Time-resolved Coulomb collision of single electrons.

A series of recent experiments have shown that collision of ballistic electrons in semiconductors can be used to probe the indistinguishability of single-electron wavepackets. Perhaps surprisingly, their Coulomb interaction has not been seen due to screening. Here we show Coulomb-dominated collision of high-energy single electrons in counter-propagating ballistic edge states, probed by measuring partition statistics while adjusting the collision timing. Although some experimental data suggest antibunching behaviour, we show that this is not due to quantum statistics but to strong repulsive Coulomb interactions. This prevents the wavepacket overlap needed for fermionic exchange statistics but suggests new ways to utilize Coulomb interactions: microscopically isolated and time-resolved interactions between ballistic electrons can enable the use of the Coulomb interaction for high-speed sensing or gate operations on flying electron qubits.

Electrically Controllable Kondo Correlation in Spin-Orbit-Coupled Quantum Point Contacts.

Integrating the Kondo correlation and spin-orbit interactions, each of which have individually offered unprecedented means to manipulate electron spins, in a controllable way can open up new possibilities for spintronics. We demonstrate electrical control of the Kondo correlation by coupling the bound spin to leads with tunable Rashba spin-orbit interactions, realized in semiconductor quantum point contacts. We observe a transition from single to double peak zero-bias anomalies in nonequilibrium transport-the manifestation of the Kondo effect-indicating a controlled Kondo spin reversal using only spin-orbit interactions. Universal scaling of the Kondo conductance is demonstrated, implying that the spin-orbit interactions could enhance the Kondo temperature. A theoretical model based on quantum master equations is also developed to calculate the nonequilibrium quantum transport.

Continuous-variable tomography of solitary electrons.

A method for characterising the wave-function of freely-propagating particles would provide a useful tool for developing quantum-information technologies with single electronic excitations. Previous continuous-variable quantum tomography techniques developed to analyse electronic excitations in the energy-time domain have been limited to energies close to the Fermi level. We show that a wide-band tomography of single-particle distributions is possible using energy-time filtering and that the Wigner representation of the mixed-state density matrix can be reconstructed for solitary electrons emitted by an on-demand single-electron source. These are highly localised distributions, isolated from the Fermi sea. While we cannot resolve the pure state Wigner function of our excitations due to classical fluctuations, we can partially resolve the chirp and squeezing of the Wigner function imposed by emission conditions and quantify the quantumness of the source. This tomography scheme, when implemented with sufficient experimental resolution, will enable quantum-limited measurements, providing information on electron coherence and entanglement at the individual particle level.

Experimental Realization of a Quantum Dot Energy Harvester.

We demonstrate experimentally an autonomous nanoscale energy harvester that utilizes the physics of resonant tunneling quantum dots. Gate-defined quantum dots on GaAs/AlGaAs high-electron-mobility transistors are placed on either side of a hot-electron reservoir. The discrete energy levels of the quantum dots are tuned to be aligned with low energy electrons on one side and high energy electrons on the other side of the hot reservoir. The quantum dots thus act as energy filters and allow for the conversion of heat from the cavity into electrical power. Our energy harvester, measured at an estimated base temperature of 75 mK in a He^{3}/He^{4} dilution refrigerator, can generate a thermal power of 0.13 fW for a temperature difference across each dot of about 67 mK.

Momentum-dependent power law measured in an interacting quantum wire beyond the Luttinger limit.

Power laws in physics have until now always been associated with a scale invariance originating from the absence of a length scale. Recently, an emergent invariance even in the presence of a length scale has been predicted by the newly-developed nonlinear-Luttinger-liquid theory for a one-dimensional (1D) quantum fluid at finite energy and momentum, at which the particle's wavelength provides the length scale. We present experimental evidence for this new type of power law in the spectral function of interacting electrons in a quantum wire using a transport-spectroscopy technique. The observed momentum dependence of the power law in the high-energy region matches the theoretical predictions, supporting not only the 1D theory of interacting particles beyond the linear regime but also the existence of a new type of universality that emerges at finite energy and momentum.

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.

Controlled spatial separation of spins and coherent dynamics in spin-orbit-coupled nanostructures.

The spatial separation of electron spins followed by the control of their individual spin dynamics has recently emerged as an essential ingredient in many proposals for spin-based technologies because it would enable both of the two spin species to be simultaneously utilized, distinct from most of the current spintronic studies and technologies wherein only one spin species could be handled at a time. Here we demonstrate that the spatial spin splitting of a coherent beam of electrons can be achieved and controlled using the interplay between an external magnetic field and Rashba spin-orbit interaction in semiconductor nanostructures. The technique of transverse magnetic focusing is used to detect this spin separation. More notably, our ability to engineer the spin-orbit interactions enables us to simultaneously manipulate and probe the coherent spin dynamics of both spin species and hence their correlation, which could open a route towards spintronics and spin-based quantum information processing.

Nonlinear spectra of spinons and holons in short GaAs quantum wires.

