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Bending and flexural phonon scattering: Generalized Dirac equation for an electron moving in curved graphene

2012; Elsevier BV; Volume: 407; Issue: 12 Linguagem: Inglês

10.1016/j.physb.2012.01.129

1873-2135

Richard Kerner, Gerardo G. Naumis, Wilfrido A. Gómez-Arias,

Quantum and Classical Electrodynamics

A generalized Dirac equation is derived in order to describe charge carriers moving in curved graphene, which is the case for temperatures above 10 K due to the presence of flexural phonons, or in bent graphene. Such interaction is taken into account by considering an induced metric, in the same spirit as the general relativity approach for the description of fermionic particle moving in a curved space-time. The resulting equation allows to include in a natural way the presence of other phonon branches as well as an external electromagnetic field. For a monochromatic sinusoidal bending of the graphene, the problem can be recasted as a Mathieu equation with a complex driven parameter, indicating the possibility of a resonance pattern.