Self-energy matrices for electron transport calculations within the real-space finite-difference formalism

Abstract

The self-energy term used in transport calculations, which describes the coupling between electrode and transition regions, is able to be evaluated only from a limited number of the propagating and evanescent waves of a bulk electrode. This obviously contributes toward the reduction of the computational expenses in transport calculations. In this paper, we present a mathematical formula for reducing the computational expenses further without using any approximation and without losing accuracy. So far, the self-energy term has been handled as a matrix with the same dimension as the Hamiltonian submatrix representing the interaction between an electrode and a transition region. In this work, through the singular-value decomposition of the submatrix, the self-energy matrix is handled as a smaller matrix, whose dimension is the rank number of the Hamiltonian submatrix. This procedure is practical in the case of using the pseudopotentials in a separable form, and the computational expenses for determining the self-energy matrix are reduced by 90% when employing a code based on the real-space finite-difference formalism and projector-augmented wave method. In addition, this technique is applicable to the transport calculations using atomic or localized basis sets. Adopting the self-energy matrices obtained from this procedure, we present the calculation of the electron transport properties of C_{20} molecular junctions. The application demonstrates that the electron transmissions are sensitive to the orientation of the molecule with respect to the electrode surface. In addition, channel decomposition of the scattering wave functions reveals that some unoccupied C_{20} molecular orbitals mainly contribute to the electron conduction through the molecular junction.

Scalable atomistic simulations of quantum electron transport using empirical pseudopotentials

“…The calculation of contact self-energies using iterative and direct approaches (as used here) is already well established in literature. [29,[36][37][38] Nonetheless, we will detail the procedure here. Our reasons for this are twofold; (1) our basis, being non-orthogonal, introduces additional complexity that, to our knowledge, has not been previously described for the direct approach, and (2) our numerical approach avoids some numerical errors in calculating the self-energies directly.…”

Improvement of accuracy in the wave-function-matching method for transport calculations

“…( 3) by the unitary transformation. 22,23 The solution of Eq. ( 2) is obtained by solving the following eigenvalue problem:…”

“…The Dirac triangles agree well with the classification of graphene transport behavior by Yazyev and Louie. 45 The electron transport calculations of the graphene sheets with the B-N line defects are carried out using the code 11,12,15,22,23 incorporating the aforementioned technique together with the WFM method based on the density functional theory. 27,28,33 The generalized Bloch wave func-tions and scattering wave functions are determined in a non-self-consistent manner to a set of given potential and pseudopotential parameters, which are used for constructing the Kohn-Sham matrix ES − H in Eqs.…”

Efficient calculation of the Green's function in scattering region for electron-transport simulations

“…However, real-space finite-difference (RSFD) formalism is also recognized as suitable for large-scale calculations requiring high computational accuracy because it has a high affinity to massively parallel architectures and can avoid problems arising from the basis sets. [13][14][15][16][17][18][19][20] Fujimoto and Hirose developed the overbridging boundary matching (OBM) method based on the RSFD formalism 13 by exploiting the advantages for electron-transport calculations, where a whole system is divided along the z direction (see Fig. 1) into three regions: the left electrode, the transition region and the right electrode.…”