3,141 research outputs found
Dissipative Chaos in Semiconductor Superlattices
We consider the motion of ballistic electrons in a miniband of a
semiconductor superlattice (SSL) under the influence of an external,
time-periodic electric field. We use the semi-classical balance-equation
approach which incorporates elastic and inelastic scattering (as dissipation)
and the self-consistent field generated by the electron motion. The coupling of
electrons in the miniband to the self-consistent field produces a cooperative
nonlinear oscillatory mode which, when interacting with the oscillatory
external field and the intrinsic Bloch-type oscillatory mode, can lead to
complicated dynamics, including dissipative chaos. For a range of values of the
dissipation parameters we determine the regions in the amplitude-frequency
plane of the external field in which chaos can occur. Our results suggest that
for terahertz external fields of the amplitudes achieved by present-day free
electron lasers, chaos may be observable in SSLs. We clarify the nature of this
novel nonlinear dynamics in the superlattice-external field system by exploring
analogies to the Dicke model of an ensemble of two-level atoms coupled with a
resonant cavity field and to Josephson junctions.Comment: 33 pages, 8 figure
Wigner-Poisson and nonlocal drift-diffusion model equations for semiconductor superlattices
A Wigner-Poisson kinetic equation describing charge transport in doped
semiconductor superlattices is proposed. Electrons are supposed to occupy the
lowest miniband, exchange of lateral momentum is ignored and the
electron-electron interaction is treated in the Hartree approximation. There
are elastic collisions with impurities and inelastic collisions with phonons,
imperfections, etc. The latter are described by a modified BGK
(Bhatnagar-Gross-Krook) collision model that allows for energy dissipation
while yielding charge continuity. In the hyperbolic limit, nonlocal
drift-diffusion equations are derived systematically from the kinetic
Wigner-Poisson-BGK system by means of the Chapman-Enskog method. The
nonlocality of the original quantum kinetic model equations implies that the
derived drift-diffusion equations contain spatial averages over one or more
superlattice periods. Numerical solutions of the latter equations show
self-sustained oscillations of the current through a voltage biased
superlattice, in agreement with known experiments.Comment: 20 pages, 1 figure, published as M3AS 15, 1253 (2005) with
correction
Direct current generation due to harmonic mixing: From bulk semiconductors to semiconductor superlattices
We discuss an effect of dc current and dc voltage (stopping bias) generation
in a semiconductor superlattice subjected by an ac electric field and its
phase-shifted n-th harmonic. In the low field limit, we find a simple
dependence of dc voltage on a strength, frequency, and relative phase of mixing
harmonics for an arbitrary even value of n.
We show that the generated dc voltage has a maximum when a frequency of ac
field is of the order of a scattering constant of electrons in a superlattice.
This means that for typical semiconductor superlattices at room temperature
operating in the THz frequency domain the effect is really observable.
We also made a comparison of a recent paper describing an effect of a
directed current generation in a semiconductor superlattice subjected by ac
field and its second harmonic (n=2) [K.Seeger, Appl.Phys.Lett. 76(2000)82] with
our earlier findings describing the same effect [K.Alekseev et al., Europhys.
Lett. 47(1999)595; cond-mat/9903092 ].
For the mixing of an ac field and its n-th harmonic with n>=4, we found that
additionally to the phase-shift controlling of the dc current, there is a
frequency control. This frequency controlling of the dc current direction is
absent in the case of n=2. The found effect is that, both the dc current
suppression and the dc current reversals exist for some particular values of ac
field frequency. For typical semiconductor superlattices such an interesting
behavior of the dc current should be observable also in the THz domain.
Finally, we briefly review the history of the problem of the dc current
generation at mixing of harmonics in semiconductors and semiconductor
microstructures.Comment: 9 pages, 1 figure, RevTEX, EPS
Artificial graphene as a tunable Dirac material
Artificial honeycomb lattices offer a tunable platform to study massless
Dirac quasiparticles and their topological and correlated phases. Here we
review recent progress in the design and fabrication of such synthetic
structures focusing on nanopatterning of two-dimensional electron gases in
semiconductors, molecule-by-molecule assembly by scanning probe methods, and
optical trapping of ultracold atoms in crystals of light. We also discuss
photonic crystals with Dirac cone dispersion and topologically protected edge
states. We emphasize how the interplay between single-particle band structure
engineering and cooperative effects leads to spectacular manifestations in
tunneling and optical spectroscopies.Comment: Review article, 14 pages, 5 figures, 112 Reference
Nonequilibrium free energy, H theorem and self-sustained oscillations for Boltzmann-BGK descriptions of semiconductor superlattices
Semiconductor superlattices (SL) may be described by a Boltzmann-Poisson
kinetic equation with a Bhatnagar-Gross-Krook (BGK) collision term which
preserves charge, but not momentum or energy. Under appropriate boundary and
voltage bias conditions, these equations exhibit time-periodic oscillations of
the current caused by repeated nucleation and motion of charge dipole waves.
Despite this clear nonequilibrium behavior, if we `close' the system by
attaching insulated contacts to the superlattice and keeping its voltage bias
to zero volts, we can prove the H theorem, namely that a free energy
of the kinetic equations is a Lyapunov functional (, ). Numerical simulations confirm that the free energy decays to its
equilibrium value for a closed SL, whereas for an `open' SL under appropriate
dc voltage bias and contact conductivity oscillates in time with the
same frequency as the current self-sustained oscillations.Comment: 15 pages, 3 figures, minor revision of latex fil
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