60 research outputs found
Harper-Hofstadter problem for 2D electron gas with -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 and on the
sublattices and 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 . Moreover, in this case the initial wave packet splits
into two parts moving with opposite velocities along . If the
initial direction of pseudospin coincides with average momentum the splitting
is absent and the center of wave packet is displaced at 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 ,
where is the Fermi velocity and is a function of
the parameter ( 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 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
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 ( is
the average momentum vector and is the packet width) two scenarios of
evolution are realized. For 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 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 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
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