Lateral Quantum Dot Research Articles

Orbital and spin relaxation in single and coupled quantum dots

Phonon-induced orbital and spin relaxation rates of single electron states in lateral single and double quantum dots are obtained numerically for realistic materials parameters. The rates are calculated as a function of magnetic field and interdot coupling, at various field and quantum dot orientations. It is found that orbital relaxation is due to deformation potential phonons at low magnetic fields, while piezoelectric phonons dominate the relaxation at high fields. Spin relaxation, which is dominated by piezoelectric phonons, in single quantum dots is highly anisotropic due to the interplay of the Bychkov-Rashba and Dresselhaus spin-orbit couplings. Orbital relaxation in double dots varies strongly with the interdot coupling due to the cyclotron effects on the tunneling energy. Spin relaxation in double dots has an additional anisotropy due to anisotropic spin hot spots which otherwise cause giant enhancement of the rate at useful magnetic fields and interdot couplings. Conditions for the absence of the spin hot spots in in-plane magnetic fields (easy passages) and perpendicular magnetic fields (weak passages) are formulated analytically for different growth directions of the underlying heterostructure. It is shown that easy passages disappear (spin hot spots reappear) if the double dot system loses symmetry by an xy-like perturbation.

Multi-scale ordering of self-assembled InAs/GaAs(001) quantum dots

Ordering phenomena related to the self-assembly of InAs quantum dots (QD) grown on GaAs(001) substrates are experimentally investigated on different length scales. On the shortest length-scale studied here, we examine the QD morphology and observe two types of QD shapes, i.e., pyramids and domes. Pyramids are elongated along the [1-10] directions and are bounded by {137} facets, while domes have a multi-facetted shape. By changing the growth rates, we are able to control the size and size homogeneity of freestanding QDs. QDs grown by using low growth rate are characterized by larger sizes and a narrower size distribution. The homogeneity of buried QDs is measured by photoluminescence spectroscopy and can be improved by low temperature overgrowth. The overgrowth induces the formation of nanostructures on the surface. The fabrication of self-assembled nanoholes, which are used as a template to induce short-range positioning of QDs, is also investigated. The growth of closely spaced QDs (QD molecules) containing 2–6 QDs per QD molecule is discussed. Finally, the long-range positioning of self-assembled QDs, which can be achieved by the growth on patterned substrates, is demonstrated. Lateral QD replication observed during growth of three-dimensional QD crystals is reported.

Theory of Phonon-Induced Spin Relaxation in Laterally Coupled Quantum Dots

Phonon-induced spin relaxation in coupled lateral quantum dots in the presence of spin-orbit coupling is calculated. The calculation for single dots is consistent with experiment. Spin relaxation in double dots at useful interdot couplings is dominated by spin-hot spots that are strongly anisotropic. Spin-hot spots are ineffective for a diagonal crystallographic orientation of the dots with a transverse in-plane field. This geometry is proposed for spin-based quantum information processing.

Phase transition, spin-charge separation, and spin filtering in a quantum dot

We consider low temperature transport through a lateral quantum dot asymmetrically coupled to two conducting leads, and tuned to the mixed-valence region separating two adjacent Coulomb blockade valleys with spin S=1/2 and S=1 on the dot. We demonstrate that this system exhibits a quantum phase transition driven by the gate voltage. In the vicinity of the transition the spin on the dot is quantized, even though the fluctuations of charge are strong. The spin-charge separation leads to an unusual Fano-like dependence of the conductance on the gate voltage and to an almost perfect spin polarization of the current through the dot in the presence of a magnetic field.

Photon‐assisted tunneling in ac driven double quantum dot spin pumps

AbstractIn this work, we study the effect of an applied ac gate voltage on the spin filtering and pumping properties of a lateral double quantum dot, in the Coulomb blockade and weak coupling regimes, considering not only the effect of the ac potential on the inter‐dot tunneling but also on the tunneling through the leads. This last effect accounts for additional photon absorption and emission processes and therefore affects the spin polarization of the pumped current. In particular, we find that the spin down filtering property can be affected depending on the intensity of the ac field. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mode Softening, Ferroelectric Transition, and Tunable Photonic Band Structures in a Point-Dipole Crystal

We study the photonic band structure of cubic crystals of point dipoles. It is shown that in contrast to earlier claims these systems cannot have an omnidirectional photonic band gap. For sufficiently large plasma frequencies, however, they exhibit softening of photonic bands, leading to (anti)ferroelectric ordering of the dipoles and the possibility to open and tune directional band gaps by external electric fields. The model studied may be realized through lattices of quantum dots.

