Complementary local-global approach for phonon mode connectivities

Chee Kwan Gan,Zhun-Yong Ong

doi:10.1088/2399-6528/abd8ed

Abstract

Sorting and assigning phonon branches (e.g., longitudinal acoustic) of phonon modes is important for characterizing the phonon bands of a crystal and the determination of phonon properties such as the Grüneisan parameter and group velocity. To do this, the phonon band indices (including the longitudinal and transverse acoustic) have to be assigned correctly to all phonon modes across a path or paths in the Brillouin zone. As our solution to this challenging problem, we propose a computationally efficient and robust two-stage hybrid method that combines two approaches with their own merits. The first is the perturbative approach in which we connect the modes using degenerate perturbation theory. In the second approach, we use numerical fitting based on least-squares fits to circumvent local connectivity errors at or near exact degenerate modes. The method can be easily generalized to other condensed matter problems involving Hermitian matrix operators such as electronic bands in tight-binding Hamiltonians or in a standard density-functional calculation, and photonic bands in photonic crystals.

Highlights

To assess the efficacy of the proposed hybrid method, we carry out density-functional theory (DFT) calculations within the local density approximation as implemented in the Vienna Ab initio Simulation Package (VASP)[31], with projected augmented-wave (PAW) pseudopotentials
In this paper we have proposed a two-stage hybrid method that uses local and global information for phonon mode connectivity
We connect the actual eigenvalues at qi to actual eigenvalues at qi+1 through the use of first-order degenerate perturbation theory in which the perturbed eigenvalues at qi+1 are predicted from the eigenvectors at qi

Summary

Introduction

Lattice dynamical studies[1, 2] are indispensable for a detailed understanding of the thermodynamics, phase stabilities, phase transitions, and thermal properties of materials[3–6]. The methods in the second category use small atomic displacements[11–16] to numerically compute the interatomic force constants from the induced forces based on the Hellman-Feynman theorem[17] Common to these two categories of methods is the problem of dealing with small changes in the dynamical matrices for the evaluation of phonon frequency derivatives with respect to strain or volume for the Grüneisen parameters[6, 18, 19] or with respect to wavevectors (or q vectors) for phonon group velocities. In this case, the perturbation method from quantum mechanics is extremely useful[20–22]

Methods

Results

Conclusion