Local normal modes and lattice dynamics

Abstract

The calculation of phonon dispersion for crystalline solids with r atoms in a unit cell requires solving a 3r-dimensional eigenvalue problem. In this paper we propose a simplified approach to lattice dynamics which yields approximate analytical expressions and accurate numerical solutions to phonon dispersion without solving the eigenvalue problem. This is accomplished by making coordinate transformations to the normal modes of the isolated unit cell, which are extended over the entire crystal by Fourier transformations, so each phonon branch is labelled by the irreducible representations of the symmetry group of the unit cell from which the atomic displacements can be readily identified. The resulting dynamical matrix can be analyzed perturbatively, with the diagonal elements as the zeroth order matrix and the off-diagonal elements as the perturbation. The zeroth-order matrix provides approximate analytical expressions for the phonon dispersions, the first-order terms vanish, and the higher-order terms converge to the exact solutions. We describe the application of this method to a one-dimensional diatomic chain, graphene, and hexagonal closepacked zirconium. In all cases, the zeroth-order solution provides reasonable approximations, while the second-order solutions are close to the exact dispersion curves. This approach provides insight into the lattice dynamics of crystals, molecular solids and Jahn-Teller systems, while significantly reducing the computational cost.

Assessment of optical phonons in BeTe, BexZn1-xTe, p-BeTe epilayers and BeTe/ZnTe/GaAs (001) superlattices

“…There exist two types of theoretical methods for assessing the structural and lattice dynamical properties of perfect/imperfect semiconductors. These are: (a) the microscopic methods [26][27][28][29][30][31][32][33][34][35][36][37][38] which start with ionic potentials screened by electron gas for gaining the optical, electronic, and phonon traits, and (b) the macroscopic techniques, which employ phenomenological models [39][40][41][42][43][44][45][46][47][48][49] to simulate phonon and impurity-induced vibrational characteristics. In the former techniques, the interatomic forces of the perfect/imperfect materials are usually evaluated using self-consistent density functional theory (SC-DFT) [26][27][28][29][30][31][32][33][34][35][36][37][38] to comprehend the structural, optical, and phonon properties by employing an ABINIT software package.…”

“…These are: (a) the microscopic methods [26][27][28][29][30][31][32][33][34][35][36][37][38] which start with ionic potentials screened by electron gas for gaining the optical, electronic, and phonon traits, and (b) the macroscopic techniques, which employ phenomenological models [39][40][41][42][43][44][45][46][47][48][49] to simulate phonon and impurity-induced vibrational characteristics. In the former techniques, the interatomic forces of the perfect/imperfect materials are usually evaluated using self-consistent density functional theory (SC-DFT) [26][27][28][29][30][31][32][33][34][35][36][37][38] to comprehend the structural, optical, and phonon properties by employing an ABINIT software package. One must note that the SC-DFT methods are computationally demanding for semiconductor materials to study the defect vibrational modes of isoelectronic impurities and are much more cumbersome for non-isoelectronic (i.e., charged) defects [29].…”

“…One must note that the SC-DFT methods are computationally demanding for semiconductor materials to study the defect vibrational modes of isoelectronic impurities and are much more cumbersome for non-isoelectronic (i.e., charged) defects [29]. The first-principles methods have offered not only accurate phonon properties of alloy semiconductors [26][27][28][29][30][31][32][33][34][35][36][37][38] but also facilitated assessing FIR reflectivity and Raman intensity profiles of perfect/imperfect GaN/AlN SLs [31][32]. As compared to the ab initio techniques, the benefits of using macroscopic methods for investigating the lattice dynamics of perfect/imperfect [39][40][41][42][43][44][45][46][47][48][49] semiconductors are quite discernable.…”

Phase Stability of the Tin Monochalcogenides SnS and SnSe: A Quasi-Harmonic Lattice-Dynamics Study

“…The quasi-harmonic approximation (QHA) takes into account the volume dependence of the phonon frequencies by applying the harmonic approximation at a series of compressions and expansions. 43,44 The Gibbs free energy ( , ) 38 is generally a more experimentally-relevant free energy and is calculated as the minimum of ( ; ) + over a range of volumes:…”