514 research outputs found
Diagrammatic Quantum Monte Carlo for Two-Body Problem: Exciton
We present a novel method for precise numerical solution of the irreducible
two-body problem and apply it to excitons in solids. The approach is based on
the Monte Carlo simulation of the two-body Green function specified by
Feynman's diagrammatic expansion. Our method does not rely on the specific form
of the electron and hole dispersion laws and is valid for any attractive
electron-hole potential. We establish limits of validity of the Wannier (large
radius) and Frenkel (small radius) approximations, present accurate data for
the intermediate radius excitons, and give evidence for the charge transfer
nature of the monopolar exciton in mixed valence materials.Comment: 4 pages, 5 figure
Quantum Dynamics of the Hubbard-Holstein Model in Equilibrium and Non-Equilibrium: Application to Pump-Probe Phenomena
The spectral response and physical features of the 2D Hubbard-Holstein model
are calculated both in equilibrium at zero and low chemical dopings, and after
an ultra short powerful light pulse, in undoped systems. At equilibrium and at
strong charge-lattice couplings, the optical conductivity reveals a 3-peak
structure in agreement with experimental observations. After an ultra short
pulse and at nonzero electron-phonon interaction, phonon and spin subsystems
oscillate with the phonon period fs. The decay time of the
phonon oscillations is about 150-200 fs, similar to the relaxation time of the
charge system. We propose a criterion for observing these oscillations in high
compounds: the time span of the pump light pulse has to be
shorter than the phonon oscillation period .Comment: 4 pages, 4 figure
Mesoscopic Spin-Hall Effect in 2D electron systems with smooth boundaries
Spin-Hall effect in ballistic 2D electron gas with Rashba-type spin-orbit
coupling and smooth edge confinement is studied. We predict that the interplay
of semiclassical electron motion and quantum dynamics of spins leads to several
distinct features in spin density along the edge that originate from
accumulation of turning points from many classical trajectories. Strong peak is
found near a point of the vanishing of electron Fermi velocity in the lower
spin-split subband. It is followed by a strip of negative spin density that
extends until the crossing of the local Fermi energy with the degeneracy point
where the two spin subbands intersect. Beyond this crossing there is a wide
region of a smooth positive spin density. The total amount of spin accumulated
in each of these features exceeds greatly the net spin across the entire edge.
The features become more pronounced for shallower boundary potentials,
controlled by gating in typical experimental setups.Comment: 4 pages, 4 figures, published versio
Small-angle impurity scattering and the spin Hall conductivity in 2D systems
An arbitrarily small concentration of impurities can affect the spin Hall
conductivity in a two-dimensional semiconductor system. We develop a
Boltzmann-like equation that can be used for impurity scattering with arbitrary
angular dependence, and for arbitrary angular dependence of the spin-orbit
field b(k) around the Fermi surface. For a model applicable to a 2D hole system
in GaAs, if the impurity scattering is not isotropic, we find that the spin
Hall conductivity depends on the derivative of b with respect to the energy and
on deviations from a parabolic band structure, as well as on the angular
dependence of the scattering. In principle, the resulting spin Hall
conductivity can be larger or smaller than the ``intrinsic value'', and can
have opposite sign. In the limit of small angle scattering, in a model
appropriate for small hole concentrations, where the band is parabolic and b ~
k^3, the spin Hall conductivity has opposite sign from the intrinsic value, and
has larger magnitude. Our analysis assumes that the spin-orbit splitting
and the transport scattering rate tau^{-1} are both small compared to the Fermi
energy, but the method is valid for for arbitrary value of b*tau.Comment: Errors corrected, references adde
The strong Novikov conjecture for low degree cohomology
We show that for each discrete group G, the rational assembly map
K_*(BG) \otimes Q \to K_*(C*_{max} G) \otimes \Q is injective on classes dual
to the subring generated by cohomology classes of degree at most 2 (identifying
rational K-homology and homology via the Chern character). Our result implies
homotopy invariance of higher signatures associated to these cohomology
classes. This consequence was first established by Connes-Gromov-Moscovici and
Mathai.
