Far-infrared absorption in parallel quantum wires with weak tunneling

We study collective and single-particle intersubband excitations in a system of quantum wires coupled via weak tunneling. For an isolated wire with parabolic confinement, the Kohn's theorem guarantees that the absorption spectrum represents a single sharp peak centered at the frequency given by the bare confining potential. We show that the effect of weak tunneling between two parabolic quantum wires is twofold: (i) additional peaks corresponding to single-particle excitations appear in the absorption spectrum, and (ii) the main absorption peak acquires a depolarization shift. We also show that the interplay between tunneling and weak perpendicular magnetic field drastically enhances the dispersion of single-particle excitations. The latter leads to a strong damping of the intersubband plasmon for magnetic fields exceeding a critical value.Comment: 18 pages + 6 postcript figure

Gauge invariant grid discretization of Schr\"odinger equation

Using the Wilson formulation of lattice gauge theories, a gauge invariant grid discretization of a one-particle Hamiltonian in the presence of an external electromagnetic field is proposed. This Hamiltonian is compared both with that obtained by a straightforward discretization of the continuous Hamiltonian by means of balanced difference methods, and with a tight-binding Hamiltonian. The proposed Hamiltonian and the balanced difference one are used to compute the energy spectrum of a charged particle in a two-dimensional parabolic potential in the presence of a perpendicular, constant magnetic field. With this example we point out how a "naive" discretization gives rise to an explicit breaking of the gauge invariance and to large errors in the computed eigenvalues and corresponding probability densities; in particular, the error on the eigenfunctions may lead to very poor estimates of the mean values of some relevant physical quantities on the corresponding states. On the contrary, the proposed discretized Hamiltonian allows a reliable computation of both the energy spectrum and the probability densities.Comment: 7 pages, 4 figures, discussion about tight-binding Hamiltonians adde

Magnetoplasmon excitations in arrays of circular and noncircular quantum dots

We have investigated the magnetoplasmon excitations in arrays of circular and noncircular quantum dots within the Thomas-Fermi-Dirac-von Weizs\"acker approximation. Deviations from the ideal collective excitations of isolated parabolically confined electrons arise from local perturbations of the confining potential as well as interdot Coulomb interactions. The latter are unimportant unless the interdot separations are of the order of the size of the dots. Local perturbations such as radial anharmonicity and noncircular symmetry lead to clear signatures of the violation of the generalized Kohn theorem. In particular, the reduction of the local symmetry from SO(2) to $C_4$ results in a resonant coupling of different modes and an observable anticrossing behaviour in the power absorption spectrum. Our results are in good agreement with recent far-infrared (FIR) transmission experiments.Comment: 25 pages, 6 figures, typeset in RevTe

Thomas-Fermi-Dirac-von Weizsacker hydrodynamics in laterally modulated electronic systems

We have studied the collective plasma excitations of a two-dimensional electron gas with an arbitrary lateral charge-density modulation. The dynamics is formulated using a previously developed hydrodynamic theory based on the Thomas-Fermi-Dirac-von Weizsacker approximation. In this approach, both the equilibrium and dynamical properties of the periodically modulated electron gas are treated in a consistent fashion. We pay particular attention to the evolution of the collective excitations as the system undergoes the transition from the ideal two-dimensional limit to the highly-localized one-dimensional limit. We also calculate the power absorption in the long-wavelength limit to illustrate the effect of the modulation on the modes probed by far-infrared (FIR) transmission spectroscopy.Comment: 27 page Revtex file, 15 Postscript figure

A Simple Shell Model for Quantum Dots in a Tilted Magnetic Field

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi-system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters and the slab thickness is found.Comment: 15 pages (Latex), 3 epsi figures, to appear in PhysRev B, 55 Nr. 20 (1997

High Magnetic Field Microwave Conductivity of 2D Electrons in an Array of Antidots

We measure the high magnetic field ($B$) microwave conductivity, Re$\sigma_{xx}$, of a high mobility 2D electron system containing an antidot array. Re$\sigma_{xx}$ vs frequency ($f$) increases strongly in the regime of the fractional quantum Hall effect series, with Landau filling $1/3<\nu<2/3$. At microwave $f$, Re$\sigma_{xx}$ vs $B$ exhibits a broad peak centered around $\nu=1/2$. On the peak, the 10 GHz Re$\sigma_{xx}$ can exceed its dc-limit value by a factor of 5. This enhanced microwave conductivity is unobservable for temperature $T \gtrsim 0.5$ K, and grows more pronounced as $T$ is decreased. The effect may be due to excitations supported by the antidot edges, but different from the well-known edge magnetoplasmons.Comment: 4 pages, 3 figures, revtex

Magnetization of noncircular quantum dots

We calculate the magnetization of quantum dots deviating from circular symmetry for noninteracting electrons or electrons interacting according to the Hartree approximation. For few electrons the magnetization is found to depend on their number, and the shape of the dot. The magnetization is an ideal probe into the many-electron state of a quantum dot.Comment: 11 RevTeX pages with 6 included Postscript figure

Far-infrared edge modes in quantum dots

We have investigated edge modes of different multipolarity sustained by quantum dots submitted to external magnetic fields. We present a microscopic description based on a variational solution of the equation of motion for any axially symmetric confining potential and multipole mode. Numerical results for dots with different number of electrons whose ground-state is described within a local Current Density Functional Theory are discussed. Two sum rules, which are exact within this theory, are derived. In the limit of a large neutral dot at B=0, we have shown that the classical hydrodynamic dispersion law for edge waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size effects are taken into account.Comment: We have changed some figures as well as a part of the tex

Far-infrared edge modes in quantum dots

We have investigated edge modes of different multipolarity sustained by quantum dots submitted to external magnetic fields. We present a microscopic description based on a variational solution of the equation of motion for any axially symmetric confining potential and multipole mode. Numerical results for dots with different number of electrons whose ground-state is described within a local Current Density Functional Theory are discussed. Two sum rules, which are exact within this theory, are derived. In the limit of a large neutral dot at B=0, we have shown that the classical hydrodynamic dispersion law for edge waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size effects are taken into account.Comment: We have changed some figures as well as a part of the tex

Electronic structure of rectangular quantum dots

We study the ground state properties of rectangular quantum dots by using the spin-density-functional theory and quantum Monte Carlo methods. The dot geometry is determined by an infinite hard-wall potential to enable comparison to manufactured, rectangular-shaped quantum dots. We show that the electronic structure is very sensitive to the deformation, and at realistic sizes the non-interacting picture determines the general behavior. However, close to the degenerate points where Hund's rule applies, we find spin-density-wave-like solutions bracketing the partially polarized states. In the quasi-one-dimensional limit we find permanent charge-density waves, and at a sufficiently large deformation or low density, there are strongly localized stable states with a broken spin-symmetry.Comment: 8 pages, 9 figures, submitted to PR