Scattering problems and boundary conditions for 2D electron gas and graphene

Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's function technique. In particular, the reflection wave function contains terms inversely proportional to the distance to the graphene lattice edge. The Dirac equation and the momentum dependence of the wave functions of the quasi-particles near the conical points are also found by the perturbation theory with degeneracy in terms of the Bloch functions taken at the degeneracy points. The developed approach allows to formulated the validity criteria for the Dirac equation in a rather simple way.Comment: 7 pages, 2 figure

Enhancement of magnetic ordering by the stress fields of grain boundaries in ferromagnets

In the paper we predict a distinctive change of magnetic properties and considerable increase of the Curie temperature caused by the strain fields of grain boundaries in ferromagnetic films. It is shown that a sheet of spontaneous magnetization may arise along a grain boundary at temperatures greater than the bulk Curie temperature. The temperature dependence and space distribution of magnetization in a ferromagnetic film with grain boundaries are calculated. We found that $45^\circ$ grain boundaries can produce long-range strain fields that results in the width of the magnetic sheet along the boundary of the order of $0.5 \div 1 \mu m$ at temperatures grater than the bulk Curie temperature by about $10^2$ K.Comment: 5 pages, 3 Figures include

Giant oscillations of the current in a dirty 2D electron system flowing perpendicular to a lateral barrier under magnetic field

The charge transport in a dirty 2-dimensional electron system biased in the presence of a lateral potential barrier under magnetic field is theoretically studied. The quantum tunneling across the barrier provides the quantum interference of the edge states localized on its both sides that results in giant oscillations of the charge current flowing perpendicular to the lateral junction. Our theoretical analysis is in a good agreement with the experimental observations presented in Ref.8. In particular, positions of the conductance maxima coincide with the Landau levels while the conductance itself is essentially suppressed even at the energies at which the resonant tunneling occurs and hence these puzzling observations can be resolved without taking into account the electron-electron interaction.Comment: 6 pages, 4 figure

Giant conductance oscillations in a normal mesoscopic ring induced by an SNS Josephson current

A theoretical explanation of giant conductance oscillations observed in normal mesoscopic rings with superconducting ``mirrors" is proposed. The effect is due to resonant tuning of Andreev levels to the Fermi level, which enhances the transparency of the system to the normal current. The mechanism is demonstrated for a one-dimensional model system.Comment: 10 pages, RevTeX, 3 fig. available upon request, Appl. Phys. Report 94-

Excess Resistance Effect in a Normal Metal Contacting a Superconductor

In relatively pure normal samples contacting a superconductor we consider the excess resistance effect (that is a decrease of the total electrical resistance of the sample after transition of the superconducting part into the normal state) and determine conditions under which the effect arises.Comment: 3 pages, 2 postscript figures all in uuencoded forma

Magnetotransport in the presence of a longitudinal barrier: multiple quantum interference of edge states

Transport in a two-dimensional electron gas subject to an external magnetic field is analyzed in the presence of a \textit{longitudinal barrier.} We show that \textit{quantum interference of the edge states} bound by the longitudinal barrier results in a drastic change of the electron motion: the degenerate discrete Landau levels are transformed into an alternating sequence of energy bands and energy gaps. These features of the electron spectrum should result in a high sensitivity of thermodynamic and transport properties of the 2D electron gas to external fields. In particular, we predict giant oscillations of the ballistic conductance and discuss nonlinear current-voltage characteristics, coherent Bloch oscillations and effects of impuritiesComment: 4 pages, 3 figure