I. V. Fialkovsky

Finite temperature Casimir effect for graphene

We adopt the Dirac model for quasiparticles in graphene and calculate the finite temperature Casimir interaction between a suspended graphene layer and a parallel conducting surface. We find that at high temperature the Casimir interaction in such system is just one half of that for two ideal conductors separated by the same distance. In this limit single graphene layer behaves exactly as a Drude metal. In particular, the contribution of the TE mode is suppressed, while one of the TM mode saturates the ideal metal value. Behaviour of the Casimir interaction for intermediate temperatures and separations accessible for an experiment is studied in some detail. We also find an interesting interplay between two fundamental constants of graphene physics: the fine structure constant and the Fermi velocity.

Casimir interaction between a perfect conductor and graphene described by the Dirac model

We adopt the Dirac model for graphene and calculate the Casimir interaction energy between a plane suspended graphene sample and a parallel plane perfect conductor. This is done in two ways. First, we use the quantum-field-theory approach and evaluate the leading-order diagram in a theory with

Parity-odd effects and polarization rotation in graphene

2+1

Exponentially Localized Solutions to the Klein–Gordon Equation

-dimensional fermions interacting with

Renormalizable mean field calculation in QED with fermion background

3+1

Graphene through the looking glass of QFT

-dimensional photons. Next, we consider an effective theory for the electromagnetic field with matching conditions induced by quantum quasiparticles in graphene. The first approach turns out to be the leading order in the coupling constant of the second one. The Casimir interaction for this system appears to be rather weak. It exhibits a strong dependence on the mass of the quasiparticles in graphene.

SUSPENDED GRAPHENE FILMS AND THEIR CASIMIR INTERACTION WITH IDEAL CONDUCTOR

We show that the presence of parity-odd terms in the conductivity (i.e. in the polarization tensor of Dirac quasiparticles in graphene) leads to the rotation of polarization of the electromagnetic waves passing through suspended samples of graphene. Parity-odd Chern–Simons-type contributions appear in external magnetic fields, giving rise to a quantum Faraday effect (though other sources of parity-odd effects may also be discussed). The estimated order of the effect is well above the sensitivity limits of modern optical instruments.

Casimir-type effects for scalar fields interacting with material slabs

Exponentially localized solutions of the Klein–Gordon equation for two and three space variables are presented. The solutions depend on four free parameters. For some relations between the parameters, the solutions describe wave packets filled with oscillations whose amplitudes decrease in the Gaussian way with distance from a point running with group velocity along a ray. The solutions are constructed by using exact complex solutions of the eikonal equation and may be regarded as ray solutions with amplitudes involving one term. It is also shown that the multidimensional nonlinear Klein–Gordon equation can be reduced to an ordinary differential equation with respect to the complex eikonal. Bibliography: 12 titles.

Resonance Interaction of Bending and Shear Modes in a Nonuniform Timoshenko Beam

We study quantum electrodynamics coupled to the matter field on a singular background, which we call defect. For defect on an infinite plane we calculated the mean electromagnetic field. Quantum corrections determining the field near the plane are calculated in the leading order of perturbation theory. We analyse the normalization conditions for the parameters of the defect and calculate the photoelectric function of the charged particle from the defect.

CASIMIR ENERGY OF FINITE WIDTH MIRRORS: RENORMALIZATION, SELF-INTERACTION LIMIT AND LIFSHITZ FORMULA

This paper is aimed to review and promote the main applications of the methods of Quantum Field Theory to description of quantum effects in graphene. We formulate the effective electromagnetic action following from the Dirac model for the quasiparticles in graphene and apply it for derivation of different observable effects like the induced mean charge, quantized conductivity, Faraday effect, and Casimir interaction involving graphene samples.