as a distribution of energy states for the case of no antiferromagnetism. For diamond, comparisons are made with the calculations of Herman, using the orthogonalized plane-wave method. The case of such crystals as InSb is discussed, and it is shown that their properties fit in with the energy band picture.
3,696 citations
TL;DR: In this article, the density of states n(E) and other aspects of electronic structure in a tight-binding band, without use of Bloch's theorem or the band structure E(k), are presented.
Abstract: Some new methods are presented for calculating the density of states n(E) and other aspects of electronic structure in a tight-binding band, without use of Bloch's theorem or the band structure E(k). The methods are therefore applicable to calculating the local density of states at surfaces, impurities etc. and relate the electronic structure to the local atomic environment. They depend on developing the Green function as an infinite continued fraction. There is no difficulty in obtaining n(E) in a few minutes computing time correct to the first 50 moments for an s-band and 10 moments for d-bands. The present paper discusses the methods and ideas, with specific applications to follow.
930 citations
TL;DR: In this article, for each of the two-dimensional lattice types, the mean value point, the set of generating wave vectors, and the sets of special points in the Brillouin zone are presented.
Abstract: Using the method of Chadi and Cohen, we present, for each of the two-dimensional lattice types, the mean-value point, the set of generating wave vectors, and the sets of special points in the two-dimensional Brillouin zone which are the most efficient in finding accurate averages of a periodic function over the Brillouin zone.
294 citations
TL;DR: In this paper, the authors present a very simple scheme for calculating the Green's function of a semi-infinite surface system described within a localized orbital basis by generating a series of matching conditions.
Abstract: We present a very simple scheme for calculating the Green's function of a semi-infinite surface system described within a localized orbital basis. By generating a series of matching conditions for the Green's function we can calculate its matrix elements much faster than any method currently available. We present the formalism for a specific class of systems and include a simple example to illustrate the use of the technique.
257 citations
TL;DR: In this paper, a simple, efficient scheme for calculating the electronic structure of a surface is presented, which is applicable to any general Hamiltonian that can be described within a localized-orbital basis.
Abstract: A simple, efficient scheme for calculating the electronic structure of a surface is presented. The scheme is applicable to any general Hamiltonian that can be described within a localized-orbital basis. The method is much faster than the current techniques available. The basic concept is that of wave-function matching through a transfer matrix. The eigensolutions of this matrix then provide all the information concerning the projected band structure, surface-state energies, orbital character, and decay lengths. A rather detailed discussion of the formalism is presented for a general surface system. A comprehensive and illustrative example is also presented for readers who are interested in using the scheme but not in the details of the theory.
222 citations