Efficient and Scalable Calculation of Complex Band Structure using Sakurai-Sugiura Method

TL;DR

This paper introduces a scalable and efficient computational approach for calculating complex band structures of large materials systems by combining quadratic eigenvalue problem formulation with the Sakurai-Sugiura method, enabling high-performance parallel computation.

Contribution

The paper presents a novel method that significantly reduces computational cost and enhances scalability for first-principles CBS calculations of large atomic systems.

Findings

Achieved faster runtime and lower memory usage compared to traditional methods.

Demonstrated scalability on a 10,000+ atom system using high-performance computing resources.

Enabled CBS calculation for large systems with over 10,000 atoms efficiently.

Abstract

Complex band structures (CBSs) are useful to characterize the static and dynamical electronic properties of materials. Despite the intensive developments, the first-principles calculation of CBS for over several hundred atoms is still computationally demanding. We here propose an efficient and scalable computational method to calculate CBSs. The basic idea is to express the Kohn-Sham equation of the real-space grid scheme as a quadratic eigenvalue problem and compute only the solutions which are necessary to construct the CBS by Sakurai-Sugiura method. The serial performance of the proposed method shows a significant advantage in both runtime and memory usage compared to the conventional method. Furthermore, owing to the hierarchical parallelism in Sakurai-Sugiura method and the domain-decomposition technique for real-space grids, we can achieve an excellent scalability in the CBS calculation of a boron and nitrogen doped carbon nanotube consisting of more than 10,000 atoms using 2,048 nodes (139,264 cores) of Oakforest-PACS.