One-dimensional electronic fluids are peculiar conducting systems, where the fundamental role of interactions leads to exotic, emergent phenomena, such as spin-charge (spinon-holon) separation. The distinct low-energy properties of these 1D metals are successfully described within the theory of linear Luttinger liquids, but the challenging task of describing their high-energy nonlinear properties has long remained elusive. Recently, novel theoretical approaches accounting for nonlinearity have been developed, yet the rich phenomenology that they predict remains barely explored experimentally. Here, we probe the nonlinear spectral characteristics of short GaAs quantum wires by tunnelling spectroscopy, using an advanced device consisting of 6000 wires. We find evidence for the existence of an inverted (spinon) shadow band in the main region of the particle sector, one of the central predictions of the new nonlinear theories. A (holon) band with reduced effective mass is clearly visible in the particle sector at high energies.

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.

Hierarchy of modes in an interacting one-dimensional system.

Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R^{2}/L^{2}, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.

All-electric all-semiconductor spin field-effect transistors.

The spin field-effect transistor envisioned by Datta and Das opens a gateway to spin information processing. Although the coherent manipulation of electron spins in semiconductors is now possible, the realization of a functional spin field-effect transistor for information processing has yet to be achieved, owing to several fundamental challenges such as the low spin-injection efficiency due to resistance mismatch, spin relaxation and the spread of spin precession angles. Alternative spin transistor designs have therefore been proposed, but these differ from the field-effect transistor concept and require the use of optical or magnetic elements, which pose difficulties for incorporation into integrated circuits. Here, we present an all-electric and all-semiconductor spin field-effect transistor in which these obstacles are overcome by using two quantum point contacts as spin injectors and detectors. Distinct engineering architectures of spin-orbit coupling are exploited for the quantum point contacts and the central semiconductor channel to achieve complete control of the electron spins (spin injection, manipulation and detection) in a purely electrical manner. Such a device is compatible with large-scale integration and holds promise for future spintronic devices for information processing.

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).

Confocal microphotoluminescence mapping of coupled and detuned states in photonic molecules.

We study the coupling of cavities defined by the local modulation of the waveguide width using confocal photoluminescence microscopy. We are able to spatially map the profile of the antisymmetric (antibonding) and symmetric (bonding) modes of a pair of strongly coupled cavities (photonic molecule) and follow the coupled cavity system from the strong coupling to the weak coupling regime in the presence of structural disorder. The effect of disorder on this photonic molecule is also investigated numerically with a finite-difference time-domain method and a semi-analytical approach, which enables us to quantify the light localization observed in either cavity as a function of detuning.

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.

Unraveling quantum Hall breakdown in bilayer graphene with scanning gate microscopy.

Investigating the structure of quantized plateaus in the Hall conductance of graphene is a powerful way of probing its crystalline and electronic structure and will also help to establish whether graphene can be used as a robust standard of resistance for quantum metrology. We use low-temperature scanning gate microscopy to image the interplateau breakdown of the quantum Hall effect in an exfoliated bilayer graphene flake. Scanning gate images captured during breakdown exhibit intricate patterns where the conductance is strongly affected by the presence of the scanning probe tip. The maximum density and intensity of the tip-induced conductance perturbations occur at half-integer filling factors, midway between consecutive quantum Hall plateau, while the intensity of individual sites shows a strong dependence on tip-voltage. Our results are well-described by a model based on quantum percolation which relates the points of high responsivity to tip-induced scattering in a network of saddle points separating localized states.

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.

Compressibility measurements of quasi-one-dimensional quantum wires.

We report measurements of the compressibility of a one-dimensional quantum wire, defined in the upper well of a GaAs/AlGaAs double quantum well heterostructure. A wire defined simultaneously in the lower well probes the ability of the upper wire to screen the electric field from a biased surface gate. The technique is sensitive enough to resolve spin splitting of the subbands in the presence of an in-plane magnetic field. We measure a compressibility signal due to the 0.7 structure and study its evolution with increasing temperature and magnetic field. We see no evidence of the formation of the quasibound state predicted by the Kondo model, instead our data are consistent with theories which predict that the 0.7 structure arises as a result of spontaneous spin polarization.

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.

Probing spin-charge separation in a Tomonaga-Luttinger liquid.

In a one-dimensional (1D) system of interacting electrons, excitations of spin and charge travel at different speeds, according to the theory of a Tomonaga-Luttinger liquid (TLL) at low energies. However, the clear observation of this spin-charge separation is an ongoing challenge experimentally. We have fabricated an electrostatically gated 1D system in which we observe spin-charge separation and also the predicted power-law suppression of tunneling into the 1D system. The spin-charge separation persists even beyond the low-energy regime where the TLL approximation should hold. TLL effects should therefore also be important in similar, but shorter, electrostatically gated wires, where interaction effects are being studied extensively worldwide.

Electronic refrigeration of a two-dimensional electron gas.

Measurements are presented of a device designed to cool a 6 microm;{2} region of 2D electron gas using quantum dots. Electrostatic effects are found to be significant in the device, and a model that accounts for them is developed. At ambient electron temperatures above 120 mK the results are consistent with the model and the base temperature of the cooled region is estimated. At an ambient electron temperature of 280 mK, the 6 microm;{2} region is found to be cooled below 190 mK. Below 120 mK the results deviate from predictions, which is attributed to reduced electron-electron scattering rates.