Single-electron Charging Effects Research Articles

Mesoscopic normal metal-superconductor junction systems: The effective action approach

Single electron charging effects in systems containing small normal and superconducting islands have recently attracted much interest. The theoretical description of these effects usually involves a perturbation theory in the tunneling conductance. While this perturbation theory can be developed on a case-by-case basis, the effective action approach provides a unified and transparent formulation. We use this approach to discuss single electron tunneling, Andreev reflection, the proximity effect and the supercurrent through normal-superconductor systems in the presence of charging effects. We also show that in a real-time formulation the effective action approach can be used to calculate single electron tunneling and co-tunneling rates.

Bistable saturation due to single electron charging in rings of tunnel junctions

The behavior of rings of four small-capacitance tunnel junctions that are charged with two extra electrons is examined. Single electron charging effects result in quantization of charge on the metal electrode islands. To minimize the total electrostatic energy, the electrons localize on opposite electrodes, leading to a charge alignment in one of two configurations. We consider such rings as cells that may be capacitively coupled to each other in a cellular automaton architecture. The interaction between cells results in strong bistable saturation in the cell’s charge alignment which may be used to encode binary information. Lines of such cells can be viewed as binary wires.

Conductance oscillations in Ge/Si heterostructures containing quantum dots

The conductance of the Si/p+-Ge/Si epitaxial heterostructure associated with hole tunnelling into isolated ultrasmall ( approximately 10 nm) quantum dots p+-Ge has been studied. Quantum dots have been obtained after islanding of 1.3 nm Ge film during MBE growth by the Stransky-Krastanov mode method. Conductance oscillations as a function of bias voltage were observed. The experimental data are analysed in terms of a model that involves the interplay of single-electron charging effects and resonant tunnelling through individual energy levels.

Self-consistent analysis of single-electron charging effects in quantum-dot nanostructures.

Self-consistent analysis of single-electron charging effects in quantum-dot nanostructures.

Confined quantum systems in one dimension and conductance oscillations in narrow channels.

An exactly solvable electron model of a confined system with inverse-square interaction is presented. The ground state is given by the Jastrow-product wavefunction of power-law form. We discuss the results in connection with conductance oscillations observed in semiconductor nanostructures, for which single-electron charging effects play a crucial role. Due to the internal spin degrees of freedom, there appear two independent periods of the conductance oscillations in very narrow channels even at zero temperature.

Quantum interferences and charge effects in amorphous alloys near the metal-insulator transition

The magnetoconductance of insulating amorphous alloys is investigated at very low temperature. In bulk 3D samples we observe a crossover at T=100mK from a high temperature Mott hopping regime to an activated regime. The latter regime extends up to higher temperature in thin films, and the I-V curves indicate the existence of single electron charging effects. The magnetic field reinforces the electronic localization in these insulators with strong spin-orbit scattering.

Properties of locally doped bi-crystal grain boundary junctions

A new type of locally doped superconducting weak link has been developed. Fe and Pt were introduced locally in bi-crystal based grain boundaries in YBa 2Cu 3O 7-δ thin films. Pt doping did not influence supercurrent transport noticeably. For Fe doped weak links, a Josephson effect was initially observed but it transformed into a highly resistive, low critical current state after thermal cycling. At that stage, an increased tunneling resistance at low bias and an off-set in voltage at high bias current were observed at temperatures up to 77K. The behavior is interpreted as due to single electron charging effects as narrow superconducting channels across the boundary break up into small metallic particles in an insulating barrier region.

Observation of single-electron charging effect in NbN submicron bridges

Submicron NbN bridges whose thickness, width and length are 10nm, 100nm and 100–300nm respectively, have been fabricated, and their conduction properties and electrical field effect are measured. The samples having resistances larger than ∼ 100kΩ exhibit nonlinear I-V characteristics with offset voltage of 2mV∼12mV at 4.2K which are obviously similar to those of the single-electron charging effect in small tunnel junction arrays. The field effect modulation of the junction conductance is observed by applying a voltage to a gate electrode which is made over the NbN bridge. These charging effects are thought to arise from the granular structure of NbN bridges. The simulation result using one-dimensional SET junction arrays coincide well with experimental result.

