In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of ``Brownian motors.'' In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where single-particle currents were first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noise-assisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.

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Artificial Brownian motors: Controlling transport on the nanoscale

The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly described. The electronic structure is analyzed in terms of simple single-particle models, density-functional theory, and "exact" diagonalization methods. The spontaneous magnetization due to Hund's rule, spin-density wave states, and electron localization are addressed. As a function of the magnetic field, the electronic structure goes through several phases with qualitatively different properties. The formation of the so-called maximum-density droplet and its edge reconstruction is discussed, and the regime of strong magnetic fields in finite dot is examined. In addition, quasi-one-dimensional rings, deformed dots, and dot molecules are considered. (Less)

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Electronic structure of quantum dots

We review some electron transport experiments on few-electron, vertical quantum dot devices. The measurement of current versus source–drain voltage and gate voltage is used as a spectroscopic tool to investigate the energy characteristics of interacting electrons confined to a small region in a semiconducting material. Three energy scales are distinguished: the single-particle states, which are discrete due to the confinement involved; the direct Coulomb interaction between electron charges on the dot; and the exchange interaction between electrons with parallel spins. To disentangle these energies, a magnetic field is used to reorganize the occupation of electrons over the single-particle states and to induce changes in the spin states. We discuss the interactions between small numbers of electrons (between 1 and 20) using the simplest possible models. Nevertheless, these models consistently describe a large set of experiments. Some of the observations resemble similar phenomena in atomic physics, such as shell structure and periodic table characteristics, Hund’s rule, and spin singlet and triplet states. The experimental control, however, is much larger than for atoms: with one device all the artificial elements can be studied by adding electrons to the quantum dot when changing the gate voltage.

https://iopscience.iop.org/article/10.1088/0034-4885/64/6/201/pdf

Few-electron quantum dots

Energy storage devices that can deliver high powers have many applications, including hybrid vehicles and renewable energy. Much research has focused on increasing the power output of lithium batteries by reducing lithium-ion diffusion distances, but outputs remain far below those of electrochemical capacitors and below the levels required for many applications. Here, we report an alternative approach based on the redox reactions of functional groups on the surfaces of carbon nanotubes. Layer-by-layer techniques are used to assemble an electrode that consists of additive-free, densely packed and functionalized multiwalled carbon nanotubes. The electrode, which is several micrometres thick, can store lithium up to a reversible gravimetric capacity of approximately 200 mA h g(-1)(electrode) while also delivering 100 kW kg(electrode)(-1) of power and providing lifetimes in excess of thousands of cycles, both of which are comparable to electrochemical capacitor electrodes. A device using the nanotube electrode as the positive electrode and lithium titanium oxide as a negative electrode had a gravimetric energy approximately 5 times higher than conventional electrochemical capacitors and power delivery approximately 10 times higher than conventional lithium-ion batteries.

High-Power Lithium Batteries from Functionalized Carbon Nanotube Electrodes

It is conventionally assumed that the growth of monodisperse colloidal nanocrystals requires a temporally discrete nucleation followed by monomer attachment onto the existing nuclei. However, recent studies have reported violations of this classical growth model, and have suggested that inter-particle interactions are also involved during the growth. Mechanisms of nanocrystal growth still remain controversial. Using in situ transmission electron microscopy, we show that platinum nanocrystals can grow either by monomer attachment from solution onto the existing particles or by coalescence between the particles. Surprisingly, an initially broad size distribution of the nanocrystals can spontaneously narrow. We suggest that nanocrystals take different pathways of growth based on their size- and morphology-dependent internal energies. These observations are expected to be highly relevant for other nanocrystal systems.

Observation of Single Colloidal Platinum Nanocrystal Growth Trajectories

Single-shot measurement of the charge arrangement and spin state of a double quantum dot are reported with measurement times down to 100 ns. Sensing uses radio-frequency reflectometry of a proximal quantum dot in the Coulomb blockade regime. The sensor quantum dot is up to 30 times more sensitive than a comparable quantum point-contact sensor and yields three times greater signal to noise in rf single-shot measurements. Numerical modeling is qualitatively consistent with experiment and shows that the improved sensitivity of the sensor quantum dot results from reduced lifetime broadening and screening.

