N-independent Localized Krylov-Bogoliubov-de Gennes Method: Ultra-fast Numerical Approach to Large-scale Inhomogeneous Superconductors

被引：16

作者：

Nagai, Yuki ^{[1
,2
]}

机构：

[1] Japan Atom Energy Agcy, CCSE, Kashiwa, Chiba 2770871, Japan

[2] RIKEN, Math Sci Team, Ctr Adv Intelligence Project AIP, Chuo Ku, Tokyo 1030027, Japan

来源：

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN | 2020年 / 89卷 / 07期

关键词：

D O I：

10.7566/JPSJ.89.074703

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We propose the ultra-fast numerical approach to large-scale inhomogeneous superconductors, which we call the Localized Krylov-Bogoliubov-de Gennes method (LK-BdG). In the LK-BdG method, the computational complexity of the local Green's function, which is used to calculate the local density of states and the mean-fields, does not depend on the system size N. The calculation cost of self-consistent calculations is O(N), which enables us to open a new avenue for treating extremely large systems with millions of lattice sites. To show the power of the LK-BdG method, we demonstrate a self-consistent calculation on the 143806-site Penrose quasicrystal lattice with a vortex and a calculation on 1016064-site two-dimensional nearest-neighbor square-lattice tight-binding model with many vortices. We also demonstrate that it takes less than 30 s with one CPU core to calculate the local density of states with whole energy range in 100-millions-site tight-binding model.

引用

页数：6