Absence of correlation between built-in electric dipole moment and quantum Stark effect in InAs/GaAs self-assembled quantum dots

We report significant deviations from the usual quadratic dependence of the ground state interband transition energy on applied electric fields in InAs/GaAs self-assembled quantum dots. In particular, we show that conventional second-order perturbation theory fails to correctly describe the Stark shift for electric field below $F = 10$ kV/cm in high dots. Eight-band ${\bf k}\cdot{\bf p}$ calculations demonstrate this effect is predominantly due to the three-dimensional strain field distribution which for various dot shapes and stoichiometric compositions drastically affects the hole ground state. Our conclusions are supported by two independent experiments.Comment: 4 pages, 4 figure

Anomalous quantum confined Stark effects in stacked InAs/GaAs self-assembled quantum dots

Vertically stacked and coupled InAs/GaAs self-assembled quantum dots (SADs) are predicted to exhibit a strong non-parabolic dependence of the interband transition energy on the electric field, which is not encountered in single SAD structures nor in other types of quantum structures. Our study based on an eight-band strain-dependent ${\bf k}\cdot{\bf p}$ Hamiltonian indicates that this anomalous quantum confined Stark effect is caused by the three-dimensional strain field distribution which influences drastically the hole states in the stacked SAD structures.Comment: 4 pages, 4 figure

Hubble Space Telescope Evidence for an Intermediate-Mass Black Hole in the Globular Cluster M15: II. Kinematical Analysis and Dynamical Modeling

We analyze HST/STIS spectra (see Paper I) of the central region of the dense globular cluster M15. We infer the velocities of 64 individual stars, two-thirds of which have their velocity measured for the first time. This triples the number of stars with measured velocities in the central 1 arcsec of M15 and doubles the number in the central 2 arcsec. Combined with existing ground-based data we obtain the radial profiles of the projected kinematical quantities. The RMS velocity sigma_RMS rises to 14 km/s in the central few arcsec, somewhat higher than the values of 10-12 km/s inferred previously from ground-based data. To interpret the results we construct dynamical models based on the Jeans equation, which imply that M15 must have a central concentration of non-luminous material. If this is due to a single black hole, then its mass is M_BH = (3.9 +/- 2.2) x 10^3 solar masses. This is consistent with the relation between M_BH and sigma_RMS that has been established for galaxies. Also, the existence of intermediate-mass black holes in globular clusters is consistent with several scenarios for globular cluster evolution proposed in the literature. Therefore, these results may have important implications for our understanding of the evolution of globular clusters, the growth of black holes, the connection between globular cluster and galaxy formation, and the nature of the recently discovered `ultra-luminous' X-ray sources in nearby galaxies. Instead of a single black hole, M15 could have a central concentration of dark remnants (e.g., neutron stars) due to mass segregation. However, the best-fitting Fokker-Planck models that have previously been constructed for M15 do not predict a central mass concentration that is sufficient to explain the observed kinematics.[ABRIDGED]Comment: 43 pages, LaTeX, with 14 PostScript figures. Astronomical Journal, in press (Dec 2002). Please note that the results reported here are modified by the Addendum available at astro-ph/0210158 (Astronomical Journal, in press, Jan 2003). This second version submitted to astro-ph is identical to first, with the exception of the preceeding remar

Electronic structure of strained InP/GaInP quantum dots

We calculate the electronic structure of nm scale InP islands embedded in $Ga_{0.51}In_{0.49}P$. The calculations are done in the envelope approximation and include the effects of strain, piezoelectric polarization, and mixing among 6 valence bands. The electrons are confined within the entire island, while the holes are confined to strain induced pockets. One pocket forms a ring at the bottom of the island near the substrate interface, while the other is above the island in the GaInP. The two sets of hole states are decoupled. Polarization dependent dipole matrix elements are calculated for both types of hole states.Comment: Typographical error corrected in strain Hamiltonia

Theoretical interpretation of the experimental electronic structure of lens shaped, self-assembled InAs/GaAs quantum dots

We adopt an atomistic pseudopotential description of the electronic structure of self-assembled, lens shaped InAs quantum dots within the ``linear combination of bulk bands'' method. We present a detailed comparison with experiment, including quantites such as the single particle electron and hole energy level spacings, the excitonic band gap, the electron-electron, hole-hole and electron hole Coulomb energies and the optical polarization anisotropy. We find a generally good agreement, which is improved even further for a dot composition where some Ga has diffused into the dots.Comment: 16 pages, 5 figures. Submitted to Physical Review

Tight-binding study of the influence of the strain on the electronic properties of InAs/GaAs quantum dots