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Fast Sensing of Double-Dot Charge Arrangement and Spin State with a Radio-Frequency Sensor Quantum Dot

We employ density-functional theory to calculate the self-consistent electronic structure, free energy, and linear source-drain conductance of a lateral semiconductor quantum dot patterned via surface gates on the two-dimensional electron gas formed at the interface of a GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure. The Schr\"odinger equation is reduced from 3D to multicomponent 2D and solved via an eigenfunction expansion in the dot. This permits the solution of the electronic structure for dot electron number N\ensuremath{\sim}100. We present details of our derivation of the total dot-lead-gates interacting free energy in terms of the electronic structure results, which is free of capacitance parameters. Statistical properties of the dot level spacings and connection coefficients to the leads are computed in the presence of varying degrees of order in the donor layer. Based on the self-consistently computed free energy as a function of gate voltages, ${\mathit{V}}_{\mathit{i}}$, and N, we modify the semiclassical expression for the tunneling conductance as a function of gate voltage through the dot in the linear source-drain, Coulomb blockade regime. Among the many results presented, we demonstrate the existence of a shell structure in the dot levels which (a) results in envelope modulation of Coulomb oscillation peak heights, (b) influences the dot capacitances and should be observable in terms of variations in the activation energy for conductance in a Coulomb oscillation minimum, and (c) possibly contributes to departure of recent experimental results from the predictions of random-matrix theory. \textcopyright{} 1996 The American Physical Society.

Quantum dot self-consistent electronic structure and the Coulomb blockade.

We used a hybrid vertical-lateral double-dot device, consisting of laterally coupled vertical quantum dots, to measure the interdot tunnel coupling. By using nonlinear transport measurements of "Coulomb diamonds," we showed that an inherent asymmetry in the capacitances of the component dots influences the diamond slopes, thereby allowing for the determination of the dot through which the electron has passed. We used this technique to prepare a delocalized one-electron state and Heitler-London (HL) two-electron state, and we showed that the interdot tunnel coupling, which determines whether HL is the ground state, is tunable. This implies that our device may be useful for implementing two-electron spin entanglement.

http://science.sciencemag.org/content/sci/309/5732/268.full.pdf

Single-electron delocalization in hybrid vertical-lateral double quantum dots.

Three tunnel-coupled quantum dots in the Coulomb blockade regime act as a molecular rectifier. We have realized this device in a GaAs∕Al0.3Ga0.7As heterostructure containing a two-dimensional electron gas using lithographically patterned gates. The current through two tunnel-coupled dots in series is recorded versus applied voltage. Ratchet behavior is created by a third dot, with one lead, tunnel-coupled to one of the two dots. An electron enters the third dot where it is trapped, producing a jamming effect where no other electron may enter the device. The current–voltage characteristics show rectification and negative resistance arising from charging of the third dot.

Triple quantum dot charging rectifier

We study the effects of chemical bonding on Raman scattering from benzenethiol chemisorbed on silver clusters using time-dependent density functional theory (TDDFT). Raman scattering cross sections are computed using a formalism that employs analytical derivatives of frequency-dependent electronic polarizabilities, which treats both off-resonant and resonant enhancement within the same scheme. In the off-resonant regime, Raman scattering into molecular vibrational modes is enhanced by one order of magnitude and shows pronounced dependence on the orientation and the local symmetry of the molecule. Additional strong enhancement of the order of 10(2) arises from resonant transitions to mixed metal-molecular electronic states. The Raman enhancement is analyzed using Raman excitation profiles (REPs) for the range of excitation energies 1.6-3.0 eV, in which isolated benzenethiol does not have electronic transitions. The computed vibrational frequency shifts and relative Raman scattering cross sections of the metal-molecular complexes are in good agreement with experimental data on surface enhanced Raman scattering (SERS) from benzenethiol adsorbed on silver surfaces. Characterization and understanding of these effects, associated with chemical enhancement mechanism, may be used to improve the detection sensitivity in molecular Raman scattering.

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Michael Stopa

Papers

Fast Sensing of Double-Dot Charge Arrangement and Spin State with a Radio-Frequency Sensor Quantum Dot

Quantum dot self-consistent electronic structure and the Coulomb blockade.

Single-electron delocalization in hybrid vertical-lateral double quantum dots.

Triple quantum dot charging rectifier

On the chemical bonding effects in the Raman response: Benzenethiol adsorbed on silver clusters