Non-adiabatic quantized charge pumping with tunable-barrier quantum dots: a review of current progress.

Precise manipulation of individual charge carriers in nanoelectronic circuits underpins practical applications of their most basic quantum property--the universality and invariance of the elementary charge. A charge pump generates a net current from periodic external modulation of parameters controlling a nanostructure connected to source and drain leads; in the regime of quantized pumping the current varies in steps of [Formula: see text] as function of control parameters, where [Formula: see text] is the electron charge and f is the frequency of modulation. In recent years, robust and accurate quantized charge pumps have been developed based on semiconductor quantum dots with tunable tunnel barriers. These devices allow modulation of charge exchange rates between the dot and the leads over many orders of magnitude and enable trapping of a precise number of electrons far away from equilibrium with the leads. The corresponding non-adiabatic pumping protocols focus on understanding of separate parts of the pumping cycle associated with charge loading, capture and release. In this report we review realizations, models and metrology applications of quantized charge pumps based on tunable-barrier quantum dots.

Self-referenced single-electron quantized current source.

The future redefinition of the international system of units in terms of natural constants requires a robust, high-precision quantum standard for the electrical base unit ampere. However, the reliability of any single-electron current source generating a nominally quantized output current I=ef by delivering single electrons with charge e at a frequency f is eventually limited by the stochastic nature of the underlying quantum mechanical tunneling process. We experimentally explore a path to overcome this fundamental limitation by serially connecting clocked single-electron emitters with multiple in situ single-electron detectors. Correlation analysis of the detector signatures during current generation reveals erroneous pumping events and enables us to determine the deviation of the output current from the nominal quantized value ef. This demonstrates the concept of a self-referenced single-electron source for electrical quantum metrology.

Counting statistics for electron capture in a dynamic quantum dot.

We report noninvasive single-charge detection of the full probability distribution P(n) of the initialization of a quantum dot with n electrons for rapid decoupling from an electron reservoir. We analyze the data in the context of a model for sequential tunneling pinch-off, which has generic solutions corresponding to two opposing mechanisms. One limit considers sequential "freeze-out" of an adiabatically evolving grand canonical distribution, the other one is an athermal limit equivalent to the solution of a generalized decay cascade model. We identify the athermal capturing mechanism in our sample, testifying to the high precision of our combined theoretical and experimental methods. The distinction between the capturing mechanisms allows us to derive efficient experimental strategies for improving the initialization.

A molecular quantized charge pump.

A novel single electron pump based on individual molecules (a single wall carbon nanotube) is discussed in terms of the hybrid superconducting-normal conducting pumping principle. A concept demonstration device has been built based on a carbon nanotube contacted by Nb-Ti leads. Charge current quantization is achieved through rf modulation of the back gate voltage. The device is able to transfer a given number of electrons per pumping cycle. Single electron pumping is achieved for pumping frequencies up to 80 MHz.

Universal decay cascade model for dynamic quantum dot initialization.

Dynamic quantum dots can be formed by time-dependent electrostatic potentials, such as in gate- or surface-acoustic-wave-driven electron pumps. In this work we propose and quantify a scheme to initialize quantum dots with a controllable number of electrons. It is based on a rapid increase of the electron potential energy and simultaneous decoupling from the source lead. The full probability distribution for the final number of captured electrons is obtained by solving a master equation for stochastic cascade of single electron escape events. We derive an explicit fitting formula to extract the sequence of decay rate ratios from the measurements of averaged current in a periodically driven device. This provides a device-specific fingerprint which allows us to compare different architectures, and predict the upper limits of initialization accuracy from low precision measurements.