3,049 research outputs found
Boundary conditions in the Dirac approach to graphene devices
We study a family of local boundary conditions for the Dirac problem
corresponding to the continuum limit of graphene, both for nanoribbons and
nanodots. We show that, among the members of such family, MIT bag boundary
conditions are the ones which are in closest agreement with available
experiments. For nanotubes of arbitrary chirality satisfying these last
boundary conditions, we evaluate the Casimir energy via zeta function
regularization, in such a way that the limit of nanoribbons is clearly
determined.Comment: 10 pages, no figure. Section on Casimir energy adde
Dirac Operator on a disk with global boundary conditions
We compute the functional determinant for a Dirac operator in the presence of
an Abelian gauge field on a bidimensional disk, under global boundary
conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the
connection between our result and the index theorem.Comment: RevTeX, 11 pages. References adde
Zeroes of combinations of Bessel functions and mean charge of graphene nanodots
We establish some properties of the zeroes of sums and differences of
contiguous Bessel functions of the first kind. As a byproduct, we also prove
that the zeroes of the derivatives of Bessel functions of the first kind of
different orders are interlaced the same way as the zeroes of Bessel functions
themselves. As a physical motivation, we consider gated graphene nanodots
subject to Berry-Mondragon boundary conditions. We determine the allowed energy
levels and calculate the mean charge at zero temperature. We discuss in detail
its dependence on the gate (chemical) potential.Comment: vesrion accepted to Theoretical and Mathematical Physics, 18 pages, 1
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