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Title: Scattering matrix of arbitrary tight-binding Hamiltonians

Abstract

A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.

Authors:
;
Publication Date:
OSTI Identifier:
22617485
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 378; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HAMILTONIANS; MATRICES; NANOSTRUCTURES; RENORMALIZATION; SCATTERING; TETRAGONAL LATTICES

Citation Formats

Ramírez, C., E-mail: carlos@ciencias.unam.mx, and Medina-Amayo, L.A. Scattering matrix of arbitrary tight-binding Hamiltonians. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2017.01.015.
Ramírez, C., E-mail: carlos@ciencias.unam.mx, & Medina-Amayo, L.A. Scattering matrix of arbitrary tight-binding Hamiltonians. United States. doi:10.1016/J.AOP.2017.01.015.
Ramírez, C., E-mail: carlos@ciencias.unam.mx, and Medina-Amayo, L.A. Wed . "Scattering matrix of arbitrary tight-binding Hamiltonians". United States. doi:10.1016/J.AOP.2017.01.015.
@article{osti_22617485,
title = {Scattering matrix of arbitrary tight-binding Hamiltonians},
author = {Ramírez, C., E-mail: carlos@ciencias.unam.mx and Medina-Amayo, L.A.},
abstractNote = {A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.},
doi = {10.1016/J.AOP.2017.01.015},
journal = {Annals of Physics},
number = ,
volume = 378,
place = {United States},
year = {Wed Mar 15 00:00:00 EDT 2017},
month = {Wed Mar 15 00:00:00 EDT 2017}
}
  • This paper extends work done to date on quantum computation by association of potentials with different types of steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding Hamiltonians each with a different potential distribution. Which distribution applies is determined by the initial state. An example, which enumerates the integers in succession as binary strings, is analyzed. It is seen that for some initial states, the potential distributions have quasicrystalline properties and are similar to a substitution sequence. {copyright} {ital 1997} {ital The American Physical Society}
  • One-dimensional (1D) systems with deterministic disorder, such as those with quasiperiodic or substitutional sequence potential distributions, have been extensively studied. It was recently shown that a generalization of quantum Turing machines (QTM`s), in which potentials are associated with elementary steps or transitions of the computation, generates potential distributions along computation paths of states in some basis B, which are computable and are thus periodic or have deterministic disorder. These generalized machines (GQTM`s) can be used to investigate the effect of potentials in causing reflections and reducing the completion probability of computations. This paper expands on this work by determining themore » spectral and transmission properties of an example GQTM, which enumerates the integers in succession as binary strings. A potential is associated with just one type of step. For many computation paths the potential distributions are initial segments of a distribution that is quasiperiodic and corresponds to a substitution sequence. Thus the methods developed in the study of 1D systems can be used to calculate the energy band spectra and Landauer resistance (LR). For energies below the barrier height, the LR fluctuates rapidly with momentum with minima close to or at band-gap edges. Also for several values of the parameters involved there is good transmission over some momentum regions. {copyright} {ital 1997} {ital The American Physical Society}« less
  • We present accurate tight-binding parametrizations of the first-principles augmented-plane-wave or linear-augmented-plane-wave band structures of LaCuO/sub 3/, La/sub 2/CuO/sub 4/, Ba/sub 2/CuO/sub 4/, and the high-temperature superconductor YBa/sub 2/Cu/sub 3/O/sub 7/. We discuss the methodology and efficient application of these fits, including as an example our tight-binding coherent-potential-approximation (CPA) calculations of the effects of disorder on the electronic structure of La/sub 2-//sub x/Ba/sub x/CuO/sub 4-//sub y/. Our CPA calculations support the hypothesis of a rigid-band lowering of the Fermi level for La/sub 2-//sub x/Ba/sub x/CuO/sub 4/, enhancing the density of states there. However, for La/sub 2/BaCuO/sub 4-//sub y/ they yield themore » interesting result that oxygen vacancies also lower E/sub F/ and raise N(E/sub F/). This is a significant result for the theory of superconductivity in these materials. In addition to CPA calculations, our parametrizations of the band structures should prove to be a useful tool for other studies which will enhance our understanding of these materials.« less
  • We propose a method for including the fractional occupancy of electronic energy levels within a tight-binding density-matrix formalism. This method is based on successful techniques used in first-principles methods. Molecular-dynamics test simulations show that the density-matrix technique accurately reproduces the physics of a direct-diagonalization simulation using Fermi-Dirac occupancy. {copyright} {ital 1996 The American Physical Society.}
  • We present a tight-binding model for silicon which incorporates two-center intra-atomic parameters. The model is fitted to density-functional-theory band structures for silicon in the diamond structure over a number of volumes. It is shown that with only a two-center, orthogonal basis, reasonable total energies can be obtained for many different structures. Thus it eliminates the need to use structure-dependent terms in the total-energy model.