The dynamics of charge particles described by Gaussian wave packet in monolayer graphene is studied analytically and numerically. We demonstrate that the shape of wave packet at arbitrary time depends on correlation between the initial electron amplitudes $\psi_1(\vec r,0)$ and $\psi_2(\vec r,0)$ on the sublattices $A$ and $B$ correspondingly (i.e. pseudospin polarization). For the transverse pseudospin polarization the motion of the center of wave packet occurs in the direction perpendicular to the average momentum $ {\vec p_0}=\hbar \vec{k_0}$. Moreover, in this case the initial wave packet splits into two parts moving with opposite velocities along $ {\vec p_0}$. If the initial direction of pseudospin coincides with average momentum the splitting is absent and the center of wave packet is displaced at $t>0$ along the same direction. The results of our calculations show that all types of motion experience {\it zitterbewegung}. Besides, depending on initial polarization the velocity of the packet center may have the constant component $v_c=uf(a)$, where $u\approx 10^8 cm/s$ is the Fermi velocity and $f(a)$ is a function of the parameter $a=k_0d$ ($d$ is the initial width of wave packet). As a result, the direction of the packet motion is determined not only by the orientation of the average momentum, but mainly by the phase difference between the up- and low- components of the wave functions. Similar peculiarities of the dynamics of 2D electron wave packet connected with initial spin polarization should take place in the semiconductor quantum well under the influence of the Rashba spin-orbit coupling.Comment: 7 pages, 8 figures, to be published in Phys. Rev.

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Graphene-based superlattice (SL) formed by a periodic gap modulation is studied theoretically using a Dirac-type Hamiltonian. Analyzing the dispersion relation we have found that new Dirac points arise in the electronic spectrum under certain conditions. As a result, the gap between conduction and valence minibands disappears. The expressions for the positions of these Dirac points in k-space and threshold value of the potential for their emergence were obtained. Also, the dispersion law and renormalized group velocities around the new Dirac points were calculated. At some parameters of the system, we have revealed interface states which form the top of the valence miniband.

PACS. 74.60.Ec -Mixed state, critical fields, and surface sheath.Abstract. -The field-dependent critical current Ic(H) and current-voltage characteristics are found within a generalized critical-state model that accounts for both surface barrier and bulk pinning as major irreversibility mechanisms in type-II superconductors. Calculations are made for an exactly solvable case of a thin-film superconductor taking into account the GinzburgLandau nonlinearity of the order-parameter equation. The shape of the current-voltage characteristics of the film is determined for arbitrary magnetic field. The nonmonotonous field dependence of the differential film resistivity is discovered, which is characterized by a negative magnetoresistance in a low-field region and by the Bardeen-Stephen-like behaviour in a high-field region.Introduction. -The edge/surface barrier effect on transport properties of type-two superconductors is at present under extensive investigation. The essential barrier influence on superconductor resistivity, that arises due to thermoactivative barrier overcoming, was recently demonstrated in [1, 2] on Bi-based single crystals with high demagnetization factor. The importance of surface barrier (SB) for a wide range of materials (including low-T c superconductors [3]) in affecting the transport as well as the magnetic properties of superconductors is at present widely recognized. The interplay between the barrier and bulk pinning being responsible for the emergence of the nontrivial magnetic flux structures in an external magnetic field [4,5] or in a transport-current-carry state [6,7] to a great extent determines both magnetic and resistive characteristics of low-dimensional superconductors.Some progress in describing magnetization features of superconducting samples with a reduced dimensionality (thin-film or single-crystalline sample with high demagnetization) is due to a highly developed technique employed to solve the corresponding integral equations [4,6]. However, the essentially long-range intervortex repulsion complicates significantly the theoretical investigation of the transport properties of superconductors with a high demagnetization factor. Therefore it is highly desirable to formulate an exactly solvable model of the critical/resistive state in thin-film superconductors, which accounts for major irreversibility mechanisms (edge barrier and bulk pinning).In the present letter we provide first a self-consistent consideration of the combined influence of the edge barrier and bulk pinning on the field dependence of the critical current, the