Extending solid-state calculations to ultra long-range length scales

TL;DR

This paper introduces a novel method that extends density functional theory calculations to micron-scale systems by generalizing Bloch states, enabling the study of large systems with microscopic electronic detail.

Contribution

A new approach generalizing Bloch states to perform ultra long-range density functional theory calculations on systems of nearly unlimited size.

Findings

Successfully modeled bulk LiF with 3500 atoms under external potential.

Validated method accuracy with spin density wave state of bcc Cr.

Reproduced spin spiral state of γ-Fe and verified screening in silicon.

Abstract

We present a method which enables solid-state density functional theory calculations to be applied to systems of almost unlimited size. Computations of physical effects up to the micron length scale but which nevertheless depend on the microscopic details of the electronic structure, are made possible. Our approach is based on a generalization of the Bloch state which involves an additional sum over a finer grid in reciprocal space around each ${\bf k}$-point. We show that this allows for modulations in the density and magnetization of arbitrary length on top of a lattice-periodic solution. Based on this, we derive a set of ultra long-range Kohn-Sham equations. We demonstrate our method with a sample calculation of bulk LiF subjected to an arbitrary external potential containing nearly 3500 atoms. We also confirm the accuracy of the method by comparing the spin density wave state of bcc Cr against a direct supercell calculation starting from a random magnetization density. Furthermore, the spin spiral state of $\gamma$-Fe is correctly reproduced and the screening by the density of a saw-tooth potential over 20 unit cells of silicon is verified.