Planar Heterostructure Graphene -- Narrow-Gap Semiconductor -- Graphene

We investigate a planar heterostructure composed of two graphene films separated by a narrow-gap semiconductor ribbon. We show that there is no the Klein paradox when the Dirac points of the Brillouin zone of graphene are in a band gap of a narrow-gap semiconductor. There is the energy range depending on an angle of incidence, in which the above-barrier damped solution exists. Therefore, this heterostructure is a "filter" transmitting particles in a certain range of angles of incidence upon a potential barrier. We discuss the possibility of an application of this heterostructure as a "switch".Comment: 9 pages, 2 figure

Fermi-liquid and Fermi surface geometry effects in propagation of low frequency electromagnetic waves through thin metal films

In the present work we theoretically analyze the contribution from a transverse Fermi-liquid collective mode to the transmission of electromagnetic waves through a thin film of a clean metal in the presence of a strong external magnetic field. We show that at the appropriate Fermi surface geometry the transverse Fermi-liquid wave may appear in conduction electrons liquid at frequencies $\omega$ significantly smaller than the cyclotron frequency of charge carriers $\Omega$ provided that the mean collision frequency $\tau^{-1}$ is smaller than $\omega.$ Also, we show that in realistic metals size oscillations in the transmission coefficient associated with the Firmi-liquid mode may be observable in experiments. Under certain conditions these oscillations may predominate over the remaining size effects in the transmission coefficient.Comment: 9 pages, 5 figures, text adde

Boundary States in Graphene Heterojunctions

A new type of states in graphene-based planar heterojunctions has been studied in the envelope wave function approximation. The condition for the formation of these states is the intersection between the dispersion curves of graphene and its gap modification. This type of states can also occur in smooth graphene-based heterojunctions.Comment: 5 pages, 3 figure

Fermi-liquid theory of the surface impedance of a metal in a normal magnetic field

In this paper we present detailed theoretical analysis of the frequency and/or magnetic field dependence of the surface impedance of a metal at the anomalous skin effect. We calculate the surface impedance in the presence of a magnetic field directed along the normal to the metal surface. The effects of the Fermi-liquid interactions on the surface impedance are studied. It is shown that the cyclotron resonance in a normal magnetic field may be revealed {\it only and exclusively} in such metals whose Fermi surfaces include segments where its Gaussian curvature turns zero. The results could be applied to extract extra informations concerning local anomalies in the Fermi surface curvature in conventional and quasi-two-dimensional metals.Comment: 10 pages, 1 figure, text added and rearranged, computational details are moved into Appendice

Cooper pairing of electrons and holes in graphene bilayer: Correlation effects

Cooper pairing of spatially separated electrons and holes in graphene bilayer is studied beyond the mean-field approximation. Suppression of the screening at large distances, caused by appearance of the gap, is considered self-consistently. A mutual positive feedback between appearance of the gap and enlargement of the interaction leads to a sharp transition to correlated state with greatly increased gap above some critical value of the coupling strength. At coupling strength below the critical, this correlation effect increases the gap approximately by a factor of two. The maximal coupling strength achievable in experiments is close to the critical value. This indicated importance of correlation effects in closely-spaced graphene bilayers at weak substrate dielectric screening. Another effect beyond mean-field approximation considered is an influence of vertex corrections on the pairing, which is shown to be very weak.Comment: 6 pages, 5 figures; some references were adde