### Abstract

The electron transmission probability in nanodevices is calculated by solving an eigenvalue problem. The eigenvalues are the transmission probabilities and the number of nonzero eigenvalues is equal to the number of open quantum transmission eigenchannels. The number of open eigenchannels is typically a few dozen at most, thus the computational cost amounts to the calculation of a few outer eigenvalues of a complex Hermitian matrix (the transmission matrix). The method is implemented on a real space grid basis providing an alternative to localized atomic orbital based quantum transport calculations. Numerical examples are presented to illustrate the efficiency of the method.

Original language | English |
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Article number | 465306 |

Journal | Journal of Physics Condensed Matter |

Volume | 22 |

Issue number | 46 |

DOIs | |

Publication status | Published - Nov 24 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Materials Science(all)

### Cite this

*Journal of Physics Condensed Matter*,

*22*(46), [465306]. https://doi.org/10.1088/0953-8984/22/46/465306

**Calculation of transmission probability by solving an eigenvalue problem.** / Bubin, Sergiy; Varga, Kálmán.

Research output: Contribution to journal › Article

*Journal of Physics Condensed Matter*, vol. 22, no. 46, 465306. https://doi.org/10.1088/0953-8984/22/46/465306

}

TY - JOUR

T1 - Calculation of transmission probability by solving an eigenvalue problem

AU - Bubin, Sergiy

AU - Varga, Kálmán

PY - 2010/11/24

Y1 - 2010/11/24

N2 - The electron transmission probability in nanodevices is calculated by solving an eigenvalue problem. The eigenvalues are the transmission probabilities and the number of nonzero eigenvalues is equal to the number of open quantum transmission eigenchannels. The number of open eigenchannels is typically a few dozen at most, thus the computational cost amounts to the calculation of a few outer eigenvalues of a complex Hermitian matrix (the transmission matrix). The method is implemented on a real space grid basis providing an alternative to localized atomic orbital based quantum transport calculations. Numerical examples are presented to illustrate the efficiency of the method.

AB - The electron transmission probability in nanodevices is calculated by solving an eigenvalue problem. The eigenvalues are the transmission probabilities and the number of nonzero eigenvalues is equal to the number of open quantum transmission eigenchannels. The number of open eigenchannels is typically a few dozen at most, thus the computational cost amounts to the calculation of a few outer eigenvalues of a complex Hermitian matrix (the transmission matrix). The method is implemented on a real space grid basis providing an alternative to localized atomic orbital based quantum transport calculations. Numerical examples are presented to illustrate the efficiency of the method.

UR - http://www.scopus.com/inward/record.url?scp=78149424869&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78149424869&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/22/46/465306

DO - 10.1088/0953-8984/22/46/465306

M3 - Article

VL - 22

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 46

M1 - 465306

ER -