Harper-Hofstadter problem for 2D electron gas with k{\bf k}-linear Rashba spin-orbit coupling

The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum, spinor wave functions as well as the spin density and average spin polarization are calculated for actual parameters of semiconductor structure. Our calculations show that in two-dimensional electron gas subject to periodic potential and uniform magnetic field the effects of energy spectrum splitting caused by large spin-orbit Rashba coupling can be observed experimentally.Comment: 8 pages, 6 figures. submitted to Europhys. Letter

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 $\psi_1(\vec r,0)$ 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.

Periodic Structures with Rashba Interaction in Magnetic Field

We analyze the behaviour of a system of particles living on a periodic crystal in the presence of a magnetic field B. This can be done by involving a periodic potential U(x) and the Rashba interaction of coupling constant k_{so}. By resorting the corresponding spectrum, we explicitly determine the band structures and the Bloch spinors. These allow us to discuss the system symmetries in terms of the polarizations where they are shown to be broken. The dynamical spin will be studied by calculating different quantities. In the limits: k_{so} and U(x)=0, we analyze again the system by deriving different results. Considering the strong $B$ case, we obtain an interesting result that is the conservation of the polarizations. Analyzing the critical point \lambda_{k,\sigma}=\pm\sq{1\over 2}, we show that the Hilbert space associated to the spectrum in z-direction has a zero mode energy similar to that of massless Dirac fermions in graphene. Finally, we give the resulting energy spectrum when B=0 and U(x) is arbitrary.Comment: 24 pages, references added, misprints corrected. Version to appear in JP

Symmetry of Quantum Phase Space in a Degenerate Hamiltonian System

Using Husimi function approach, we study the ``quantum phase space'' of a harmonic oscillator interacting with a plane monochromatic wave. We show that in the regime of weak chaos, the quantum system has the same symmetry as the classical system. Analytical results agree with the results of numerical calculations.Comment: 11 pages LaTex, including 2 Postscript figure

Wave packet dynamics in hole Luttinger systems

For hole systems with an effective spin 3/2 we analyzed analytically and numerically the evolution of wave packets with the different initial polarizations. The dynamics of such systems is determined by the $4\times 4$ Luttinger Hamiltonian. We work in the space of arbitrary superposition of light- and heavy-hole states of the "one-particle system". For 2D packets we obtained the analytical solution for the components of wave function and analyzed the space-time dependence of probability densities as well as angular momentum densities. Depending on the value of the parameter $a=k_0d$ ($k_0$ is the average momentum vector and $d$ is the packet width) two scenarios of evolution are realized. For $a>>1$ the initial wave packet splits into two parts and the coordinates of packet center experience the transient oscillations or {\it Zitterbewegung} (ZB) as for other two-band systems. In the case when $a0$ remains almost cylindrically symmetric and the ripples arise at the circumference of wave packet. The ZB in this case is absent. We evaluated and visualized for different values of parameter $a$ the space-time dependence of angular momentum densities, which have the multipole structure. It was shown that the average momentum components can precess in the absence of external or effective magnetic fields due to the interference of the light- and heavy hole states. For localized initial states this precession has a transient character.Comment: 9 pages, 8 gigur