Large-Scale Electronic-Structure Calculations in the Real-Space Scheme: Bilayer Graphene and Silicene
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Large-Scale Electronic-Structure Calculations in the Real-Space Scheme: Bilayer Graphene and Silicene Kazuyuki Uchida, Zhixin Guo, Jun-ichi Iwata, and Atsushi Oshiyama Department of Applied Physics, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ABSTRACT We have developed our original DFT (density-functional theory) calculation code “RSDFT” using real-space schemes. The code is FFT-free, leading to high-performance computing in massively-parallel supercomputers. The code allows us to deal with systems including huge numbers of atoms from first-principles. We have applied our schemes to clarify atomic and electronic structures of two relevant nano-scale systems: twisted bilayer graphene and silicene on Ag substrate. INTRODUCTION Computational condensed matter science has been initiated in 80s of the previous century and contributed tremendously to the progress in physics and chemistry of materials. Densityfunctional theory (DFT) has been a powerful tool to reveal atom-scale mechanisms for a variety of phenomena in materials. However, target systems which DFT has treated in the past are relatively small: calculations for 100-atom systems are typical and those for 1000-atom systems are rare. On the other hand, nanometer-scale structures that realize success of nanotechnology in the present century are constituted of dozens of thousands atoms. In those nano-structures, nanoscale shapes substantially affect electron wave functions and thus novel physical properties emerge [1]: In addition to chemical elements, the nano-morphology plays an important role in materials design. Hence it is highly demanded to perform DFT calculations with suitable accuracy for dozens-of-thousands-atom systems. Performance of supercomputers has been certainly improved year by year. Yet it does not necessarily mean that advanced computations in physical science become feasible in accord. The multi-core massively parallel architecture of the current supercomputers is not easy to treat in obtaining the high performance of computations on materials. Also in the next generation, some acceleration devices such as SOC (system-on-a-chip) may be introduced. The supercomputers are now monsters which threaten us physical scientists. Hence, in order to utilize capability of the supercomputers and perform advanced computations in materials science, interdisciplinary collaboration between physical science and computer science is imperative. We call such interdisciplinary and indispensable field of science computics [2]. Real-Space DFT (RSDFT) Code We have newly developed our RSDFT code in which all the necessary quantities are computed on the grid points in the real space [3,4]. It is essentially free from the Fast Fourier Transform (FFT) which is a heavy burden in the massively parallel architecture. There are a lot of important details which make our RSDFT code run excellently on parallel architecture
computers (The 100,000-atom DFT calculations are now feasible on the K computer). We here just mention one of such details, Gram-Sc
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