Direct calculation of lattice Green function with arbitrary interactions for general crystals

TL;DR

This paper presents an efficient method to compute the lattice Green function for general crystals with arbitrary interactions, enabling accurate modeling of defect geometries in complex materials.

Contribution

It extends a Green function calculation method from Bravais lattices to general crystals with multiple atoms and complex interactions, including optical modes and symmetry loss.

Findings

Successfully computes Green functions for complex crystal models.

Demonstrates accuracy control by treating poles and discontinuities.

Applicable to 2D and 3D crystals with arbitrary basis.

Abstract

Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic strain. Flexible boundary condition methods embedded a defect in infinite harmonic bulk through the lattice Green function. We demonstrate an efficient and accurate calculation of the lattice Green function from the force-constant matrix for general crystals with an arbitrary basis by extending a method for Bravais lattices. New terms appear due to the presence of optical modes and the possible loss of inversion symmetry. By separately treating poles and discontinuities in reciprocal space, numerical accuracy is controlled at all distances. We compute the lattice Green function for a two-dimensional model with broken symmetry to elucidate the role of different coupling terms. The algorithm is generally applicable in two and three dimensions, to crystals with arbitrary number of atoms in the unit cell, symmetry, and interactions.