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arXiv · 1609.00665

$PT$-symmetric graphene under a magnetic field

Fabio Bagarello·Naomichi Hatano
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Abstract

We propose a $PT$-symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyze the structure of the spectra and the eigenvectors of the Hamiltonians around the $K$ and $K'$ points, both in the $PT$-symmetric and $PT$-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 $PT$-symmetric and $PT$-broken regions.

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Fabio Bagarello, Naomichi Hatano. 2016-09-02. $PT$-symmetric graphene under a magnetic field. https://doi.org/10.1098/rspa.2016.0365

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