Interdot Separations Research Articles

Spin excitation frequencies in magnetostatically coupled arrays of vortex state circular Permalloy dots

Broadband ferromagnetic resonance in square arrays of Permalloy circular dots with different interdot separations was measured in the vortex ground state. The detected spin excitations show a complicated dependence of their frequencies on the interdot coupling strength. A considerable influence of the interdot separation on the gyrotropic vortex frequency and splitting of the azimuthal spin wave frequencies was detected. The gyrotropic frequency and the first azimuthal doublet frequency splitting depend nonmonotonously on the interdot spacing, whereas the dependence of the second doublet frequency splitting on this parameter is monotonous. The observed effects are explained by the influence of both the dipolar and quadrupolar contributions to the dynamic magnetostatic interactions.

Two Electrons with Spin-Orbit Interactions in InAs Coupled Quantum Dots

We theoretically study the spin properties of two interacting electrons confined in the InAs parallel coupled quantum dots (CQDs) with spin-orbit interactions (SOI) by exact diagonalization method. Through the SOI induced spin mixing of the singlet and the triplet states, we show the different spin properties for the weak and strong SOI. We investigate the coherent singlet-triplet spin oscillations of the two electrons under the SOI, and demonstrate the detailed behaviors of the spin oscillations depending on the SOI strengths, the inter-dot separations and the external magnetic fields. To better understand the underlying physics of the spin dynamics, we introduce a four-level model Hamiltonian for both weak and strong SOI, and find that the SOI induced in plane effective magnetic fields can be quantitatively extracted from the two-electron excitation energy spectra.

Probing Arrays of Circular Magnetic Microdots by Ferromagnetic Resonance

X-band ferromagnetic resonance (FMR) was used to characterize in-plane magnetic anisotropies in rectangular and square arrays of circular nickel and Permalloy microdots. In the case of a rectangular lattice, as interdot distances in one direction decrease, the in-plane uniaxial anisotropy field increases, in good agreement with a simple theory of magnetostatically interacting uniformly magnetized dots. In the case of a square lattice a four-fold anisotropy of the in-plane FMR field H(r) was found when the interdot distance a gets comparable to the dot diameter D. This anisotropy, not expected in the case of uniformly magnetized dots, was explained by a non-uniform magnetization m(r) in a dot in response to dipolar forces in the patterned magnetic structure. It is well described by an iterative solution of a continuous variation procedure. In the case of perpendicular magnetization multiple sharp resonance peaks were observed below the main FMR peak in all the samples, and the relative positions of these peaks were independent of the interdot separations. Quantitative description of the observed multiresonance FMR spectra was given using the dipole-exchange spin wave dispersion equation for a perpendicularly magnetized film where in-plane wave vector is quantized due to the finite dot radius, and the inhomogenetiy of the intradot static demagnetization field in the nonellipsoidal dot is taken into account. It was demonstrated that ferromagnetic resonance force microscopy (FMRFM) can be used to determine both local and global properties of patterned submicron ferromagnetic samples. Local spectroscopy together with the possibility to vary the tip-sample spacing enables the separation of those two contributions to a FMRFM spectrum. The global FMR properties of circular submicron dots determined using magnetic resonance force microscopy are in a good agreement with results obtained using conventional FMR and with theoretical descriptions.

Effective tuning of exciton polarization splitting in coupled quantum dots

The polarization splitting of the exciton ground state in two laterally coupled quantum dots under an in-plane electric field is investigated, and its effective tuning is designed. It is found that there are significant Stark effect and anticrossing in energy levels. Due to the coupling between inter- and intradot states, the absolute value of polarization splitting is significantly reduced, and it could be tuned to zero by the electric field for proper interdot separations. The scheme of the authors is interesting for the research on the quantum dot–based entangled-photon source.

Singlet-triplet splitting, correlation, and entanglement of two electrons in quantum dot molecules

Starting with an accurate pseudopotential description of the single-particle states, and following by configuration-interaction treatment of correlated electrons in vertically coupled, self-assembled InAs/GaAs quantum dot-molecules, we show how simpler, popularly-practiced approximations, depict the basic physical characteristics including the singlet-triplet splitting, degree of entanglement (DOE) and correlation. The mean-field-like single-configuration approaches such as Hartree-Fock and local spin density, lacking correlation, incorrectly identify the ground state symmetry and give inaccurate values for the singlet-triplet splitting and the DOE. The Hubbard model gives qualitatively correct results for the ground state symmetry and singlet-triplet splitting, but produces significant errors in the DOE because it ignores the fact that the strain is asymmetric even if the dots within a molecule are identical. Finally, the Heisenberg model gives qualitatively correct ground state symmetry and singlet-triplet splitting only for rather large inter-dot separations, but it greatly overestimates the DOE as a consequence of ignoring the electron double occupancy effect.

