Interdot Interaction Research Articles

Excitation spectra of harmonic quantum dot lattices with Coulomb interaction between the dots and the broken generalized Kohn theorem

Lattices of parabolic quantum dots with different dot species per unit cell and Coulomb interaction between the dots are investigated. As examples, we solve the Schr\odinger equation for square lattices with two different dots per unit cell: (i) two different circular dots, and (ii) two elliptical dots, which are rotated by $90\ifmmode^\circ\else\textdegree\fi{}$ relative to each other. The interaction between the dots is considered in a dipole approximation, and excitation spectra are calculated. For vanishing momentum transfer $(\mathbf{q}=0),$ the energy spectrum of the first case can be expressed as a superposition of two noninteracting dots with an effective confinement frequency, which includes the effect of dot interaction. Only in the second case is there a splitting of degenerate absorption lines, and an anticrossing occurs, which is a qualitative indication of interdot interaction. If the interaction becomes very strong and if all lattice sites (not necessarily confinement potentials) are equivalent, then the contribution of the dot interaction outweighs possible differences in the confinement potentials and the generalized Kohn theorem gradually reenters, in the sense that one pair of excitation modes (pseudo-Kohn modes) becomes independent of the interaction strength. For finite momentum transfer $(\mathbf{q}\ensuremath{\ne}0),$ we investigated mode softening and the influence of changing the interaction strength between dots of different sublattices. The latter effect may be implemented by putting different electron numbers in different dot species. It is shown that strengthening the next-nearest-neighbor interaction versus the nearest-neighbor interaction stabilizes the square lattice.

Transport in coupled quantum dots: Kondo effect versus antiferromagnetic correlation

The interplay between the Kondo effect and the interdot magnetic interaction in a coupled-dot system is studied. An exact result for the transport properties at zero temperature is obtained by diagonalizing a cluster, composed by the double dot and its vicinity, which is connected to leads. It is shown that the system goes continuously from the Kondo regime to an antiferromagnetic state as the interdot interaction is increased. The conductance, the charge at the dots, and the spin-spin correlation are obtained as a function of the gate potential.

Solution of the Schrödinger equation for quantum-dot lattices with Coulomb interaction between the dots

The Schr\"odinger equation for quantum dot lattices with non-cubic, non-Bravais lattices built up from elliptical dots is investigated. The Coulomb interaction between the dots is considered in dipole approximation. Then only the center of mass (c.m.) coordinates of different dots couple with each other. This c.m. subsystem can be solved exactly and provides magneto- phonon like collective excitations. The inter-dot interaction is involved only through a single interaction parameter. The relative coordinates of individual dots form decoupled subsystems giving rise to intra-dot excitations. As an example, the latter are calculated exactly for two-electron dots. Emphasis is layed on qualitative effects like: i) Influence of the magnetic field on the lattice instability due to inter-dot interaction, ii) Closing of the gap between the lower and the upper c.m. mode at B=0 for elliptical dots due to dot interaction, and iii) Kinks in the single dot excitation energies (versus magnetic field) due to change of ground state angular momentum. It is shown that for obtaining striking qualitative effects one should go beyond simple cubic lattices with spherical dots. We also prove a more general version of the Kohn Theorem for quantum dot lattices. It is shown that for observing effects of electron- electron interaction between the dots in FIR spectra (breaking Kohn's Theorem) one has to consider dot lattices with at least two dot species with different confinement tensors.

Transport through a coupled quantum dot system: Role of interdot interactions

The coupled double quantum dot system is modeled by a two impurity Anderson-type Hamiltonian and interdot Coulomb interaction is included. The conductance of this system is calculated using a nonequilibrium Green's-function formalism. We have evaluated conductance, peak splitting, and amplitude of conductance peaks as a function of Fermi energy for various values of parameters of the model Hamiltonian. It is demonstrated that an interdot interaction whose strength is assumed to be 10% of the ondot Coulomb interaction produces significant changes in the conductance in a coupled double quantum dot system.

Radiative damping of collective excitations in periodic arrays of quantum wires and dots

The problem of electromagnetic response and collective excitations in arrays of quantum wires and dots is solved taking into account electrodynamic (radiative) effects and the interwire (interdot) interaction. The radiative contribution (Γ) to the total linewidth of collective modes is calculated. It is shown that the interwire (interdot) interaction increases the radiative damping of collective modes by several orders of magnitude, and the radiative contribution to the linewidth of plasma excitations, which has been always neglected so far, can exceed the collisional contribution (γ). The result allows us to remove the discrepancy between observed and calculated linewidths of the collective modes. The related problem of optical properties of small polarizable particles is discussed.

Effects of coupling and nonresonant tunneling on Coulomb blockade oscillations in an asymmetric double dot structure

We report on single electron transport through an asymmetric double dot structure with well-defined dot potential profiles. As the two dots are coupled, the conductance exhibits two pronounced types of Coulomb blockade oscillations. An analysis of the small short-period oscillations indicates the presence of interdot interaction. When the coupling strength is reduced, the oscillations become few irregular peaks but they develop into periodic oscillations again as the drain voltage is increased to 0.6 mV. This appearance with increasing drain voltage is well explained by our model which is based on the stochastic Coulomb blockade model and nonresonant tunneling.

Long-range resonance transfer of electronic excitations in close-packed CdSe quantum-dot solids

We show spectroscopically that electronic energy transfer in close-packed CdSe quantum-dot (QD) solids arises from dipole-dipole interdot interactions between proximal dots. We use cw and time-resolved photoluminescence to study electronic energy transfer in optically thin and clear, close-packed QD solids prepared from CdSe QD samples tunable from 17 to 150 \AA{} in diameter (\ensuremath{\sigma}4.5%). High-resolution scanning electron microscopy and small-angle x-ray scattering are used to build a well-defined structural model for the QD solids. In mixed QD solids of small and large dots, we measure quenching of the luminescence (lifetime) of the small dots accompanied by enhancement of the luminescence (lifetime) of the large dots consistent with electronic energy transfer from the small to the large dots. In QD solids of single size dots, a redshifted and modified emission line shape is consistent with electronic energy transfer within the sample inhomogeneous distribution. We use F\orster theory for long-range resonance transfer through dipole-dipole interdot interactions to explain electronic energy transfer in these close-packed QD solids. \textcopyright{} 1996 The American Physical Society.