We report electronic transport experiments on a graphene single electron transistor. The device consists of a graphene island connected to source and drain electrodes via two narrow graphene constrictions. It is electrostatically tunable by three lateral graphene gates and an additional back gate. The tunneling coupling is a strongly nonmonotonic function of gate voltage indicating the presence of localized states in the barriers. We investigate energy scales for the tunneling gap, the resonances in the constrictions, and for the Coulomb blockade resonances. From Coulomb diamond measurements in different device configurations (i.e., barrier configurations) we extract a charging energy of ≈3.4 meV and estimate a characteristic energy scale for the constriction resonances of ≈10 meV.

/pdf/tunable-graphene-single-electron-transistor-37i0bt5z0a.pdf

Tunable Graphene Single Electron Transistor

The control electrons at the level of the elementary charge e was demonstrated experimentally already in the 1980s. Ever since, the production of an electrical current ef, or its integer multiple, at a drive frequency f has been in a focus of research for metrological purposes.This review discusses the generic physical phenomena and technical constraints that influence single-electron charge transport and presents a broad variety of proposed realizations. Some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently ‘‘just’’ wild ideas, still often potentially competitive if technical constraints can be lifted. The important issues of readout of singleelectron events and potential error correction schemes based on them are also discussed. Finally, an account is given of the status of single-electron current sources in the bigger framework of electric quantum standards and of the future international SI system of units, and applications and uses of single-electron devices outside the metrological context are briefly discussed.

/pdf/single-electron-current-sources-toward-a-refined-definition-5atnvohwg2.pdf

Single-electron current sources: Toward a refined definition of the ampere

We report on Coulomb blockade and Coulomb diamond measurements on an etched, tunable single-layer graphene quantum dot. The device consisting of a graphene island connected via two narrow graphene constrictions is fully tunable by three lateral graphene gates. Coulomb blockade resonances are observed and from Coulomb diamond measurements, a charging energy of ≈3.5meV is extracted. For increasing temperatures, we detect a peak broadening and a transmission increase of the nanostructured graphene barriers.

https://people.phys.ethz.ch/~ihn/papers/Stampfer08.pdf

Tunable Coulomb blockade in nanostructured graphene

Single electron pumps have been proposed as potential candidates for redefining the ampere. This study reports measurements of the quantized current flowing through a semiconductor electron pump with a precision that makes a substantial step towards establishing a direct metric for electrical currents.

/pdf/towards-a-quantum-representation-of-the-ampere-using-single-3ht3itrd1r.pdf

Towards a quantum representation of the ampere using single electron pumps

The introduction of disorder into thin superconducting films induces a droplet-like electronic texture, with superconducting islands immersed in a normal matrix. By fine-tuning this disorder, the system can be transformed from superconductor to insulator. A paper in this issue presents experimental evidence for the involvement of a previously uncharacterized 'superinsulating' state of matter in this process, a 'mirror image' equivalent of a superconductor with infinite resistance. During the transition from superconductor to insulator, a distinct conductivity state is formed, a Cooper-pair insulator, with thermally activated conductivity. Experiments in titanium nitride films show that at a certain finite temperature, a Cooper-pair insulator becomes a superinsulator, a state resembling superconductivity in that it is destroyed by a sufficiently strong critical magnetic field, and breaks down at some critical voltage. This paper shows that at a certain finite temperature, a Cooper-pair insulator undergoes a transition to a superinsulating state with infinite resistance. Experimental evidence of this transition in titanium nitride films is presented and it is demonstrated that the superinsulating state is dual to the superconducting state: it is destroyed by a sufficiently strong critical magnetic field, and breaks down at some critical voltage which is analogous to the critical current in superconductors. Synchronized oscillators are ubiquitous in nature1, and synchronization plays a key part in various classical and quantum phenomena. Several experiments2,3,4 have shown that in thin superconducting films, disorder enforces the droplet-like electronic texture—superconducting islands immersed into a normal matrix—and that tuning disorder drives the system from superconducting to insulating behaviour. In the vicinity of the transition, a distinct state4 forms: a Cooper-pair insulator, with thermally activated conductivity. It results from synchronization of the phase of the superconducting order parameter at the islands across the whole system5. Here we show that at a certain finite temperature, a Cooper-pair insulator undergoes a transition to a superinsulating state with infinite resistance. We present experimental evidence of this transition in titanium nitride films and show that the superinsulating state is dual to the superconducting state: it is destroyed by a sufficiently strong critical magnetic field, and breaks down at some critical voltage that is analogous to the critical current in superconductors.

