Wave packet dynamics in a monolayer graphene

Abstract

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 ${\vec{p}}_0=\hslash \overrightarrow{k_0}$. 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 $a=k_{0}d$ ($d$ 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 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.

7 pages, 8 figures, to be published in Phys. Rev. B

References in corpus (12)

• The electronic properties of graphene
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Zitterbewegung of electronic wave packets in semiconductor nanostructures
• Unified description of the Zitterbewegung for spintronic, graphene and superconducting systems
• Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes
• Photon-assisted electron transport in graphene
• Oscillatory multiband dynamics of free particles: The ubiquity of zitterbewegung effects
• Wave packet dynamics in 2DEG with spin orbit coupling: splitting and zitterbewegung
• Cyclotron motion and magnetic focusing in semiconductor quantum wells with spin-orbit coupling
• Zitterbewegung of nearly-free and tightly bound electrons in solids
• Visualizing the kinematics of relativistic wave packets