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

Sub-Wavelength Terahertz Spin-Flip Laser Based on a Magnetic Point-Contact Array

We present a novel design for a single-mode, truly sub-wavelength THz disk laser based on a nano-composite gain medium comprising an array of metal/ferromagnetic point contacts embedded in a thin dielectric layer. Stimulated emission of light occurs in the point contacts as a result of spin-flip relaxation of spin-polarized electrons that are injected from the ferromagnetic side of the contacts. Ultra-high electrical current densities in the contacts and a dielectric material with a large refractive index, neither condition being achievable in conventional semiconductor media, allows the thresholds of lasing to be overcome for the lowest-order modes of the disk, hence making single-mode operation possible.Comment: 9 pages,4 figure

Peierls-type structural phase transition in a crystal induced by magnetic breakdown

We predict a new type of phase transition in a quasi-two dimensional system of electrons at high magnetic fields, namely the stabilization of a density wave which transforms a two dimensional open Fermi surface into a periodic chain of large pockets with small distances between them. The quantum tunneling of electrons between the neighboring closed orbits enveloping these pockets transforms the electron spectrum into a set of extremely narrow energy bands and gaps which decreases the total electron energy, thus leading to a magnetic breakdown induced density wave (MBIDW) ground state. We show that this DW instability has some qualitatively different properties in comparison to analogous DW instabilities of Peierls type. E. g. the critical temperature of the MBIDW phase transition arises and disappears in a peculiar way with a change of the inverse magnetic field

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