46 research outputs found
Size-dependent bandgap and particle size distribution of colloidal semiconductor nanocrystals
A new analytical expression for the size-dependent bandgap of colloidal
semiconductor nanocrystals is proposed within the framework of the finite-depth
square-well effective mass approximation in order to provide a quantitative
description of the quantum confinement effect. This allows one to convert
optical spectroscopic data (photoluminescence spectrum and absorbance edge)
into accurate estimates for the particle size distributions of colloidal
systems even if the traditional effective mass model is expected to fail, which
occurs typically for very small particles belonging to the so-called strong
confinement limit. By applying the reported theoretical methodologies to CdTe
nanocrystals synthesized through wet chemical routes, size distributions are
inferred and compared directly to those obtained from atomic force microscopy
and transmission electron microscopy. This analysis can be used as a
complementary tool for the characterization of nanocrystal samples of many
other systems such as the II-VI and III-V semiconductor materials.Comment: 9 pages, 5 figure
Scaling near the upper critical dimensionality in the localization theory
The phenomenon of upper critical dimensionality d_c2 has been studied from
the viewpoint of the scaling concepts. The Thouless number g(L) is not the only
essential variable in scale transformations, because there is the second
parameter connected with the off-diagonal disorder. The investigation of the
resulting two-parameter scaling has revealed two scenarios, and the switching
from one to another scenario determines the upper critical dimensionality. The
first scenario corresponds to the conventional one-parameter scaling and is
characterized by the parameter g(L) invariant under scale transformations when
the system is at the critical point. In the second scenario, the Thouless
number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation
of the Wegner relation s=\nu(d-2) between the critical exponents for
conductivity (s) and for localization radius (\nu), which takes the form
s=\nu(d_c2-2). The resulting formulas for g(L) are in agreement with the
symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous
version of Mott's argument concerning localization due topological disorder has
been proposed.Comment: PDF, 7 pages, 6 figure
Fermionic SK-models with Hubbard interaction: Magnetism and electronic structure
Models with range-free frustrated Ising spin- and Hubbard interaction are
treated exactly by means of the discrete time slicing method. Critical and
tricritical points, correlations, and the fermion propagator, are derived as a
function of temperature T, chemical potential \mu, Hubbard coupling U, and spin
glass energy J. The phase diagram is obtained. Replica symmetry breaking
(RSB)-effects are evaluated up to four-step order (4RSB). The use of exact
relations together with the 4RSB-solutions allow to model exact solutions by
interpolation. For T=0, our numerical results provide strong evidence that the
exact density of states in the spin glass pseudogap regime obeys \rho(E)=const
|E-E_F| for energies close to the Fermi level. Rapid convergence of \rho'(E_F)
under increasing order of RSB is observed. The leading term resembles the
Efros-Shklovskii Coulomb pseudogap of localized disordered fermionic systems in
2D. Beyond half filling we obtain a quadratic dependence of the fermion filling
factor on the chemical potential. We find a half filling transition between a
phase for U>\mu, where the Fermi level lies inside the Hubbard gap, into a
phase where \mu(>U) is located at the center of the upper spin glass pseudogap
(SG-gap). For \mu>U the Hubbard gap combines with the lower one of two SG-gaps
(phase I), while for \mu<U it joins the sole SG-gap of the half-filling regime
(phase II). We predict scaling behaviour at the continuous half filling
transition. Implications of the half-filling transition between the deeper
insulating phase II and phase I for delocalization due to hopping processes in
itinerant model extensions are discussed and metal-insulator transition
scenarios described.Comment: 29 pages, 26 Figures, 4 jpeg- and 3 gif-Fig-files include
Spontaneous emission from large quantum dots in nanostructures: exciton-photon interaction beyond the dipole approximation
We derive a rigorous theory of the interaction between photons and spatially
extended excitons confined in quantum dots in inhomogeneous photonic materials.
We show that, beyond the dipole approximation, the radiative decay rate is
proportional to a non-local interaction function, which describes the
interaction between light and spatially extended excitons. In this regime,
light and matter degrees of freedom cannot be separated and a complex interplay
between the nanostructured optical environment and the exciton envelope
function emerges. We illustrate this by specific examples and derive a series
of important analytical relations, which are useful for applying the formalism
to practical problems. In the dipole limit, the decay rate is proportional to
the projected local density of optical states and we obtain the strong and weak
confinement regimes as special cases.Comment: 14 pages, 4 figure