Wave packet dynamics in a monolayer graphene

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 ${\ensuremath{\psi}}_{1}(\stackrel{P\vec}{r},0)$ and ${\ensuremath{\psi}}_{2}(\stackrel{P\vec}{r},0)$ 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 ${\stackrel{P\vec}{p}}_{0}=\ensuremath{\hbar}{\stackrel{P\vec}{k}}_{0}$. Moreover, in this case the initial wave packet splits into two parts moving with opposite velocities along ${\stackrel{P\vec}{p}}_{0}$. 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 Zitterbewegung. Besides, depending on initial polarization the velocity of the packet center may have the constant component ${v}_{c}=uf(a)$, where $u\ensuremath{\approx}{10}^{8}\text{ }\text{cm}/\text{s}$ is the Fermi velocity and $f(a)$ is a function of the parameter $a={k}_{0}d$ ($d$ 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 two-dimensional 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.

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