Our approach is based on the construction of flat twisting bundles out of
sequences of almost flat bundles as first described in our previous work. In
contrast to the argument of Mathai, our approach is independent of (and indeed
gives a new proof of) the result of Hilsum-Skandalis on the homotopy invariance
of the index of the signature operator twisted with bundles of small curvature.Comment: 11 page
Universality of conductivity in interacting graphene
The Hubbard model on the honeycomb lattice describes charge carriers in
graphene with short range interactions. While the interaction modifies several
physical quantities, like the value of the Fermi velocity or the wave function
renormalization, the a.c. conductivity has a universal value independent of the
microscopic details of the model: there are no interaction corrections,
provided that the interaction is weak enough and that the system is at half
filling. We give a rigorous proof of this fact, based on exact Ward Identities
and on constructive Renormalization Group methods
Decay of a plasmon into neutral modes in a carbon nanotube
We evaluate the rate of energy loss of a plasmon in a disorder-free carbon
nanotube. The plasmon decays into neutral bosonic excitations of the electron
liquid. The process is mediated either by phonon-assisted backscattering of a
single electron, or Umklapp backscattering of two electrons. To lowest order in
the backscattering interactions the partial decay rates are additive. At zero
doping the corresponding decay rates scale as power-laws of the temperature
with positive and negative exponents for the two mechanisms, respectively. The
precise values of the exponents depend on the Luttinger liquid parameter. At
finite doping the decay rates are described by universal crossover functions of
frequency and chemical potential measured in units of temperature. In the
evaluation of the plasmon decay, we concentrate on a finite-length geometry
allowing excitation of plasma resonances.Comment: 10 pages, 4 figure
Optical Conductivity of a Two-Dimensional Electron Liquid with Spin-Orbit Interaction
The interplay of electron-electron interactions and spin-orbit coupling leads
to a new contribution to the homogeneous optical conductivity of the electron
liquid. The latter is known to be insensitive to many-body effects for a
conventional electron system with parabolic dispersion. The parabolic spectrum
has its origin in the Galilean invariance which is broken by spin-orbit
coupling. This opens up a possibility for the optical conductivity to probe
electron-electron interactions. We analyze the interplay of interactions and
spin-orbit coupling and obtain optical conductivity beyond RPA.Comment: 5 pages, 3 figures; final version, fig. 3 added, minor change
Spin current and polarization in impure 2D electron systems with spin-orbit coupling
We derive the transport equations for two-dimensional electron systems with
spin-orbit interaction and short-range spin-independent disorder. In the limit
of slow spatial variations of the electron distribution we obtain coupled
diffusion equations for the electron density and spin. Using these equations we
calculate electric-field induced spin accumulation in a finite-size sample for
arbitrary ratio between spin-orbit energy splitting and elastic scattering
rate. We demonstrate that the spin-Hall conductivity vanishes in an infinite
system independent of this ratio.Comment: 5 pages, 1 figure; revised version according to referee's commment
Optical conductivity of the Frohlich polaron
We present accurate results for optical conductivity of the three dimensional
Frohlich polaron in all coupling regimes. The systematic-error free
diagrammatic quantum Monte Carlo method is employed where the Feynman graphs
for the momentum-momentum correlation function in imaginary time are summed up.
The real-frequency optical conductivity is obtained by the analytic
continuation with stochastic optimization. We compare numerical data with
available perturbative and non-perturbative approaches to the optical
conductivity and show that the picture of sharp resonances due to relaxed
excited states in the strong coupling regime is ``washed out''by large
broadening of these states. As a result, the spectrum contains only a
single-maximum broad peak with peculiar shape and a shoulder.Comment: 4 pages, 6 ps-figure
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