Single-electron transistor in strained Si/SiGe heterostructures

A split gate technique is used to form a lateral quantum dot in a two-dimensional electron gas of a modulation-doped silicon/silicon–germanium heterostructure. e-beam lithography was employed to produce split gates. By applying negative voltages to these gates the underlying electron gas is depleted and a lateral quantum dot is formed, the size of which can be adjusted by the gate voltage. We observe single-electron operation with Coulomb blockade behavior below 1 K. Gate leakage currents are well controlled, indicating that the recently encountered problems with Schottky gates for this type of application are not an inherent limitation of modulation-doped Si/SiGe heterostructures, as had been speculated.

Hysteretic effects in lateral nanostructures caused by long-lived quantum-Hall eddy currents

Coulomb blockade studies of lateral quantum dots and measurements of the quantised conductance of quantum point contacts, in high magnetic fields, reveal novel features which are hysteretic in magnetic-field sweep direction. These features are associated with long-lived eddy currents, induced in the 2D electron gas leads in these devices as the magnetic field sweeps and the 2DEG enters the quantum Hall effect state. Torsion-balance magnetometry measurements confirm the presence of these induced currents, and their influence on the nanostructures. The decay of the eddy currents, after the magnetic field sweep is stopped, exhibits two distinct regimes: a fast initial exponential decay followed by a much longer power-law decay in which the size of the eddy current falls typically to 60% of its original value in one day. The interpretation of these observations is that the Coulomb blockade and quantum point contact devices are influenced by the local Hall potential at the edges of the 2DEG leads. The Hall potential changes the local chemical potential of the leads, and hence the properties of the devices, in a manner which reverses when the field sweep direction is reversed.

Quantum Hall droplets in coupled lateral quantum dots

We present a theory and Coulomb and spin blockade spectroscopy experiments on quantum Hall droplets with controlled electron numbers ( N 1 , N 2 ) in laterally coupled gated quantum dots. The theory is based on the configuration interaction method (CI) coupled with the unrestricted Hartree–Fock (URHF) basis. It allows us to calculate the magnetic field evolution of ground and excited states of coupled quantum dots with large electron numbers. The method is applied to the spin transitions in the ( 5 , 5 ) droplet. Preliminary experimental results demonstrate the creation of the ( 5 , 5 ) droplet and its spin blockade spectra.

Lateral quantum dots in Si∕SiGe realized by a Schottky split-gate technique

Lateral quantum dots are formed in the two-dimensional electron gases of a high-mobility Si∕SiGe heterostructures by means of split Schottky gates. Palladium gates, defined by e-beam lithography and lift-off, show Schottky barriers with very well controlled leakage currents. At low temperatures we observe Coulomb-blockade and stability diamonds on lateral quantum dots containing a total charge of about 25 electrons. The experiments demonstrate that, in contrast to recent reports, Schottky gates are a feasible approach for the fabrication and integration of single electron transistors in the strained Si∕SiGe heterosystem.

Tuning of tunneling rates in quantum dots using a quantum point contact

We study the influence of asymmetric tunneling rates of a lateral quantum dot connected to source and drain leads. We use a quantum point contact (QPC) to detect charging events on the dot. Since the mean charge depends on the ratio of the tunneling rates the QPC can be used to detect symmetric configurations where both rates are equal. Thus, the transport properties of the dot can be investigated concerning this symmetry. We concentrate on the visibility of features that correspond to transitions with excited states. We interpret the results with the number of channels used for transport, the electron flow direction and the rate symmetry.

Quantum Light Emission of Two Lateral Tunnel-Coupled(In,Ga)As/GaAsQuantum Dots Controlled by a Tunable Static Electric Field

Lateral quantum coupling between two self-assembled (In,Ga)As quantum dots has been observed. Photon statistics measurements between the various excitonic and biexcitonic transitions of these lateral quantum dot molecules display strong antibunching confirming the presence of coupling. Furthermore, we observe an anomalous exciton Stark shift with respect to static electric field. A simple model indicates that the lateral coupling is due to electron tunneling between the dots when the ground states are in resonance. The electron probability can then be shifted to either dot and the system can be used to create a wavelength-tunable single-photon emitter by simply applying a voltage.

Excitation Spectrum of Two Correlated Electrons in a Lateral Quantum Dot with Negligible Zeeman Splitting

The excitation spectrum of a two-electron quantum dot is investigated by tunneling spectroscopy in conjunction with theoretical calculations. The dot made from a material with negligible Zeeman splitting has a moderate spatial anisotropy leading to a splitting of the two lowest triplet states at zero magnetic field. In addition to the well-known triplet excitation at zero magnetic field, two additional excited states are found at finite magnetic field. The lower one is identified as the second excited singlet state on the basis of an avoided crossing with the first excited singlet state at finite fields. The measured spectra are in remarkable agreement with exact-diagonalization calculations. The results prove the significance of electron correlations and suggest the formation of a state with Wigner-molecular properties at low magnetic fields.

