# Supersymmetric analysis of the Dirac-Weyl operator within PT symmetry

## Abstract

Two-dimensional effective Hamiltonian for a massless Dirac electron interacting with a hyperbolic magnetic field is discussed within PT symmetry. Factorization method and polynomial procedures are used to solve Dirac equation for the constant Fermi velocity and the effective potential which is complex Scarf II potential. The more general effective Scarf II potential models are also obtained within pseudo-supersymmetry. Finally, an extension of Panella and Roy's work [Phys. Lett. A 376, 2580–2583 (2012)] to the both PT symmetric and real Scarf II partner potentials is given using the position dependent Fermi velocity.

- Authors:

- Department of Physics, Faculty of Science, Gazi University, 06500 Ankara (Turkey)

- Publication Date:

- OSTI Identifier:
- 22306082

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIRAC EQUATION; ELECTRONS; HAMILTONIANS; MAGNETIC FIELDS; POLYNOMIALS; POTENTIALS; SUPERSYMMETRY; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Yeşiltaş, Özlem, E-mail: yesiltas@gazi.edu.tr.
```*Supersymmetric analysis of the Dirac-Weyl operator within PT symmetry*. United States: N. p., 2014.
Web. doi:10.1063/1.4891925.

```
Yeşiltaş, Özlem, E-mail: yesiltas@gazi.edu.tr.
```*Supersymmetric analysis of the Dirac-Weyl operator within PT symmetry*. United States. doi:10.1063/1.4891925.

```
Yeşiltaş, Özlem, E-mail: yesiltas@gazi.edu.tr. Fri .
"Supersymmetric analysis of the Dirac-Weyl operator within PT symmetry". United States.
doi:10.1063/1.4891925.
```

```
@article{osti_22306082,
```

title = {Supersymmetric analysis of the Dirac-Weyl operator within PT symmetry},

author = {Yeşiltaş, Özlem, E-mail: yesiltas@gazi.edu.tr},

abstractNote = {Two-dimensional effective Hamiltonian for a massless Dirac electron interacting with a hyperbolic magnetic field is discussed within PT symmetry. Factorization method and polynomial procedures are used to solve Dirac equation for the constant Fermi velocity and the effective potential which is complex Scarf II potential. The more general effective Scarf II potential models are also obtained within pseudo-supersymmetry. Finally, an extension of Panella and Roy's work [Phys. Lett. A 376, 2580–2583 (2012)] to the both PT symmetric and real Scarf II partner potentials is given using the position dependent Fermi velocity.},

doi = {10.1063/1.4891925},

journal = {Journal of Mathematical Physics},

number = 8,

volume = 55,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}

DOI: 10.1063/1.4891925

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