Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 316

The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.

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

Open access
Rungger, Ivan, Sanvito, Stefano·2008·Physical Review B
DOI 10.1103/physrevb.78.035407
Open this paper in CoChat — free account

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.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevb.78.035407

Cites

22 of 22 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Metadata

Authors
Rungger, I., & Sanvito, S.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2008-07-03
Volume
78
Issue
3
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.78.035407
OpenAlex
W2170555669
Cited by
316
References
22
FWCI
8.70
Type
journal article
Language
en
Open access
green

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.