PT-symmetric graphene under a magnetic field

Fabio Bagarello, Naomichi Hatano

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We propose a [Formula: see text]-symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyse the structure of the spectra and the eigenvectors of the Hamiltonians around the K and K' points, both in the [Formula: see text]-symmetric and [Formula: see text]-broken regions. In particular, we show that the presence of the deformation parameter V produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which turns out to be different in the [Formula: see text]-symmetric and [Formula: see text]-broken regions.
Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalPROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A
Volume472
Publication statusPublished - 2016

Fingerprint

Graphene
Magnetic Field
Eigenvector
Biorthogonality
Tight-binding
Asymmetry
Breakdown
Completeness
Text
Zero
Energy

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

PT-symmetric graphene under a magnetic field. / Bagarello, Fabio; Hatano, Naomichi.

In: PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A, Vol. 472, 2016, p. 1-17.

Research output: Contribution to journalArticle

@article{dd8901ab79974e64be4816fc6ec71a62,
title = "PT-symmetric graphene under a magnetic field",
abstract = "We propose a [Formula: see text]-symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyse the structure of the spectra and the eigenvectors of the Hamiltonians around the K and K' points, both in the [Formula: see text]-symmetric and [Formula: see text]-broken regions. In particular, we show that the presence of the deformation parameter V produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which turns out to be different in the [Formula: see text]-symmetric and [Formula: see text]-broken regions.",
author = "Fabio Bagarello and Naomichi Hatano",
year = "2016",
language = "English",
volume = "472",
pages = "1--17",
journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",
issn = "0080-4630",
publisher = "The Royal Society",

}

TY - JOUR

T1 - PT-symmetric graphene under a magnetic field

AU - Bagarello, Fabio

AU - Hatano, Naomichi

PY - 2016

Y1 - 2016

N2 - We propose a [Formula: see text]-symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyse the structure of the spectra and the eigenvectors of the Hamiltonians around the K and K' points, both in the [Formula: see text]-symmetric and [Formula: see text]-broken regions. In particular, we show that the presence of the deformation parameter V produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which turns out to be different in the [Formula: see text]-symmetric and [Formula: see text]-broken regions.

AB - We propose a [Formula: see text]-symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyse the structure of the spectra and the eigenvectors of the Hamiltonians around the K and K' points, both in the [Formula: see text]-symmetric and [Formula: see text]-broken regions. In particular, we show that the presence of the deformation parameter V produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which turns out to be different in the [Formula: see text]-symmetric and [Formula: see text]-broken regions.

UR - http://hdl.handle.net/10447/222447

M3 - Article

VL - 472

SP - 1

EP - 17

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

ER -