188 research outputs found
Strong Attraction between Charged Spheres due to Metastable Ionized States
We report a mechanism which can lead to long range attractions between
like-charged spherical macroions, stemming from the existence of metastable
ionized states. We show that the ground state of a single highly charged
colloid plus a few excess counterions is overcharged. For the case of two
highly charged macroions in their neutralizing divalent counterion solution we
demonstrate that, in the regime of strong Coulomb coupling, the counterion
clouds are very likely to be unevenly distributed, leading to one overcharged
and one undercharged macroion. This long-living metastable configuration in
turn leads to a long range Coulomb attraction.Comment: REVTEX-published versio
Cyclotron resonance of correlated electrons in semiconductor heterostructures
The cyclotron resonance absorption of two-dimensional electrons in
semiconductor heterostructures in high magnetic fields is investigated. It is
assumed that the ionized impurity potential is a dominant scattering mechanism,
and the theory explicitly takes the Coulomb correlation effect into account
through the Wigner phonons. The cyclotron resonance linewidth is in
quantitative agreement with the experiment in the Wigner crystal regime at
T=4.2K. Similar to the cyclotron resonance theory of the charge density waves
pinned by short-range impurities, the present results for the long-range
scattering also show the doubling of the resonance peaks. However, unlike the
case of the charge density waves, our theory gives the pinning mode independent
of the bulk compressibility of the substrate materials.Comment: 6 pages, 5 figure
Harmonic Solid Theory of Photoluminescence in the High Field Two-Dimensional Wigner Crystal
Motivated by recent experiments on radiative recombination of two-dimensional
electrons in acceptor doped GaAs-AlGaAs heterojunctions as well as the success
of a harmonic solid model in describing tunneling between two-dimensional
electron systems, we calculate within the harmonic approximation and the time
dependent perturbation theory the line shape of the photoluminescence spectrum
corresponding to the recombination of an electron with a hole bound to an
acceptor atom. The recombination process is modeled as a sudden perturbation of
the Hamiltonian for the in-plane degrees of freedom of the electron. We include
in the perturbation, in addition to changes in the equilibrium positions of
electrons, changes in the curvatures of the harmonically approximated
potential. The computed spectra have line shapes similar to that seen in a
recent experiment. The spectral width, however, is roughly a factor of 3
smaller than that seen in experiment if one assumes a perfect Wigner crystal
for the initial state state of the system, whereas a simple random disorder
model yields a width a factor of 3 too large. We speculate on the possible
mechanisms that may lead to better quantitative agreement with experiment.Comment: 22 pages, RevTex, 8 figures. Submitted to the Physical Review
Theory of Phonon Shakeup Effects on Photoluminescence from the Wigner Crystal in a Strong Magnetic Field
We develop a method to compute shakeup effects on photoluminescence from a
strong magnetic field induced two-dimensional Wigner crystal. Only localized
holes are considered. Our method treats the lattice electrons and the tunneling
electron on an equal footing, and uses a quantum-mechanical calculation of the
collective modes that does not depend in any way on a harmonic approximation.
We find that shakeup produces a series of sidebands that may be identified with
maxima in the collective mode density of states, and definitively distinguishes
the crystal state from a liquid state in the absence of electron-hole
interaction. In the presence of electron-hole interaction, sidebands also
appear in the liquid state coming from short-range density fluctuations around
the hole. However, the sidebands in the liquid state and the crystal state have
different qualitative behaviors. We also find a shift in the main luminescence
peak, that is associated with lattice relaxation in the vicinity of a vacancy.
