833 research outputs found
Transient Zitterbewegung of charge carriers in graphene and carbon nanotubes
Observable effects due to trembling motion (Zitterbewegung, ZB) of charge
carriers in bilayer graphene, monolayer graphene and carbon nanotubes are
calculated. It is shown that, when the charge carriers are prepared in the form
of gaussian wave packets, the ZB has a transient character with the decay time
of femtoseconds in graphene and picoseconds in nanotubes. Analytical results
for bilayer graphene allow us to investigate phenomena which accompany the
trembling motion. In particular, it is shown that the transient character of ZB
in graphene is due to the fact that wave subpackets related to positive and
negative electron energies move in opposite directions, so their overlap
diminishes with time. This behavior is analogous to that of the wave packets
representing relativistic electrons in a vacuum.Comment: 7 pages, 3 figures, augmented versio
Zitterbewegung of nearly-free and tightly bound electrons in solids
We show theoretically that nonrelativistic nearly-free electrons in solids
should experience a trembling motion
(Zitterbewegung, ZB) in absence of external fields, similarly to relativistic
electrons in vacuum.
The Zitterbewegung is directly related to the influence of periodic potential
on the free electron motion.
The frequency of ZB is , where is the energy
gap. The amplitude of ZB is determined by the strength of periodic potential
and the lattice period and it can be of the order of nanometers. We show that
the amplitude of ZB does not depend much on the width of the wave packet
representing an electron in real space.
An analogue of the Foldy-Wouthuysen transformation, known from relativistic
quantum mechanics, is introduced in order to decouple electron states in
various bands. We demonstrate that, after the bands are decoupled, electrons
should be treated as particles of a finite size.
In contrast to nearly-free electrons we consider a two-band model of tightly
bound electrons.
We show that also in this case the electrons should experience the trembling
motion. It is concluded that the phenomenon of Zitterbewegung of electrons in
crystalline solids is a rule rather than an exception.Comment: 22 pages, 6 figures Published version, minor changes mad
One-dimensional semirelativity for electrons in carbon nanotubes
It is shown that the band structure of single-wall semiconducting carbon
nanotubes (CNT) is analogous to relativistic description of electrons in
vacuum, with the maximum velocity = cm/s replacing the light velocity.
One-dimensional semirelativistic kinematics and dynamics of electrons in CNT is
formulated. Two-band k.p Hamiltonian is employed to demonstrate that electrons
in CNT experience a Zitterbewegung (trembling motion) in absence of external
fields. This Zitterbewegung should be observable much more easily in CNT than
its analogue for free relativistic electrons in vacuum.Comment: 4 pages no figure
Self-consistent equilibrium of a two-dimensional electron system with a reservoir in a quantizing magnetic field: Analytical approach
An analytical approach has been developed to describe grand canonical
equilibrium between a three dimensional (3D) electron system and a two
dimensional (2D) one, an energy of which is determined self-consistently with
an electron concentration. Main attention is paid to a Landau level (LL)
pinning effect. Pinning means a fixation of the LL on a common Fermi level of
the 2D and the 3D systems in a finite range of the magnetic field due to an
electron transfer from the 2D to the 3D system. A condition and a start of LL
pinning has been found for homogeneously broadened LLs. The electronic transfer
from the 3D to the 2D system controls an extremely sharp magnetic dependency of
an energy of the upper filled LL at integer filling of the LLs. This can cause
a significant increase of inhomogeneous broadening of the upper LL that was
observed in recent local probe experiments.Comment: 12 pages, 2 figures, revtex
Conduction electrons localized by charged magneto-acceptors A in GaAs/GaAlAs quantum wells
A variational theory is presented of A and A centers, i.e. of a
negative acceptor ion localizing one and two conduction electrons,
respectively, in a GaAs/GaAlAs quantum well in the presence of a magnetic field
parallel to the growth direction. A combined effect of the well and magnetic
field confines conduction electrons to the proximity of the ion, resulting in
discrete repulsive energies above the corresponding Landau levels. The theory
is motivated by our experimental magneto-transport results which indicate that,
in a heterostructure doped in the GaAs well with Be acceptors, one observes a
boil-off effect in which the conduction electrons in the crossed-field
configuration are pushed by the Hall electric field from the delocalized Landau
states to the localized acceptor states and cease to conduct. A detailed
analysis of the transport data shows that, at high magnetic fields, there are
almost no conducting electrons left in the sample. It is concluded that one
negative acceptor ion localizes up to four conduction electrons.Comment: 8 pages, 5 figure
Temperature dependence of the electron spin g factor in GaAs
The temperature dependence of the electron spin factor in GaAs is
investigated experimentally and theoretically. Experimentally, the factor
was measured using time-resolved Faraday rotation due to Larmor precession of
electron spins in the temperature range between 4.5 K and 190 K. The experiment
shows an almost linear increase of the value with the temperature. This
result is in good agreement with other measurements based on photoluminescence
quantum beats and time-resolved Kerr rotation up to room temperature. The
experimental data are described theoretically taking into account a diminishing
fundamental energy gap in GaAs due to lattice thermal dilatation and
nonparabolicity of the conduction band calculated using a five-level kp model.
