1,283 research outputs found
Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
We present a unified theory for wave-packet dynamics of electrons in crystals
subject to perturbations varying slowly in space and time. We derive the
wave-packet energy up to the first order gradient correction and obtain all
kinds of Berry-phase terms for the semiclassical dynamics and the quantization
rule. For electromagnetic perturbations, we recover the orbital magnetization
energy and the anomalous velocity purely within a single-band picture without
invoking inter-band couplings. For deformations in crystals, besides a
deformation potential, we obtain a Berry-phase term in the Lagrangian due to
lattice tracking, which gives rise to new terms in the expressions for the
wave-packet velocity and the semiclassical force. For multiple-valued
displacement fields surrounding dislocations, this term manifests as a Berry
phase, which we show to be proportional to the Burgers vector around each
dislocation.Comment: 12 pages, RevTe
Quantum Hall effect in a p-type heterojunction with a lateral surface quantum dot superlattice
The quantization of Hall conductance in a p-type heterojunction with lateral
surface quantum dot superlattice is investigated. The topological properties of
the four-component hole wavefunction are studied both in r- and k-spaces. New
method of calculation of the Hall conductance in a 2D hole gas described by the
Luttinger Hamiltonian and affected by lateral periodic potential is proposed,
based on the investigation of four-component wavefunction singularities in
k-space. The deviations from the quantization rules for Hofstadter "butterfly"
for electrons are found, and the explanation of this effect is proposed. For
the case of strong periodic potential the mixing of magnetic subbands is taken
into account, and the exchange of the Chern numbers between magnetic subands is
discussed.Comment: 12 pages, 5 figures; reported at the 15th Int. Conf. on High Magnetic
Fields in Semicond. Phys. (Oxford, UK, 2002
Solitons on Noncommutative Torus as Elliptic Calogero Gaudin Models, Branes and Laughlin Wave Functions
For the noncommutative torus , in case of the N.C. parameter
, we construct the basis of Hilbert space {\caH}_n\thetaz_in{\cal A}_nZ_n
\times Z_n\thetagsu(n)transform covariantly by the global gauge
transformation of By acting on we establish the
isomorphism of . We embed this into the -matrix of the
elliptic Gaudin andsu_n({\cal T})D(k, u)spectral curve
describes the brane configuration, with the dynamical
variables of N.C. solitons asT^{\otimes n} / S_nthe N.C. cotangent bundle with marked points. The
eigenfunction of the Gaudin differential -operators as the
Laughli$wavefunction is solved by Bethe ansatz.Comment: 25 pages, plain latex, no figure
Spontaneous DC Current Generation in a Resistively Shunted Semiconductor Superlattice Driven by a TeraHertz Field
We study a resistively shunted semiconductor superlattice subject to a
high-frequency electric field. Using a balance equation approach that
incorporates the influence of the electric circuit, we determine numerically a
range of amplitude and frequency of the ac field for which a dc bias and
current are generated spontaneously and show that this region is likely
accessible to current experiments. Our simulations reveal that the Bloch
frequency corresponding to the spontaneous dc bias is approximately an integer
multiple of the ac field frequency.Comment: 8 pages, Revtex, 3 Postscript figure
Skyrmionic excitons
We investigate the properties of a Skyrmionic exciton consisting of a
negatively charged Skyrmion bound to a mobile valence hole. A variational wave
function is constructed which has the generalized total momentum P as a good
quantum number. It is shown that the Skyrmionic exciton can have a larger
binding energy than an ordinary magnetoexciton and should therefore dominate
the photoluminescence spectrum in high-mobility quantum wells and
heterojunctions where the electron-hole separation exceeds a critical value.
The dispersion relation for the Skyrmionic exciton is discussed.Comment: 9 pages, RevTex, 2 PostScript figures. Replaced with version to
appear in Phys. Rev. B Rapid Communications. Short discussion of variational
state adde
Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
We have derived a new set of semiclassical equations for electrons in
magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are
found to be modified by the Berry phase and magnetization. This semiclassical
approach is used to study general electron transport in a DC or AC electric
field. We also find a close connection between the cyclotron orbits in magnetic
Bloch bands and the energy subbands in the Hofstadter spectrum. Based on this
formalism, the pattern of band splitting, the distribution of Hall conduct-
ivities, and the positions of energy subbands in the Hofstadter spectrum can be
understood in a simple and unified picture.Comment: 26 pages, Revtex, 6 figures included, submitted to Phys.Rev.
Off-Diagonal Geometric Phases
We investigate the adiabatic evolution of a set of non-degenerate eigenstates
of a parameterized Hamiltonian. Their relative phase change can be related to
geometric measurable quantities that extend the familiar concept of Berry phase
to the evolution of more than one state. We present several physical systems
where these concepts can be applied, including an experiment on microwave
cavities for which off-diagonal phases can be determined from published data.Comment: 5 pages 2 figures - RevTeX. Revised version including geometrical
interpretatio
Light scattering from disordered overlayers of metallic nanoparticles
We develop a theory for light scattering from a disordered layer of metal
nanoparticles resting on a sample. Averaging over different disorder
realizations is done by a coherent potential approximation. The calculational
scheme takes into account effects of retardation, multipole excitations, and
interactions with the sample. We apply the theory to a system similar to the
one studied experimentally by Stuart and Hall [Phys. Rev. Lett. {\bf 80}, 5663
(1998)] who used a layered Si/SiO/Si sample. The calculated results agree
rather well with the experimental ones. In particular we find conspicuous
maxima in the scattering intensity at long wavelengths (much longer than those
corresponding to plasmon resonances in the particles). We show that these
maxima have their origin in interference phenomena in the layered sample.Comment: 19 pages, 12 figure
Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems
We clarify the algebraic structure of continuous and discrete quasi-exactly
solvable spectral problems by embedding them into the framework of the quantum
inverse scattering method. The quasi-exactly solvable hamiltonians in one
dimension are identified with traces of quantum monodromy matrices for specific
integrable systems with non-periodic boundary conditions. Applications to the
Azbel-Hofstadter problem are outlined.Comment: 15 pages, standard LaTe
Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere
We present a framework for the analytic calculations of the hierarchical wave
functions and the composite fermion wave functions in the fractional quantum
Hall effect on the sphere by using projective coordinates. Then we calculate
the overlaps between these two wave functions at various fillings and small
numbers of electrons. We find that the overlaps are all most equal to one. This
gives a further evidence that two theories of the fractional quantum Hall
effect, the hierarchical theory and the composite fermion theory, are
physically equivalent.Comment: 37 pages, revte
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