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

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 figur

Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds

We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces $S^3/{\mathbb Z}_p$. High and low temperature expansions are explicitly computed and the behavior of thermodynamic quantities under thermal duality is scrutinized. The analysis of the entropy of the different lens spaces in the high-temperature limit points out the appearance of a topological nonextensive entropy, besides the standard Stefan-Boltzmann extensive term. The remaining terms are exponentially suppressed by the temperature. The topological entropy appears as a subleading correction to the free energy that can be obtained from the determinant of the lens space conformal Laplacian operator. In the low-temperature limit the leading term in the free energy is the Casimir energy and there is no trace of any power correction in any lens space. In fact, the remaining corrections are always exponentially suppressed by the inverse of the temperature. The duality between the results of both expansions is further analyzed in the paper.Comment: 21 pages, 2 figure