Quantum dot self-consistent electronic structure and the Coulomb blockade

How Valley-Orbit States in Silicon Quantum Dots Probe Quantum Well Interfaces

The energies of valley-orbit states in silicon quantum dots are determined by an as yet poorly understood interplay between interface roughness, orbital confinement, and electron interactions. Here, we report measurements of one- and two-electron valley-orbit state energies as the dot potential is modified by changing gate voltages, and we calculate these same energies using full configuration interaction calculations. The results enable an understanding of the interplay between the physical contributions and enable a new probe of the quantum well interface.

Machine learning enables completely automatic tuning of a quantum device faster than human experts

Variability is a problem for the scalability of semiconductor quantum devices. The parameter space is large, and the operating range is small. Our statistical tuning algorithm searches for specific electron transport features in gate-defined quantum dot devices with a gate voltage space of up to eight dimensions. Starting from the full range of each gate voltage, our machine learning algorithm can tune each device to optimal performance in a median time of under 70 minutes. This performance surpassed our best human benchmark (although both human and machine performance can be improved). The algorithm is approximately 180 times faster than an automated random search of the parameter space, and is suitable for different material systems and device architectures. Our results yield a quantitative measurement of device variability, from one device to another and after thermal cycling. Our machine learning algorithm can be extended to higher dimensions and other technologies.

Spectroscopy of Quantum Dot Orbitals with In-Plane Magnetic Fields

We show that in-plane magnetic-field-assisted spectroscopy allows extraction of the in-plane orientation and full 3D size parameters of the quantum mechanical orbitals of a single electron GaAs lateral quantum dot with subnanometer precision. The method is based on measuring the orbital energies in a magnetic field with various strengths and orientations in the plane of the 2D electron gas. From such data, we deduce the microscopic confinement potential landscape and quantify the degree by which it differs from a harmonic oscillator potential. The spectroscopy is used to validate shape manipulation with gate voltages, agreeing with expectations from the gate layout. Our measurements demonstrate a versatile tool for quantum dots with one dominant axis of strong confinement.

Transmission phase of a quantum dot and statistical fluctuations of partial-width amplitudes

Experimentally, the phase of the amplitude for electron transmission through a quantum dot (transmission phase) shows the same pattern between consecutive resonances. Such universal behavior, found for long sequences of resonances, is caused by correlations of the signs of the partial-width amplitudes of the resonances. We investigate the stability of these correlations in terms of a statistical model. For a classically chaotic dot, the resonance eigenfunctions are assumed to be Gaussian distributed. Under this hypothesis, statistical fluctuations are found to reduce the tendency towards universal phase evolution. Long sequences of resonances with universal behavior only persist in the semiclassical limit of very large electron numbers in the dot and for specific energy intervals. Numerical calculations qualitatively agree with the statistical model but quantitatively are closer to universality.

Pulse-gated quantum-dot hybrid qubit

A quantum-dot hybrid qubit formed from three electrons in a double quantum dot has the potential for great speed, due to the presence of level crossings where the qubit becomes chargelike. Here, we show how to exploit the level crossings to implement fast pulsed gating. We develop one- and two-qubit dc quantum gates that are simpler than the previously proposed ac gates. We obtain closed-form solutions for the control sequences and show that the gates are fast (subnanosecond) and can achieve high fidelities.

Near-field optical mapping of quantum Hall edge states

We report on the mapping of quantum-Hall edge states by quasiresonant photovoltage measurements using a near-field scanning optical microscope. We have observed fine structures near sample edges that shift inward with an increase in magnetic field in accordance with the shift of the positions of the quantum-Hall edge states. We have found a transition from the weak disorder regime where compressible-incompressble strips are visible to the strong disorder regime where fluctuations smear out incompressible strips.

Active Brownian motion in threshold distribution of a Coulomb blockade model

Randomly distributed offset charges affect the nonlinear current-voltage property via the fluctuation of the threshold voltage above which the current flows in an array of a Coulomb blockade (CB). We analytically derive the distribution of the threshold voltage for a model of one-dimensional locally coupled CB arrays and propose a general relationship between conductance and distribution. In addition, we show that the distribution for a long array is equivalent to the distribution of the number of upward steps for aligned objects of different heights. The distribution satisfies a novel Fokker-Planck equation corresponding to active Brownian motion. The feature of the distribution is clarified by comparing it with the Wigner and Ornstein-Uhlenbeck processes. It is not restricted to the CB model but is instructive in statistical physics generally.

Magnetic-field asymmetry of electron wave packet transmission in bent channels capacitively coupled to a metal gate

We study the electron wave packet moving through a bent channel. We demonstrate that the packet transmission probability becomes an asymmetric function of the magnetic field when the electron packet is capacitively coupled to a metal plate. The coupling occurs through a nonlinear potential which translates a different kinetics of the transport for opposite magnetic-field orientations into a different potential felt by the scattered electron.