Bipolar spin filter in a quantum dot molecule

We show that the tunable hybridization between two lateral quantum dots connected to non-magnetic current leads in a `hanging-dot' configuration that can be used to implement a bipolar spin filter. The competition between Zeeman, exchange interaction, and interdot tunneling (molecular hybridization) yields a singlet-triplet transition of the double dot {\it ground state} that allows spin filtering in Coulomb blockade experiments. Its generic nature should make it broadly useful as a robust bidirectional spin polarizer.

Self-assembled lateral InAs quantum dot molecules: Dot ensemble control and polarization-dependent photoluminescence

By proper control of underlying templates, lateral InAs quantum dot molecules (QDMs) can be grown with a desired number of quantum dots (QDs) per molecule. We demonstrate that by capping as-grown InAs QDs with lattice-mismatched GaAs layer and by varying the capping temperature between 430 and 470 °C, we are able to control the span of nanoholes template to between 150 and 300 nm. InAs regrowth on this template result in nanopropellers (0.6 ML regrowth) or QDMs (1.2 ML), the latter with 4–12 QDs per molecule depending on the span of the underlying nanoholes template. All QDM samples grown share a characteristic feature with a clear preference to orient along the [ 1 1 ¯ 0 ] crystallographic direction. Room-temperature photoluminescence measurements show a strong polarization-dependent characteristic, in good agreements with the QDM’s geometry.

Controlling Planar and Vertical Ordering in Three-Dimensional (In,Ga)As Quantum Dot Lattices by GaAs Surface Orientation

Anisotropic surface diffusion and strain are used to explain the formation of three-dimensional (In,Ga)As quantum dot lattices. The diffusion characteristics of the surface, coupled with the elastic anisotropy of the matrix, provides an excellent opportunity to influence the dot positions. In particular, quantum dots that are laterally organized into long chains or chessboard two-dimensional arrays vertically organized with strict vertical ordering or vertical ordering that is inclined to the sample surface normal are accurately predicted and observed.

Semiconductor quantum dots for electron spin qubits

We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates.

Far-infrared spectra of lateral quantum dot molecules

We study effects of electron–electron interactions and confinement potential on the magneto-optical absorption spectrum in the far-infrared (FIR) range of lateral quantum dot molecules (QDMs). We calculate FIR spectra for three different QDM confinement potentials. We use an accurate exact diagonalization technique for two interacting electrons and calculate dipole transitions between two-body levels with perturbation theory. We conclude that the two-electron FIR spectra directly reflect the symmetry of the confinement potential and interactions cause only small shifts in the spectra. These predictions could be tested in experiments with non-parabolic quantum dots (QDs) by changing the number of confined electrons. We also calculate FIR spectra for up to six non-interacting electrons and observe some additional features in the spectrum.

Spin polarization in open quantum dots

We investigate coherent transport through open lateral quantum dots using recursive Green's function technique, incorporating exchange-correlation effects within the density functional theory (DFT) in the local spin-density approximation. At low electron densities the current is spin polarized and electron density in the dot shows a strong spin polarization. As the electron density increases the spin polarization in the dot gradually diminishes. These findings are consistent with available experimental observations. Results of our DFT-based modeling indicate that utilization of the simplified approaches that use phenomenological parameters and/or model Hamiltonians might not be always reliable for theoretical predictions as well as interpretations of the experiments.

Spin relaxation in lateral quantum dots: Effects of spin-orbit interaction

We report results of calculations of the effect of spin-orbit interaction on electron spin relaxation in a lateral quantum dot. Our study is motivated by puzzling results of high source-drain transport measurements of singlet-triplet transitions of two electrons in lateral and vertical devices that show a strong asymmetry as a function of the applied magnetic field. Using exact diagonalization techniques, we investigate the influence of the spin-orbit interaction on the energy levels of a two-electron droplet and we show that the spin-orbit interaction strongly affects the expectation values of the total and $z$-projection spins of the two-electron system. We then evaluate the energy relaxation rates for the two-electron droplet through the emission of longitudinal acoustic phonons and show that they are strongly dependent on the spin energy levels involved in the process. Our study shows that the spin-orbit interaction provides an effective coupling between the spin-polarized triplet states and the singlet state. However, the transition involving the spin singlet and the unpolarized triplet component is very weak even in the presence of spin-orbit interaction. The calculated scattering rates from the excited states to the ground state of the two-electron system clearly confirm this picture and reveal a microsecond time scale for the single-triplet relaxation through spin-orbit-mediated acoustic phonon emission and the relaxation mechanism presents a built-in magnetic field asymmetry, in qualitative agreement with experimental findings.