We present an atomistic investigation of the influence of strain on the electronic properties of quantum dots (QD's) within the empirical $s p^{3} s^{*}$ tight-binding (ETB) model with interactions up to 2nd nearest neighbors and spin-orbit coupling. Results for the model system of capped pyramid-shaped InAs QD's in GaAs, with supercells containing $10^{5}$ atoms are presented and compared with previous empirical pseudopotential results. The good agreement shows that ETB is a reliable alternative for an atomistic treatment. The strain is incorporated through the atomistic valence force field model. The ETB treatment allows for the effects of bond length and bond angle deviations from the ideal InAs and GaAs zincblende structure to be selectively removed from the electronic-structure calculation, giving quantitative information on the importance of strain effects on the bound state energies and on the physical origin of the spatial elongation of the wave functions. Effects of dot-dot coupling have also been examined to determine the relative weight of both strain field and wave function overlap.Comment: 22 pages, 7 figures, submitted to Phys. Rev. B (in press) In the latest version, added Figs. 3 and 4, modified Fig. 5, Tables I and II,.and added new reference

White Dwarfs in Globular Clusters: HST Observations of M4

Using WFPC2 on the Hubble Space Telescope, we have isolated a sample of 258 white dwarfs (WDs) in the Galactic globular cluster M4. Fields at three radial distances from the cluster center were observed and sizeable WD populations were found in all three. The location of these WDs in the color-magnitude diagram, their mean mass of 0.51($\pm 0.03$)M$_{\odot}$, and their luminosity function confirm basic tenets of stellar evolution theory and support the results from current WD cooling theory. The WDs are used to extend the cluster main-sequence mass function upward to stars that have already completed their nuclear evolution. The WD/red dwarf binary frequency in M4 is investigated and found to be at most a few percent of all the main-sequence stars. The most ancient WDs found are about 9 Gyr old, a level which is set solely by the photometric limits of our data. Even though this is less than the age of M4, we discuss how these cooling WDs can eventually be used to check the turnoff ages of globular clusters and hence constrain the age of the Universe.Comment: 46 pages, latex, no figures included, figures available at ftp://ftp.astro.ubc.ca/pub/richer/wdfig.uu size 2.7Mb. To be published in the Astrophysical Journa

Wavefunction and level statistics of random two dimensional gauge fields

Level and wavefunction statistics have been studied for two dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between - (1/2) Phi_0 and (1/2) Phi_0 with Phi_0 the flux quantum. All considered statistics start close to the corresponding Wigner-Dyson distribution for small system sizes and monotonically move towards Poisson statistics as the cluster size increases. Scaling is quite rapid for states close to the band edges but really difficult to observe for states well within the band. Localization properties are discussed considering two different scenarios. Experimental measurement of one of the considered statistics --wavefunction statistics seems the most promising one-- could discern between both possibilities. A real version of the previous model, i.e., a system that is invariant under time reversal, has been studied concurrently to get coincidences and differences with the Hermitian model.Comment: 12 twocolumnn pages in revtex style, 17 postscript figures, to be published in PRB, send comments to [email protected]

Density of states for the π\pi-flux state with bipartite real random hopping only: A weak disorder approach

Gade [R. Gade, Nucl. Phys. B \textbf{398}, 499 (1993)] has shown that the local density of states for a particle hopping on a two-dimensional bipartite lattice in the presence of weak disorder and in the absence of time-reversal symmetry(chiral unitary universality class) is anomalous in the vicinity of the band center $\epsilon=0$ whenever the disorder preserves the sublattice symmetry. More precisely, using a nonlinear-sigma-model that encodes the sublattice (chiral) symmetry and the absence of time-reversal symmetry she argues that the disorder average local density of states diverges as $|\epsilon|^{-1}\exp(-c|\ln\epsilon|^\kappa)$ with $c$ some non-universal positive constant and $\kappa=1/2$ a universal exponent. Her analysis has been extended to the case when time-reversal symmetry is present (chiral orthogonal universality class) for which the same exponent $\kappa=1/2$ was predicted. Motrunich \textit{et al.} [O. Motrunich, K. Damle, and D. A. Huse, Phys. Rev. B \textbf{65}, 064206 (2001)] have argued that the exponent $\kappa=1/2$ does not apply to the typical density of states in the chiral orthogonal universality class. They predict that $\kappa=2/3$ instead. We confirm the analysis of Motrunich \textit{et al.} within a field theory for two flavors of Dirac fermions subjected to two types of weak uncorrelated random potentials: a purely imaginary vector potential and a complex valued mass potential. This model is believed to belong to the chiral orthogonal universality class. Our calculation relies in an essential way on the existence of infinitely many local composite operators with negative anomalous scaling dimensions.Comment: 30 pages, final version published in PR