## Algorithm for the construction of self-energies for electronic transport calculations based on singularity elimination and singular value decomposition

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**File Type: **

PDF#####
**Item Type: **

Journal Article#####
**Date: **

2008#####
**Access: **

openAccess
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**Citation: **

*I. Rungger and S. Sanvito., Algorithm for the construction of self-energies for electronic transport calculations based on singularity elimination and singular value decomposition, Phys. Rev. B, 78, 2008, 035407*

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**Download Item: **

PhysRevB.78.035407.pdf (PDF) 411.3Kb

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**Abstract: **

We present a complete prescription for the numerical calculation of surface Green’s functions and self-
energies of semi-infinite quasi-one-dimensional systems. Our work extends previous results generating a robust
algorithm to be used in conjunction with
ab initio
electronic structure methods. We perform a detailed error
analysis of the scheme and find that the highest accuracy is found if no inversion of the usually ill conditioned
hopping matrix is involved. Even in this case however a transformation of the hopping matrix that decreases
its condition number is needed in order to limit the size of the imaginary part of the wave vectors. This is done
in two different ways: either by applying a singular value decomposition and setting a lowest bound for the
smallest singular value or by adding a random matrix of small amplitude. By using the first scheme the size of
the Hamiltonian matrix is reduced, making the computation considerably faster for large systems. For most
energies the method gives high accuracy, however in the presence of surface states the error diverges due to the
singularity in the self-energy. A surface state is found at a particular energy if the set of solution eigenvectors
of the infinite system is linearly dependent. This is then used as a criterion to detect surface states, and the error
is limited by adding a small imaginary part to the energy

**Sponsor**

**Grant Number**

Science Foundation Ireland (SFI)

SFI07/ RFP/PHY235

Science Foundation Ireland (SFI)

SFI02/IN1/I175

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**Author's Homepage: **

http://people.tcd.ie/sanvitos
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**Description: **

PUBLISHED
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**Type of material: **

Journal Article#####
**Collections:**

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**Series/Report no: **

Phys. Rev. B78

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**Availability: **

Full text available#####
**Keywords: **

Green’s functions
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**DOI: **

http://dx.doi.org/10.1103/PhysRevB.78.035407
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