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Rusin T.M.,Orange Customer Service Sp. Z O.o. | Zawadzki W.,Polish Academy of Sciences
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

Electrons in monolayer graphene in the presence of an electromagnetic (or electric) wave are considered theoretically. It is shown that the electron motion is a nonlinear combination of Zitterbewegung (ZB, trembling motion) resulting from the periodic potential of graphene lattice and the driving field of the wave. This complex motion is called "multimode Zitterbewegung." The theory is based on the time-dependent two-band Hamiltonian taking into account the graphene band structure and interaction with the wave. Our theoretical treatment includes the rotating-wave approximation and high-driving-frequency approximation for narrow wave packets, as well as numerical calculations for packets of arbitrary widths. Different regimes of electron motion are found, depending on relation between the ZB frequency ωZ and the driving frequency ωD for different strengths of the electron-wave interaction. Frequencies and intensities of the resulting oscillation modes are calculated. The nonlinearity of the problem results in a pronounced multimode behavior. Polarization of the medium is also calculated relating our theoretical results to observable quantities. The presence of driving wave, resulting in frequencies directly related to ωZ and increasing the decay time of oscillations, should facilitate observations of the Zitterbewegung phenomenon. © 2013 American Physical Society.

Rusin T.M.,Orange Customer Service Sp. Z O.o.
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2016

A single-step Eriksen transformation of 1S1/2,2P1/2, and 2P3/2 states of the relativistic hydrogenlike atom is performed exactly by expressing each transformed function (TF) as a linear combination of eigenstates of the Dirac Hamiltonian. The TFs, which are four-component spinors with vanishing two lower components, are calculated numerically and have the same symmetries as the initial states. For all nuclear charges Z [1...92] a contribution of the initial state to TFs exceeds 86% of the total probability density. Next a large contribution to TFs comes from continuum states with negative energies close to -m0c2-Eb, where Eb is the binding energy of the initial state. The contribution of other states to TFs is less than 0.1% of the total probability density. Other components of TFs are nearly 0, which confirms both the validity of the Eriksen transformation and the accuracy of the numerical calculations. The TFs of the 1S1/2 and 2P1/2 states are close to the 1s and 2p states of the nonrelativistic hydrogenlike atom, respectively, but the TF of the 2P3/2 state differs qualitatively from the 2p state. Functions calculated with the use of a linearized Eriksen transformation, being equivalent to the second-order Foldy-Wouthuysen transformation, are compared with corresponding functions obtained by Eriksen transformation. Very good agreement between the two results is obtained. © 2016 American Physical Society.

Rusin T.M.,Orange Customer Service Sp. Z O.o. | Zawadzki W.,Polish Academy of Sciences
Journal of Physics A: Mathematical and Theoretical | Year: 2011

Closed expressions for Green's functions of the stationary two-dimensional two-component Schrödinger equation for an electron moving in monolayer and bilayer graphene, in the presence of a magnetic field, are obtained in terms of the Whittaker functions. © 2011 IOP Publishing Ltd.

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