The relationship of the shakeup spectrum with previous mean-field calculations
is discussed.Comment: 14 pages, uuencoded postscript file for entire paper, also available
at (click phd14) http://rainbow.uchicago.edu/~ldz/paper/paper.htm
Wigner Crystalization in the Lowest Landau Level for
By means of exact diagonalization we study the low-energy states of seven
electrons in the lowest Landau level which are confined by a cylindric external
potential modelling the rest of a macroscopic system and thus controlling the
filling factor . Wigner crystal is found to be the ground state for
filling factors between and provided electrons
interact via the bare Coulomb potential. Even at the solid state has
lower energy than the Laughlin's one, although the two energies are rather
close. We also discuss the role of pseudopotential parameters in the lowest
Landau level and demonstrate that the earlier reported gapless state, appearing
when the short-range part of the interaction is suppressed, has nothing in
common with the Wigner crystalization in pure Coulomb case.Comment: 9 pages, LaTex, 8 figure
Magneto-shear modes and a.c. dissipation in a two-dimensional Wigner crystal
The a.c. response of an unpinned and finite 2D Wigner crystal to electric
fields at an angular frequency has been calculated in the dissipative
limit, , where is the scattering rate. For
electrons screened by parallel electrodes, in zero magnetic field the
long-wavelength excitations are a diffusive longitudinal transmission line mode
and a diffusive shear mode. A magnetic field couples these modes together to
form two new magneto-shear modes. The dimensionless coupling parameter where and are the
speeds of transverse and longitudinal sound in the collisionless limit and
and are the tensor components of the
magnetoconductivity. For , both the coupled modes contribute
to the response of 2D electrons in a Corbino disk measurement of
magnetoconductivity. For , the electron crystal rotates rigidly in
a magnetic field. In general, both the amplitude and phase of the measured a.c.
currents are changed by the shear modulus. In principle, both the
magnetoconductivity and the shear modulus can be measured simultaneously.Comment: REVTeX, 7 pp., 4 eps figure
Negative electrostatic contribution to the bending rigidity of charged membranes and polyelectrolytes screened by multivalent counterions
Bending rigidity of a charged membrane or a charged polyelectrolyte screened
by monovalent counterions is known to be enhanced by electrostatic effects. We
show that in the case of screening by multivalent counterions the electrostatic
effects reduce the bending rigidity. This inversion of the sign of the
electrostatic contribution is related to the formation of two-dimensional
strongly correlated liquids (SCL) of counterions at the charged surface due to
strong lateral repulsion between them. When a membrane or a polyelectrolyte is
bent, SCL is compressed on one side and stretched on the other so that
thermodynamic properties of SCL contribute to the bending rigidity.
Thermodynamic properties of SCL are similar to those of Wigner crystal and are
anomalous in the sense that the pressure, compressibility and screening radius
of SCL are negative. This brings about substantial negative correction to the
bending rigidity. For the case of DNA this effect qualitatively agrees with
experiment.Comment: 8 pages, 2 figure
Coupled phonon-ripplon modes in a single wire of electrons on the liquid-helium surface
The coupled phonon-ripplon modes of the quasi-one-dimensional electron chain
on the liquid helium sutface are studied. It is shown that the electron-ripplon
coupling leads to the splitting of the collective modes of the wire with the
appearance of low-frequency modes and high-frequency optical modes starting
from threshold frequencies. The effective masses of an electron plus the
associated dimple for low frequency modes are estimated and the values of the
threshold frequencies are calculated. The results obtained can be used in
experimental attempts to observe the phase transition of the electron wire into
a quasi-ordered phase.Comment: 5 pages, 1 figure, Physical Review (in press
Cyclotron resonance lineshape in a Wigner crystal
The cyclotron resonance absorption spectrum in a Wigner crystal is
calculated. Effects of spin-splitting are modelled by substitutional disorder,
and calculated in the coherent potential approximation. Due to the increasing
strength of the dipole-dipole interaction, the results show a crossover from a
double-peak spectrum at small filling factors to a single-peak spectrum at
filling factors \agt 1/6. Radiation damping and magnetophonon scattering can
also influence the cyclotron resonance. The results are in very good agreement
with experiments.Comment: 4 pages REVTEX, attempt to append 3 figures that seem to have been
lost last tim
Dynamical response of a pinned two-dimensional Wigner crystal
We re-examine a long-standing problem of a finite-frequency conductivity of a
weakly pinned two-dimensional classical Wigner crystal. In this system an
inhomogeneously broadened absorption line (pinning mode) centered at disorder
and magnetic field dependent frequency is known to appear. We show
that the relative linewidth of the pinning mode is
of the order of one in weak magnetic fields, exhibits a power-law decrease in
intermediate fields, and eventually saturates at a small value in strong
magnetic fields. The linewidth narrowing is due to a peculiar mechanism of
mixing between the stiffer longitudinal and the softer transverse components of
the collective excitations. The width of the high-field resonance proves to be
related to the density of states in the low-frequency tail of the zero-field
phonon spectrum. We find a qualitative agreement with recent experiments and
point out differences from the previous theoretical work on the subject.Comment: 19 pages, 11 figures. Supersedes cond-mat/990424
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