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Numerical solver for first-principles transport calculation based on real-space finite-difference method.

Shigeru Iwase1, Takeo Hoshi2, Tomoya Ono3

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Summary
This summary is machine-generated.

We developed an efficient method combining the shifted conjugate orthogonal conjugate gradient (COCG) and nonequilibrium Green's function (NEGF) methods for accurate, large-scale electronic transport calculations.

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Area of Science:

  • Computational physics
  • Materials science
  • Quantum chemistry

Background:

  • The nonequilibrium Green's function (NEGF) method is crucial for calculating electronic transport properties.
  • Matrix inversion of the Hamiltonian, including electrode self-energy terms, presents a significant computational bottleneck in NEGF calculations.
  • Real-space finite-difference (RSFD) approaches offer advantages for large-scale simulations but require efficient Green's function computation.

Purpose of the Study:

  • To develop an efficient and accurate computational procedure for Green's function calculation within the RSFD-NEGF framework.
  • To overcome the computational bottleneck associated with matrix inversion in large-scale transport simulations.
  • To enable accurate electronic transport calculations for complex nanostructures using massively parallel computing.

Main Methods:

  • Combining the shifted conjugate orthogonal conjugate gradient (shifted COCG) method with the real-space finite-difference (RSFD) approach for NEGF calculations.
  • Computing unperturbed Green's functions efficiently using the shifted COCG method for sparse, complex-symmetric, and shifted matrices.
  • Calculating perturbed Green's functions from unperturbed ones via a mathematically strict relation, avoiding direct large-matrix inversion.

Main Results:

  • The proposed method significantly reduces the computational cost for obtaining Green's functions across multiple energy points.
  • Demonstrated the capability for large-scale transport calculations, exemplified by a C(60)@(10,10) carbon nanotube (CNT) peapod system.
  • Achieved accurate transport property calculations without sacrificing precision due to basis set limitations.

Conclusions:

  • The combined shifted COCG-RSFD-NEGF method provides an efficient and accurate approach for electronic transport simulations.
  • This scheme facilitates large-scale, high-accuracy transport calculations on massively parallel computing platforms.
  • The method is suitable for studying complex nanostructures and materials where accurate Green's functions are essential.