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Spectral properties of a Dirac operator arising in models of graphene

Presented by: 
DM Elton Lancaster University
Tuesday 31st July 2012 - 11:45 to 12:30
INI Seminar Room 1
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.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons