LO-Phonon Emission Rate of Hot Electrons from an On-Demand Single-Electron Source in a GaAs/AlGaAs Heterostructure.

Using a recent time-of-flight measurement technique with 1 ps time resolution and electron-energy spectroscopy, we develop a method to measure the longitudinal-optical-phonon emission rate of hot electrons traveling along a depleted edge of a quantum Hall bar. Comparison to a single-particle model implies the scattering mechanism involves a two-step process via an intra-Landau-level transition. We show that this can be suppressed by control of the edge potential profile, and a scattering length >1 mm can be achieved, allowing the use of this system for scalable single-electron device applications.

Time-of-Flight Measurements of Single-Electron Wave Packets in Quantum Hall Edge States.

We report time-of-flight measurements on electrons traveling in quantum Hall edge states. Hot-electron wave packets are emitted one per cycle into edge states formed along a depleted sample boundary. The electron arrival time is detected by driving a detector barrier with a square wave that acts as a shutter. By adding an extra path using a deflection barrier, we measure a delay in the arrival time, from which the edge-state velocity v is deduced. We find that v follows 1/B dependence, in good agreement with the E[over →]×B[over →] drift. The edge potential is estimated from the energy dependence of v using a harmonic approximation.

Influence of Impurity Spin Dynamics on Quantum Transport in Epitaxial Graphene.

Experimental evidence from both spin-valve and quantum transport measurements points towards unexpectedly fast spin relaxation in graphene. We report magnetotransport studies of epitaxial graphene on SiC in a vector magnetic field showing that spin relaxation, detected using weak-localization analysis, is suppressed by an in-plane magnetic field B(∥), and thereby proving that it is caused at least in part by spinful scatterers. A nonmonotonic dependence of the effective decoherence rate on B(∥) reveals the intricate role of the scatterers' spin dynamics in forming the interference correction to the conductivity, an effect that has gone unnoticed in earlier weak localization studies.

Quantum Hall effect and quantum point contact in bilayer-patched epitaxial graphene.

We study an epitaxial graphene monolayer with bilayer inclusions via magnetotransport measurements and scanning gate microscopy at low temperatures. We find that bilayer inclusions can be metallic or insulating depending on the initial and gated carrier density. The metallic bilayers act as equipotential shorts for edge currents, while closely spaced insulating bilayers guide the flow of electrons in the monolayer constriction, which was locally gated using a scanning gate probe.

Quantum resistance metrology using graphene.

In this paper, we review the recent extraordinary progress in the development of a new quantum standard for resistance based on graphene. We discuss the unique properties of this material system relating to resistance metrology and discuss results of the recent highest-ever precision direct comparison of the Hall resistance between graphene and traditional GaAs. We mainly focus our review on graphene expitaxially grown on SiC, a system which so far resulted in the best results. We also briefly discuss progress in the two other graphene material systems, exfoliated graphene and chemical vapour deposition graphene, and make a critical comparison with SiC graphene. Finally, we discuss other possible applications of graphene in metrology.

Phase space for the breakdown of the quantum Hall effect in epitaxial graphene.

We report the phase space defined by the quantum Hall effect breakdown in polymer gated epitaxial graphene on SiC (SiC/G) as a function of temperature, current, carrier density, and magnetic fields up to 30 T. At 2 K, breakdown currents (I(c)) almost 2 orders of magnitude greater than in GaAs devices are observed. The phase boundary of the dissipationless state (ρ(xx)=0) shows a [1-(T/T(c))2] dependence and persists up to T(c)>45 K at 29 T. With magnetic field I(c) was found to increase ∝B(3/2) and T(c)∝B2. As the Fermi energy pproaches the Dirac point, the ν=2 quantized Hall plateau appears continuously from fields as low as 1 T up to at least 19 T due to a strong magnetic field dependence of the carrier density.

Clock-controlled emission of single-electron wave packets in a solid-state circuit.

We demonstrate the energy- and time-resolved detection of single-electron wave packets from a clock-controlled source transmitted through a high-energy quantum Hall edge channel. A quantum dot source is loaded with single electrons which are then emitted ~150 meV above the Fermi energy. The energy spectroscopy of emitted electrons indicates that at high magnetic field these electrons can be transported over several microns without inelastic electron-electron or electron-phonon scattering. Using a time-resolved spectroscopic technique, we deduce the wave packet size at picosecond resolution. We also show how this technique can be used to switch individual electrons into different electron waveguides (edge channels).

Disordered Fermi liquid in epitaxial graphene from quantum transport measurements.

We have performed magnetotransport measurements on monolayer epitaxial graphene and analyzed them in the framework of the disordered Fermi liquid theory. We have separated the electron-electron and weak-localization contributions to resistivity and demonstrated the phase coherence over a micrometer length scale, setting the limit of at least 50 ps on the spin relaxation time in this material.

Tunable nonadiabatic excitation in a single-electron quantum dot.

