Large-scale electronic structure theory for simulating nanostructure process

TL;DR

This paper presents scalable electronic structure calculation methods for nanostructures, focusing on accuracy, efficiency, and hybrid solver schemes to simulate large systems with thousands of atoms.

Contribution

It introduces a multi-solver scheme combining different methods for efficient large-scale simulations of nanostructures.

Findings

Validated methods on systems with 10^3-10^5 atoms

Achieved proportional computational cost with system size

Provided principles for optimal nanostructure simulation

Abstract

Fundamental theories and practical methods for large-scale electronic structure calculations are given, in which the computational cost is proportional to the system size. Accuracy controlling methods for microscopic freedoms are focused on two practical solver methods, Krylov-subspace method and generalized-Wannier-state method. A general theory called the 'multi-solver' scheme is also formulated, as a hybrid between different solver methods. Practical examples are carried out in several insulating and metallic systems with 10^3-10^5 atoms. All the theories provide general guiding principles of constructing an optimal calculation for simulating nanostructure processes, since a nanostructured system consists of several competitive regions, such as bulk and surface regions, and the simulation is designed to reproduce the competition with an optimal computational cost.