Magnetic field control of exchange and noise immunity in double quantum dots

We employ density functional calculated eigenstates as a basis for exact diagonalization studies of semiconductor double quantum dots, with two electrons, through the transition from the symmetric bias regime to the regime where both electrons occupy the same dot. We calculate the singlet-triplet splitting J(epsilon) as a function of bias detuning epsilon and explain its functional shape with a simple, double anticrossing model. A voltage noise suppression "sweet spot," where d J(epsilon)/d(epsilon) = 0 with nonzero J(epsilon), is predicted and shown to be tunable with a magnetic field B.

Linear scaling calculation of an n-type GaAs quantum dot

A linear scale method for calculating electronic properties of large and complex systems is introduced within a local density approximation. The method is based on the Chebyshev polynomial expansion and the time-dependent method, which is tested on the calculation of the electronic structure of a model n-type GaAs quantum dot.

Charge rearrangement and screening in a quantum point contact

Compressibility measurements are performed on a quantum point contact (QPC). Screening due to mobile charges in the QPC is measured quantitatively, using a second point contact. These measurements are performed from pinch-off through the opening of the first few modes in the QPC. While the measured signal closely matches a Thomas-Fermi-Poisson prediction, deviations from the classical behavior are apparent near the openings of the different modes. Density functional calculations attribute the deviations to a combination of a diverging density of states at the opening of each one-dimensional mode and exchange interaction, which is strongest for the first mode.

Charging Effects in a CdSe Nanotetrapod

The charging effects in a CdSe nanotetrapod have been theoretically investigated by using an atomistic pseudopotential method. We showed that the simple quasiparticle equation based on classical electrostatic consideration can be derived from the many-body GW equation under proper approximations. We found that the surface polarization potential can significantly change the electron wave functions, and there is an incomplete cancellation for this potential between the single particle energies and the electron-hole Coulomb interaction. Thus, it is necessary to include this potential in the calculation for complex unconvex systems. We also calculated the electron addition energies for a tetrapod. Unlike a simple spherical quantum dot, in which the addition energies are almost a constant, there is a large variation in the calculated addition energies for different numbers of electrons in a tetrapod.

Optical probing of spin polarization of electrons in quantum dot edge channels

We propose an optical method for the investigation of the quantum dot edge channels by utilizing circularly polarized photoluminescence in the integer-quantum-Hall-effect regime. One of the advantages of our method is that the degree of the spin-polarization of the electrons in the inner- and outer-compressible liquids can be probed separately. The observed polarized photoluminescence spectra can be explained by the calculated electron spin-dependent optical transition probabilities based on the local-spin density approximation.

Magnetically induced chessboard pattern in the conductance of a Kondo quantum dot

We quantitatively describe the main features of the magnetically induced conductance modulation of a Kondo quantum dot-or chessboard pattern-in terms of a constant-interaction double quantum dot model. We show that the analogy with a double dot holds down to remarkably low magnetic fields. The analysis is extended by full 3D spin density functional calculations. Introducing an effective Kondo coupling parameter, the chessboard pattern is self-consistently computed as a function of magnetic field and electron number, which enables us to explain our experimental data quantitatively.

Spin and conductance-peak-spacing distributions in large quantum dots: a density-functional theory study

We use spin-density-functional theory to study the spacing between conductance peaks and the ground-state spin of 2D model quantum dots with up to 200 electrons. Distributions for different ranges of electron number are obtained in both symmetric and asymmetric potentials. The even/odd effect is pronounced for small symmetric dots but vanishes for large asymmetric ones, suggesting substantially stronger interaction effects than expected. The fraction of high-spin ground states is remarkably large.

Rectifying behavior in Coulomb blockades: charging rectifiers

We introduce examples of tunneling and diffusive, Coulomb-regulated rectifiers based on the Coulomb blockade formalism in discrete and continuum systems, respectively. Nonlinearity of the interacting dynamics profoundly enhances the inherent asymmetry of the devices by reducing the Hilbert space of accessible states. The discrete charging rectifier is structurally similar to hybrid molecular electronic rectifiers, while the continuum-charging rectifier is based on a model of ionic flow through a pore (ion channel) with an artificial branch. The devices are formally related to ratchet systems with spatial periodicity replaced by a winding number: the current.

Dissociation of vertical semiconductor diatomic artificial molecules

We investigate the dissociation of few-electron circular vertical semiconductor double quantum dot artificial molecules at 0 T as a function of interdot distance. A slight mismatch introduced in the fabrication of the artificial molecules from nominally identical constituent quantum wells induces localization by offsetting the energy levels in the quantum dots by up to 2 meV, and this plays a crucial role in the appearance of the addition energy spectra as a function of coupling strength particularly in the weak coupling limit.

Molecule-type phases and Hund's rule in vertically coupled quantum dots

We study the ground state of two vertically coupled quantum dots as a function of the interdot distance within the spin density functional theory. The tunneling between the dots is included. For small and large interdot distances the atomic phases are recovered. For intermediate distances new molecule-type phases are predicted which can be observed experimentally in the addition energies. The results are interpreted in terms of an effective single particle picture and we find that Hund's rule breaks down for 11 and 12 electrons. The results are summarized in a phase diagram in which spin and isospin blockade regions are also found.