We report the observation of nonadiabatic excitations of single electrons in a quantum dot. Using a tunable-barrier single-electron pump, we have developed a way of reading out the excitation spectrum and level population of the dot by using the pump current as a probe. When the potential well is deformed at subnanosecond time scales, electrons are excited to higher levels. In the presence of a perpendicular magnetic field, the excited states follow a Fock-Darwin spectrum. Our experiments provide a simple model system to study nonadiabatic processes of quantum particles.

Giant quantum Hall plateaus generated by charge transfer in epitaxial graphene.

Epitaxial graphene has proven itself to be the best candidate for quantum electrical resistance standards due to its wide quantum Hall plateaus with exceptionally high breakdown currents. However one key underlying mechanism, a magnetic field dependent charge transfer process, is yet to be fully understood. Here we report measurements of the quantum Hall effect in epitaxial graphene showing the widest quantum Hall plateau observed to date extending over 50 T, attributed to an almost linear increase in carrier density with magnetic field. This behaviour is strong evidence for field dependent charge transfer from charge reservoirs with exceptionally high densities of states in close proximity to the graphene. Using a realistic framework of broadened Landau levels we model the densities of donor states and predict the field dependence of charge transfer in excellent agreement with experimental results, thus providing a guide towards engineering epitaxial graphene for applications such as quantum metrology.

Hot carrier relaxation of Dirac fermions in bilayer epitaxial graphene.

Energy relaxation of hot Dirac fermions in bilayer epitaxial graphene is experimentally investigated by magnetotransport measurements on Shubnikov-de Haas oscillations and weak localization. The hot-electron energy loss rate is found to follow the predicted Bloch-Grüneisen power-law behaviour of T(4) at carrier temperatures from 1.4 K up to ∼100 K, due to electron-acoustic phonon interactions with a deformation potential coupling constant of 22 eV. A carrier density dependence n(e)(-1.5) in the scaling of the T(4) power law is observed in bilayer graphene, in contrast to the n(e)(-0.5) dependence in monolayer graphene, leading to a crossover in the energy loss rate as a function of carrier density between these two systems. The electron-phonon relaxation time in bilayer graphene is also shown to be strongly carrier density dependent, while it remains constant for a wide range of carrier densities in monolayer graphene. Our results and comparisons between the bilayer and monolayer exhibit a more comprehensive picture of hot carrier dynamics in graphene systems.

Gigahertz quantized charge pumping in graphene quantum dots.

Single-electron pumps are set to revolutionize electrical metrology by enabling the ampere to be redefined in terms of the elementary charge of an electron. Pumps based on lithographically fixed tunnel barriers in mesoscopic metallic systems and normal/superconducting hybrid turnstiles can reach very small error rates, but only at megahertz pumping speeds that correspond to small currents of the order of picoamperes. Tunable barrier pumps in semiconductor structures are operated at gigahertz frequencies, but the theoretical treatment of the error rate is more complex and only approximate predictions are available. Here, we present a monolithic, fixed-barrier single-electron pump made entirely from graphene that performs at frequencies up to several gigahertz. Combined with the record-high accuracy of the quantum Hall effect and proximity-induced Josephson junctions, quantized-current generation brings an all-graphene closure of the quantum metrological triangle within reach. Envisaged applications for graphene charge pumps outside quantum metrology include single-photon generation via electron-hole recombination in electrostatically doped bilayer graphene reservoirs, single Dirac fermion emission in relativistic electron quantum optics and read-out of spin-based graphene qubits in quantum information processing.

Towards a quantum representation of the ampere using single electron pumps.

Electron pumps generate a macroscopic electric current by controlled manipulation of single electrons. Despite intensive research towards a quantum current standard over the last 25 years, making a fast and accurate quantized electron pump has proved extremely difficult. Here we demonstrate that the accuracy of a semiconductor quantum dot pump can be dramatically improved by using specially designed gate drive waveforms. Our pump can generate a current of up to 150 pA, corresponding to almost a billion electrons per second, with an experimentally demonstrated current accuracy better than 1.2 parts per million (p.p.m.) and strong evidence, based on fitting data to a model, that the true accuracy is approaching 0.01 p.p.m. This type of pump is a promising candidate for further development as a realization of the SI base unit ampere, following a redefinition of the ampere in terms of a fixed value of the elementary charge.

Towards a quantum resistance standard based on epitaxial graphene.

The quantum Hall effect allows the international standard for resistance to be defined in terms of the electron charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of R(K) = h/e(2) = 25,812.807557(18) Omega, the resistance quantum. Despite 30 years of research into the quantum Hall effect, the level of precision necessary for metrology--a few parts per billion--has been achieved only in silicon and iii-v heterostructure devices. Graphene should, in principle, be an ideal material for a quantum resistance standard, because it is inherently two-dimensional and its discrete electron energy levels in a magnetic field (the Landau levels) are widely spaced. However, the precisions demonstrated so far have been lower than one part per million. Here, we report a quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene at 300 mK, four orders of magnitude better than previously reported. Moreover, by demonstrating the structural integrity and uniformity of graphene over hundreds of micrometres, as well as reproducible mobility and carrier concentrations across a half-centimetre wafer, these results boost the prospects of using epitaxial graphene in applications beyond quantum metrology.