Single-electron tunneling transistors incorporating Cooper pair processes

A superconducting single-electron tunneling transistor composed of two ultrasmall capacitance Al/Al/sub 2/O/sub 3//Al tunnel junctions and a capacitively coupled gate electrode has been fabricated. Transistor operation is based on single electron and Cooper pair charging effects. This three-terminal device exhibits novel I-V characteristics not seen in either conventional superconducting tunnel junctions or normal metal Coulomb blockage devices. Current peaks appear above V approximately 2 Delta /e which originate from combined Cooper pair/quasi-particle tunneling processes. These peaks show e-periodic modulation with respect to the gate-induced charge. At lower voltages, the I-V curve shows features which are 2e-periodic. In a magnetic field, it is found that the 2e-periodicity changes into e-periodicity above a crossover line, T*(H). The data strongly suggest the existence of a free energy difference between states with an even versus an odd number of electrons on the metal island between the two junctions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fabrication and characterization of single-electron tunneling transistors in the superconducting state

Electron-beam lithography was used to fabricate single electron charging effect devices with ultrasmall capacitance Al/Al/sub 2/O/sub 3//Al tunnel junctions. The single electron transistor is a three-terminal device composed of two series tunnel junctions and a gate electrode capacitively coupled to the island between them. Typical junctions are of area 60 nm*60 nm with a capacitance of 190 aF. The authors outline the fabrication procedures, discuss operational properties, and give sample handling considerations. These devices exhibit a highly nonlinear I-V characteristic which is modulated by the gate voltage, as expected for the Coulomb blockage. In the superconducting state, the superconducting gap in the quasiparticle density of states leads to transistor action above 1.3 K, a temperature easily reached with pumped liquid /sup 4/He refrigeration. The authors also discuss the observation of an intermittent intrinsic switching noise in the offset charge of the central island. >

Sub-micron field-effect transistor using granular NbN thin films

The conductance modulation induced by an electrostatic field is observed in highly resistive NbN granular thin films at low temperatures. The measurement is performed using a three-terminal device with FET structure, whose channel is made of NbN thin films. The field effect is interpreted based on the single electron charging effect of small intergrain junctions. The submicron-size channel (0.5 mu m) is fabricated by using the electron-beam lithography technique. The conductance modulation is found to be enhanced by the reduction of the channel size. In order to assess the feasibility of the FET using FET phenomena, the gate voltage dependence of the I-V curve and of the conductance of the channel part is examined. The charging effect is discussed on the basis of a one-dimensional array model of the small tunnel junctions. >

Molecular-dynamics study of single-electron charging in semiconductor wires.

A molecular-dynamics technique is applied to single-electron charging effects in semiconductor wires, and the impact of strong electron-electron correlation on the conductance is investigated. Because of the relatively low electron density in semiconductors compared to a metal, the screening length is comparable to the sample size, which requires a treatment beyond the conventional Coulomb-blockade argument using macroscopic capacitance. Based on the molecular-dynamics method, most features of the periodic conductance oscillation in the double-barrier system are reproduced, and the feasibility of this technique in single-electron charging phenomena is demonstrated. Experimental observation of an activation energy smaller than the threshold energy of the nonlinear conductance, which the normal Coulomb-blockade model cannot explain, is reproduced in the present approach. This effect is due to the strong microscopic correlation, so that this is essential to describe accurately the single-electron charging effects in semiconductor systems.

Quantum mechanics of the electromagnetic environment in the single-junction Coulomb blockade

We discuss the interaction of a tunneling electron with its electromagnetic environment when the latter either is in equilibrium or includes an applied microwave field. The environment of an isolated tunnel junction is modeled by a set of harmonic oscillators that are suddenly displaced when an electron tunnels across the junction. We treat these displaced oscillators quantum mechanically, predicting behavior that is very different than that predicted by a semiclassical treatment. In particular, the shape of the zero-bias anomaly caused by the Coulomb blockade (a single-electron charging effect), is found to be strongly dependent on the impedance, Z(ω), of the leads connected to the junction. Comparison with three recent experiments demonstrates that the quantum mechanical treatment of this model correctly describes the essential physics in these systems.

