journal article·2020-07-01Open access

Chebyshev polynomial method to Landauer–Büttiker formula of quantum transport in nanostructures

Yan Yu, Yan-Yang Zhang, Lei Liu, Si-Si Wang, Ji-Huan Guan, Yang Xia, Shu-Shen Li

AIP Advances· Volume 10· Issue 7

Abstract

The Landauer–Büttiker formula describes the electronic quantum transport in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations. Recently, the Chebyshev polynomial method has attracted intense interest in numerical simulations of quantum systems due to the high efficiency in parallelization because the only matrix operation it involves is just the product of sparse matrices and vectors. Much progress has been made on the Chebyshev polynomial representations of physical quantities for isolated or bulk quantum structures. Here, we present the Chebyshev polynomial method to the typical electronic scattering problem, the Landauer–Büttiker formula for the conductance of quantum transport in nanostructures. We first describe the full algorithm based on the standard bath kernel polynomial method (KPM). Then, we present two simple but efficient improvements. One of them has time consumption remarkably less than that of the direct matrix calculation without KPM. Some typical examples are also presented to illustrate the numerical effectiveness.
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Research context

OpenAlex topics: Advanced Physical and Chemical Molecular Interactions · Molecular Junctions and Nanostructures · Quantum and electron transport phenomena

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

SKLSM, Institute of Semiconductors, Chinese Academy of Sciences 1 , P.O. Box 912, Beijing 100083, China

School of Physical Sciences, University of Chinese Academy of Sciences 2 , Beijing 100049, China

School of Physics and Electronic Engineering, Guangzhou University 3 , 510006 Guangzhou, China

Research Center for Advanced Information Materials, Guangzhou University 4 , 510006 Guangzhou, China

Department of Medical Physics, School of Medical Imaging, Hebei Medical University 5 , Shijiazhuang, Hebei 050017, China

College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences 6 , Beijing 100049, China

Microelectronic Instrument and Equipment Research Center, Institute of Microelectronics of Chinese Academy of Sciences 7 , Beijing 100029, China

School of Microelectronics, University of Chinese Academy of Sciences 8 , Beijing 100049, China

Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China 9 , Hefei, Anhui 230026, China

Funding

Starting Research Funding from Guangzhou University · National Natural Science Foundation of China

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