54 research outputs found
Resonance Effects in the Nonadiabatic Nonlinear Quantum Dimer
The quantum nonlinear dimer consisting of an electron shuttling between the
two sites and in weak interaction with vibrations, is studied numerically under
the application of a DC electric field. A field-induced resonance phenomenon
between the vibrations and the electronic oscillations is found to influence
the electronic transport greatly. For initially delocalization of the electron,
the resonance has the effect of a dramatic increase in the transport. Nonlinear
frequency mixing is identified as the main mechanism that influences transport.
A characterization of the frequency spectrum is also presented.Comment: 7 pages, 6 figure
Zener transitions between dissipative Bloch bands. II: Current Response at Finite Temperature
We extend, to include the effects of finite temperature, our earlier study of
the interband dynamics of electrons with Markoffian dephasing under the
influence of uniform static electric fields. We use a simple two-band
tight-binding model and study the electric current response as a function of
field strength and the model parameters. In addition to the Esaki-Tsu peak,
near where the Bloch frequency equals the damping rate, we find current peaks
near the Zener resonances, at equally spaced values of the inverse electric
field. These become more prominenent and numerous with increasing bandwidth (in
units of the temperature, with other parameters fixed). As expected, they
broaden with increasing damping (dephasing).Comment: 5 pages, LateX, plus 5 postscript figure
Extended States in a One-dimensional Generalized Dimer Model
The transmission coefficient for a one dimensional system is given in terms
of Chebyshev polynomials using the tight-binding model. This result is applied
to a system composed of two impurities located between sites of a host
lattice. It is found that the system has extended states for several values of
the energy. Analytical expressions are given for the impurity site energy in
terms of the electron's energy. The number of resonant states grows like the
number of host sites between the impurities. This property makes the system
interesting since it is a simple task to design a configuration with resonant
energy very close to the Fermi level .Comment: 4 pages, 3 figure
Scaling Properties of 1D Anderson Model with Correlated Diagonal Disorder
Statistical and scaling properties of the Lyapunov exponent for a
tight-binding model with the diagonal disorder described by a dichotomic
process are considered near the band edge. The effect of correlations on
scaling properties is discussed. It is shown that correlations lead to an
additional parameter governing the validity of single parameter scaling.Comment: 5 pages, 3 figures, RevTe
Holstein polarons in a strong electric field: delocalized and stretched states
The coherent dynamics of a Holstein polaron in strong electric fields is
considered under different regimes. Using analytical and numerical analysis, we
show that even for small hopping constant and weak electron-phonon interaction,
the original discrete Wannier-Stark (WS) ladder electronic states are each
replaced by a semi-continuous band if a resonance condition is satisfied
between the phonon frequency and the ladder spacing. In this regime, the
original localized WS states can become {\em delocalized}, yielding both
`tunneling' and `stretched' polarons. The transport properties of such a system
would exhibit a modulation of the phonon replicas in typical tunneling
experiments. The modulation will reflect the complex spectra with
nearly-fractal structure of the semi-continuous band. In the off-resonance
regime, the WS ladder is strongly deformed, although the states are still
localized to a degree which depends on the detuning: Both the spacing between
the levels in the deformed ladder and the localization length of the resulting
eigenfunctions can be adjusted by the applied electric field. We also discuss
the regime beyond small hopping constant and weak coupling, and find an
interesting mapping to that limit via the Lang-Firsov transformation, which
allows one to extend the region of validity of the analysis.Comment: 10 pages, 13 figures, submitted to PR
ac-Field-Controlled Anderson Localization in Disordered Semiconductor Superlattices
An ac field, tuned exactly to resonance with the Stark ladder in an ideal
tight binding lattice under strong dc bias, counteracts Wannier-Stark
localization and leads to the emergence of extended Floquet states. If there is
random disorder, these states localize. The localization lengths depend
non-monotonically on the ac field amplitude and become essentially zero at
certain parameters. This effect is of possible relevance for characterizing the
quality of superlattice samples, and for performing experiments on Anderson
localization in systems with well-defined disorder.Comment: 10 pages, Latex; figures available on request from [email protected]
Self-induced and induced transparencies of two-dimensional and three- dimensional superlattices
The phenomenon of transparency in two-dimensional and three-dimensional
superlattices is analyzed on the basis of the Boltzmann equation with a
collision term encompassing three distinct scattering mechanisms (elastic,
inelastic and electron-electron) in terms of three corresponding distinct
relaxation times. On this basis, we show that electron heating in the plane
perpendicular to the current direction drastically changes the conditions for
the occurrence of self-induced transparency in the superlattice. In particular,
it leads to an additional modulation of the current amplitudes excited by an
applied biharmonic electric field with harmonic components polarized in
orthogonal directions. Furthermore, we show that self-induced transparency and
dynamic localization are different phenomena with different physical origins,
displaced in time from each other, and, in general, they arise at different
electric fields.Comment: to appear in Physical Review
Upper bounds on wavepacket spreading for random Jacobi matrices
A method is presented for proving upper bounds on the moments of the position
operator when the dynamics of quantum wavepackets is governed by a random
(possibly correlated) Jacobi matrix. As an application, one obtains sharp upper
bounds on the diffusion exponents for random polymer models, coinciding with
the lower bounds obtained in a prior work. The second application is an
elementary argument (not using multiscale analysis or the Aizenman-Molchanov
method) showing that under the condition of uniformly positive Lyapunov
exponents, the moments of the position operator grow at most logarithmically in
time.Comment: final version, to appear in CM
Localization of interacting electrons in quantum dot arrays driven by an ac-field
We investigate the dynamics of two interacting electrons moving in a
one-dimensional array of quantum dots under the influence of an ac-field. We
show that the system exhibits two distinct regimes of behavior, depending on
the ratio of the strength of the driving field to the inter-electron Coulomb
repulsion. When the ac-field dominates, an effect termed coherent destruction
of tunneling occurs at certain frequencies, in which transport along the array
is suppressed. In the other, weak-driving, regime we find the surprising result
that the two electrons can bind into a single composite particle -- despite the
strong Coulomb repulsion between them -- which can then be controlled by the
ac-field in an analogous way. We show how calculation of the Floquet
quasienergies of the system explains these results, and thus how ac-fields can
be used to control the localization of interacting electron systems.Comment: 7 pages, 6 eps figures V2. Minor changes, this version to be
published in Phys. Rev.
Hidden dimers and the matrix maps: Fibonacci chains re-visited
The existence of cycles of the matrix maps in Fibonacci class of lattices is
well established. We show that such cycles are intimately connected with the
presence of interesting positional correlations among the constituent `atoms'
in a one dimensional quasiperiodic lattice. We particularly address the
transfer model of the classic golden mean Fibonacci chain where a six cycle of
the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys.
Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far
been provided, to the best of our knowledge. In addition, we show that our
prescription leads to a determination of other energy values for a mixed model
of the Fibonacci chain, for which the full matrix map may have similar cyclic
behaviour. Apart from the standard transfer-model of a golden mean Fibonacci
chain, we address a variant of it and the silver mean lattice, where the
existence of four cycles of the matrix map is already known to exist. The
underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review
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