Broken symmetry and quantum entanglement of an exciton inInxGa1−xAs∕GaAsquantum dot molecules

The ability of a quantum dot to confine photogenerated electron-hole pairs created interest in the behavior of such an exciton in a ``dot molecule,'' being a possible register in quantum computing. When two quantum dots are brought close together, the quantum state of the exciton may extend across both dots. The exciton wave function in such a dot molecule may exhibit entanglement. Atomistic pseudopotential calculations of the wave function for an electron-hole pair in a dot molecule made of two identical ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ dots reveal that the common assumption of single-particle wave functions forming bonding and antibonding states is erroneous. The true behavior of single-particle electrons and holes leads to symmetry-broken excitonic two-particle wave functions, dramatically suppressing entanglement. We find that at large interdot separations, the exciton states are built from heteronuclear single-particle states while at small interdot separations the exciton is derived from heteronuclear hole states and homonuclear electron states. We calculate the entanglement of the excitons and find a maximum value of 80% at an interdot separation of $8.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and very small values for larger and smaller distances.

Spin-wave spectra of perpendicularly magnetized circular submicron dot arrays

Dynamic microwave properties of arrays of circular Ni and Ni81Fe19 dots were studied by X-band ferromagnetic resonance (FMR) technique. All of the dots had the same radius 0.5μm, thickness 50–70nm, and were arranged into rectangular or square array with different interdot separations. In the case of perpendicular magnetization multiple (up to 8) sharp resonance peaks were observed below the main FMR peak, and the relative positions of these peaks were independent of the interdot separations. Quantitative description of the observed multiresonance FMR spectra is given using the dipole-exchange spin wave dispersion equation for a perpendicularly magnetized film where in-plane wave vector is quantized due to the finite dot radius, and the inhomogenetiy of the intradot static demagnetization field in the nonellipsoidal dot is taken into account.

Interdot interactions and band gap changes in CdSe nanocrystal arrays at elevated pressure

Three-dimensional arrays of organically passivated CdSe nanocrystals were investigated under hydrostatic pressure using photoluminescence (PL) and absorption spectroscopies. Interdot separations were varied coarsely by varying the organic ligand on the nanocrystal and finely by applying hydrostatic pressure. The PL and absorption spectra of solutions and arrays of CdSe nanocrystals capped by either tri-n-octylphosphine oxide or tri-n-butylphosphine oxide are the same up to 60 kbar, which suggests that they exhibit no interdot coupling since the interdot separations in the solutions (∼50 nm) are much greater than those in the arrays (≲1 nm). While the variation with pressure is roughly that expected from the increase in band gap energy of bulk CdSe with pressure and the increase in confinement energies of electrons and holes with increased pressure, there is still a significant difference in the energy of the PL peak and the first exciton in absorption (the Stokes shift) for both these solutions and arrays that increases with pressure. This is attributed mostly to increased vibrational relaxation due to the movement of nuclei in the excited state. In contrast, there is a distinct difference between the pressure dependence of CdSe/pyridine dots in solution and arrays; the increase of the energy of the first exciton peak in absorption with pressure becomes markedly slower above about 30 kbar in CdSe/pyridine arrays, and is lower than that in the corresponding solution by ∼50 meV at 50 kbar and ∼70 meV at 60 kbar. Experiments with CdSe/shell/pyridine dots, with large electron and hole barriers, cast doubt on the mechanism of interdot electron and/or hole tunneling leading to a decrease in electron and/or hole confinement energy. Also, interdot tunneling of single carriers may be inhibited by the charge separation energy. The differences in the dielectric medium surrounding each dot in the solution and array explain their different absorption exciton energies at ambient pressure, but not the changes at elevated pressure. The observed loss of much of the pyridine ligands during array drying could be very significant, and contact between pyridine-capped dots at elevated pressure may be important.

Relative performance of three nanoscale devices - CMOS, RTDs and QCAs - against a standard computing task

We present results to show the effects of device scaling on the relativeperformance of three device technologies, namely resonant tunnellingdiodes (RTD), electronic quantum cellular automata (QCA) andcomplementary metal-oxide-semiconductor (CMOS) transistortechnology. The minimumfeature size (MOSFET or HFET gate lengths λ) is scaled from 250 to50 nm, while QCA inter-dot separations of 20 to 2 nm are examined. Thecomparison is made using a standard digital circuit architecture, namely amemory-adder model. Our aim is to compare these device technologies on thesystem level rather than individual device level. The results show that theRTDs offer speed advantages over CMOS, but improvements in the circuit densityare limited. The electronic QCAs will suffer both from effectively low packingdensity and low operating speeds in comparison to CMOS if conventional designsand a 2D architecture are used.

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.