/pdf/superinsulator-and-quantum-synchronization-3ql8s5i7n6.pdf

Superinsulator and quantum synchronization

We report on the operation of a single-electron pump (comprising three Al/AlOx/Al tunnel junctions and two gates) connected to the bias electrodes through the compact on-chip Cr resistors, R≈60 kΩ>Rk=h/e2≈26 kΩ. The function of the resistors in this so-called R pump was to suppress electron cotunneling, the process which otherwise severely deteriorates the performance of few-junction single-electron devices. When a harmonic ac drive of frequency f of several MHz was applied to the gates, the current–voltage curve of the R pump exhibited remarkably horizontal current steps at I=ef. We show that the use of the resistors is capable of substantially increasing the accuracy of the pump in comparison to operation of the pump without resistors.

Operation of a three-junction single-electron pump with on-chip resistors

We report on the investigation of Al single electron structures equipped with miniature (8 um long) on-chip Cr resistors of R > R_k = h/e^2 = 25.8 kOhm. From the measurement of the Coulomb blockade in single-junction structures we evaluated the self-capacitance of our resistors per unit length, c = 62 aF/um. We demonstrate that the cotunneling current in the transistor samples in the Coulomb blockade regime obeys the power law, $I \propto V^{3+(R/R_k)}$, predicted by Odintsov, Bubanja and Schon for a transistor having pure ohmic-resistance leads. The concept of the three-junction single electron pump with on-chip resistors (R-pump) is developed. We demonstrate that the implementation of the R-pump with a relative accuracy of the electron transfer of 10^{-8} is quite feasible with the technology available.

Coulomb blockade and cotunneling in single electron circuits with on-chip resistors: towards the implementation of R-pump

We investigate the dynamics of individual quasiparticle excitations on a small superconducting aluminum island connected to normal metallic leads by tunnel junctions. We find the island to be free of excitations within the measurement resolution. This allows us to show that the residual heating, which typically limits experiments on superconductors, has an ultralow value of less than 0.1 aW. By injecting electrons with a periodic gate voltage, we probe electron-phonon interaction and relaxation down to a single quasiparticle excitation pair, with a measured recombination rate of 16 kHz. Our experiment yields a strong test of BCS theory in aluminum as the results are consistent with it without free parameters.

/pdf/excitation-of-single-quasiparticles-in-a-small-1ltjljs98n.pdf

Excitation of single quasiparticles in a small superconducting Al island connected to normal-metal leads by tunnel junctions.

The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 107. This paper reports the considerable progress recently achieved with a new generation of single-electron tunnelling devices. A five-junction R-pump was operated with a relative charge transfer error of five electrons in 107, and was used to successfully perform single-electron charging of a cryogenic capacitor. The preliminary result for the single-electron charge quantum has an uncertainty of less than two parts in 106 and is consistent with the value of the elementary charge.

http://iopscience.iop.org/article/10.1088/0026-1394/49/1/002/pdf

Electron Counting Capacitance Standard with an improved five-junction R-pump

The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 10^7. This paper reports the considerable progress recently achieved with a new generation of single-electron tunnelling devices. A five-junction R-pump was operated with a relative charge transfer error of five electrons in 10^7, and was used to successfully perform single-electron charging of a cryogenic capacitor. The preliminary result for the single-electron charge quantum has an uncertainty of less than two parts in 10^6 and is consistent with the value of the elementary charge.

Sergey V. Lotkhov

Papers

Operation of a three-junction single-electron pump with on-chip resistors

Coulomb blockade and cotunneling in single electron circuits with on-chip resistors: towards the implementation of R-pump

Excitation of single quasiparticles in a small superconducting Al island connected to normal-metal leads by tunnel junctions.

Electron Counting Capacitance Standard with an improved five-junction R-pump

Electron Counting Capacitance Standard with an improved five-junction R-pump