Vladimir Cvetković Zlatko Tešanović APS Meeting 2008 New Orleans, LA, March 11th, 2007 Rough edges in graphene Andres ConchaValentin Stanev Department.

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Presentation transcript:

Vladimir Cvetković Zlatko Tešanović APS Meeting 2008 New Orleans, LA, March 11th, 2007 Rough edges in graphene Andres ConchaValentin Stanev Department of Physics and Astronomy Johns Hopkins University arxiv.org/

Graphene basics Single layer graphene sheets Desirable for electronics Hexagonal lattice Massless Dirac particles A. Geim, et al.

Edge roughness Electrons as particlesElectrons are waves! Transverse channel mixing Dirac particles: not separable! Schroedinger particles: separable

``Softening’’ the rough edge Finite mass buffer layer:for Good news! The perturbation is quasi-separable. Bad news! Mass M and the buffer thickness α 0 unknown.

Elimination of the fitting parameters First order perturbative corrections due to a straight edge Without a buffer layer There are no fitting parameters!

Second order perturbative corrections The self-energy Ansatz The conductivity due to the rough edge scattering

The predicted conductivity due to rough edges Dirac (graphene) stripSchroedinger strip

Conclusions Edge scattering crucial (quantum effect) for narrow strips Dirac particles more sensitive to rough edges (as compared to Schroedinger) Buffer layer circumvents the separability problem The conductivity reveals Van Hove singularities and a peculiar power law asymptotics Mathiessen rule violated Localization length to be determined