磁场下的$PT$对称石墨烯
$PT$-symmetric graphene under a magnetic field
摘要：
我们提出了一个在磁场下的石墨烯紧束缚模型的$PT$对称变形版本。我们分析了在$PT$ -对称和$PT$ -断裂区域中的$K$和$K'$点周围的谱和哈密顿量的特征向量的结构。特别是，我们表明，变形参数$V$的存在下产生几个有趣的后果，包括不对称的零能态的哈密顿和故障的特征向量集的完整性。我们还讨论了特征向量的双正交性，这{原来是}不同的$PT$ -对称和$PT$ -破碎的区域。
英文摘要：
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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