At higher temperatures electrons populate higher Landau levels and the average
factor is obtained from a summation over many levels. A very good
description of the experimental data is obtained indicating that the observed
increase of the spin factor with the temperature is predominantly due to
band's nonparabolicity.Comment: 6 pages 4 figure
Reservoir model for two-dimensional electron gases in quantizing magnetic fields: a review
We collect and review works which treat two-dimensional electron gases in
quantum wells (mostly GaAs/GaAlAs heterostructures) in the presence of
quantizing magnetic fields as open systems in contact with outside reservoirs.
If a reservoir is sufficiently large, it pins the Fermi level to a certain
energy. As a result, in a varying external magnetic field, the thermodynamic
equilibrium will force oscillations of the electron density in and out of the
quantum well (QW). This leads to a number of physical phenomena in
magneto-transport, interband and intraband magneto-optics, magnetization,
magneto-plasma dispersion, etc. In particular, as first proposed by Baraff and
Tsui, the density oscillations in and out of QW lead to plateaus in the Integer
Quantum Hall Effect (IQHE) at values observed in experiments. The gathered
evidence, especially from magneto-optical investigations, allows us to conclude
that, indeed, in most GaAs/GaAlAs hetrostructures one deals with open systems
in which the electron density in QWs oscillates as the magnetic field varies.
Relation of the density oscillations to other factors, such as electron
localization, and their combined influence on the quantum transport in 2D
electron gases, is discussed. In particular, a validity of the classical
formula for the Hall resistivity {\rho}xy = B/Nec is considered. It is
concluded that the density oscillations are not sufficient to be regarded as
the only source of plateaus in IQHE, although such claims have been sometimes
made in the past and present. Still, our general conclusion is that the
reservoir approach should be included in various descriptions of 2D electron
gases in the present of a magnetic field. An attempt has been made to quote all
the relevant literature on the subject.Comment: 17 pages, 23 figure
Zitterbewegung of electrons in graphene in a magnetic field
Electric current and spacial displacement due to trembling motion
[Zitterbewegung (ZB)] of electrons in graphene in the presence of an external
magnetic field are described. Contributions of both inequivalent points in
the Brillouin zone of graphene are considered. It is shown that, when the
electrons are prepared in the form of wave packets, the presence of a
quantizing magnetic field has very important effects on ZB. (1) For the ZB oscillations are permanent, for B=0 they are transient. (2) For
many ZB frequencies appear, for B=0 only one frequency is at work.
(3) For both interband and intraband (cyclotron) frequencies
contribute to ZB, for B=0 there are no intraband frequencies. (4) Magnetic
field intensity changes not only the ZB frequencies but the entire character of
ZB spectrum. An emission of electromagnetic dipole radiation by the trembling
electrons is proposed and described. It is argued that graphene in a magnetic
field is a promising system for an experimental observation of Zitterbewegung.Comment: 9 pages, 8 figure
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