Resonance-level broadening by environmental fluctuations

The influence of the fluctuations of the electromagnetic environment on resonant tunneling is investigated in a rigorous way. Resonance-level broadening is found to be governed by the environmental impedance and temperature. It is found that the high-frequency limit of resonant tunneling devices is determined by the discharging time of the whole circuit. The obtained criterion for the observation of single-electron charging effects in resonant tunneling R&gt;8${\mathit{R}}_{\mathit{Q}}$=8\ensuremath{\pi}\ensuremath{\Elzxh}/${\mathit{e}}^{2}$ is much stronger than the R&gt;${\mathit{R}}_{\mathit{Q}}$ used in the theory of the Coulomb blockades.

Single-electron charging effects in insulating wires.

We present measurements of the transport properties of 0.75-\ensuremath{\mu}m-long, narrow, insulating indium oxide wires and rings. These devices have no apparent tunnel barriers, yet they exhibit effects similar to those found in series arrays of very small-capacitance tunnel junctions: highly nonlinear I-V characteristics and a zero-bias conductance which is periodic in a voltage applied by means of a lateral gate. These effects are due to the influence of single-electron charging on transport through localized states in the insulating regime.

Single electron charging effects in semiconductor quantum dots

We have studied charging effects in a lateral split-gate quantum dot defined by metal gates in the two dimensional electron gas (2 DEG) of a GaAs/AlGaAs heterostructure. The gate structure allows an independent control of the conductances of the two tunnel barriers separating the quantum dot from the two 2 DEG leads, and enables us to vary the number of electrons that are localized in the dot. We have measured Coulomb oscillations in the conductance and the Coulomb staircase in current-voltage characteristics and studied their dependence on the conductances of the tunnel barriers. We show experimentally that at zero magnetic field charging effects start to affect the transport properties when both barrier conductances are smaller than the first quantized conductance value of a point contact at 2e2/h. The experiments are described by a simple model in terms of electrochemical potentials, which includes both the discreteness of the electron charge and the quantum energy states due to confinement.

Coulomb blockade in single tunnel-junctions: Quantum mechanical effects of the electromagnetic environment

We discuss the interaction of a tunneling electron with its equilibrium electromagnetic environment. The environment of an isolated tunnel junction is modeled by a set of harmonic oscillators that are suddenly displaced when an electron tunnels across the junction. We treat these displaced oscillators quantum mechanically, predicting behavior that is very different than that predicted by a semiclassical treatment. In particular, the shape of the zero-bias anomaly caused by the Coulomb blockade (a single-electron charging effect), is found to be strongly dependent on the impedance,Z (ω), of the leads connected to the junction. Comparison with three recent experiments demonstrates that the quantum mechanical treatment of this model correctly describes the essential physics in these systems.

Quantized current in a quantum dot turnstile

We have performed RF experiments on a lateral quantum dot defined in the two dimensional electron gas (2DEG) of a GaAs/AlGaAs heterostructure. The small capacitance of the quantum dot gives rise to single-electron charging effects, which we employed to realize a quantum dot turnstile device. By modulating the tunnel barriers between the quantum dot and the 2DEG leads with two phase-shifted RF signals, we pass an integer number of electrons through the quantum dot per RF cycle. This is demonstrated by the observation of quantized current plateaus at multiples ofef in current-voltage characteristics, wheref is the frequency of the RF signals. When an asymmetry is induced by applying unequal RF voltages, our quantum dot turnstile operates as a single-electron pump producing a quantized current at zero bias voltage.

Theory of single-electron charging of quantum wells and dots.

Single-electron charging effects similar to those in small-area metallic tunnel junctions should take place in semiconductor heterostructures, in particular, small-area quantum wells. Our analysis shows that dc current-voltage characteristics of such a well should exhibit an interplay between single-electron charging and energy-quantization effects. Relative magnitude of the single-electron charging effects is determined by the same parameter which scales multielectron charging in the conventional (large-area) quantum wells.

Tunneling time and offset charging in small tunnel junctions

Measurements of single electron charging effects in serially coupled tunnel junctions are presented. The results show that the tunneling time is much longer than the barrier traversal time. We find evidence for the presence of offset charging of the junctions.