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Spectral properties of a Dirac operator arising in models of graphene

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Spectral Theory of Relativistic Operators

We consider a Dirac operator which arises in modeling conduction within potential channels in graphene. For long uniform channels this reduces to a 1-dimensional linear spectral pencil problem for a Dirac operator with mass and a potential representing the channel cross section; a coupling constant in front of the potential is considered as the spectral parameter. Basic spectral properties are studied, together with the spectral asymptotics for large coupling constants. The latter show a surprisingly subtle dependence on the variation of the potential’s sign and regions on which it is identically zero.

This talk is part of the Isaac Newton Institute Seminar Series series.

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