# Scattering matrix of arbitrary tight-binding Hamiltonians

## Abstract

A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617485

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 378; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HAMILTONIANS; MATRICES; NANOSTRUCTURES; RENORMALIZATION; SCATTERING; TETRAGONAL LATTICES

### Citation Formats

```
Ramírez, C., E-mail: carlos@ciencias.unam.mx, and Medina-Amayo, L.A.
```*Scattering matrix of arbitrary tight-binding Hamiltonians*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.01.015.

```
Ramírez, C., E-mail: carlos@ciencias.unam.mx, & Medina-Amayo, L.A.
```*Scattering matrix of arbitrary tight-binding Hamiltonians*. United States. doi:10.1016/J.AOP.2017.01.015.

```
Ramírez, C., E-mail: carlos@ciencias.unam.mx, and Medina-Amayo, L.A. Wed .
"Scattering matrix of arbitrary tight-binding Hamiltonians". United States.
doi:10.1016/J.AOP.2017.01.015.
```

```
@article{osti_22617485,
```

title = {Scattering matrix of arbitrary tight-binding Hamiltonians},

author = {Ramírez, C., E-mail: carlos@ciencias.unam.mx and Medina-Amayo, L.A.},

abstractNote = {A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kinds of fundamental structures is given, which can be used to obtain the SM of bigger systems iteratively. Also, a procedure to obtain the SM of layer-composed periodic leads is described. This method allows renormalization approaches, which permits computations over macroscopic length systems without introducing additional approximations. Finally, the transmission coefficient of a ring-shaped multiterminal system and the transmission function of a square-lattice nanoribbon with a reduced width region are calculated.},

doi = {10.1016/J.AOP.2017.01.015},

journal = {Annals of Physics},

number = ,

volume = 378,

place = {United States},

year = {Wed Mar 15 00:00:00 EDT 2017},

month = {Wed Mar 15 00:00:00 EDT 2017}

}

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