Calculation of the Green's function in the scattering region for first-principles electron-transport simulations

Yoshiyuki Egami,Shigeru Tsukamoto,Tomoya Ono

doi:10.1103/physrevresearch.3.013038

Yoshiyuki Egami, Shigeru Tsukamoto + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.3.013038

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Abstract

We propose a first-principles method of efficiently evaluating electron-transport properties of very long systems. Implementing the recursive Green's function method and the shifted conjugate gradient method in the transport simulator based on real-space finite-difference formalism, we can suppress the increase in the computational cost, which is generally proportional to the cube of the system length to a linear order. This enables us to perform the transport calculations of double-walled carbon nanotubes~(DWCNTs) with 196,608 atoms. We find that the conductance spectra exhibit different properties depending on the periodicity of doped impurities in DWCNTs and they differ from the properties for systems with less than 1,000 atoms.

Highlights

One-dimensional materials such as nanowires and nanotubes, which have unique electronic properties due to the quantum confinement effect, are expected to be applied to electronic and spintronic devices, optoelectronic circuits, and biosensors [1,2,3,4,5,6,7]
Implementing the recursive Green’s function method and the shifted conjugate gradient method in the transport simulator based on real-space finite-difference formalism, we can suppress the increase in the computational cost, which is generally proportional to the cube of the system length to a linear order
We find that the conductance spectra exhibit different properties depending on the periodicity of doped impurities in double-walled carbon nanotubes (DWCNTs) and they differ from the properties for systems with less than 1000 atoms

Summary

INTRODUCTION

One-dimensional materials such as nanowires and nanotubes, which have unique electronic properties due to the quantum confinement effect, are expected to be applied to electronic and spintronic devices, optoelectronic circuits, and biosensors [1,2,3,4,5,6,7]. Real-space finite-difference (RSFD) formalism is recognized as suitable for large-scale calculations requiring high computational accuracy [13,14,15,16,17,18,19,20]. In this formalism, a Hamiltonian matrix is expressed as a block. We propose an efficient computational procedure based on RSFD formalism to evaluate the electrontransport properties of long systems containing more than 100 000 atoms under the zero temperature and zero bias limits in the steady state without accuracy deterioration. Appendices B–D describe some of the mathematical techniques used in this paper

COMPUTATIONAL SCHEME

ACCURACY TEST AND APPLICATIONS

CONCLUSION