Absolute timing of the photoelectric effect.

Photoemission spectroscopy is central to understanding the inner workings of condensed matter, from simple metals and semiconductors to complex materials such as Mott insulators and superconductors1. Most state-of-the-art knowledge about such solids stems from spectroscopic investigations, and use of subfemtosecond light pulses can provide a time-domain perspective. For example, attosecond (10-18 seconds) metrology allows electron wave packet creation, transport and scattering to be followed on atomic length scales and on attosecond timescales2-7. However, previous studies could not disclose the duration of these processes, because the arrival time of the photons was not known with attosecond precision. Here we show that this main source of ambiguity can be overcome by introducing the atomic chronoscope method, which references all measured timings to the moment of light-pulse arrival and therefore provides absolute timing of the processes under scrutiny. Our proof-of-principle experiment reveals that photoemission from the tungsten conduction band can proceed faster than previously anticipated. By contrast, the duration of electron emanation from core states is correctly described by semiclassical modelling. These findings highlight the necessity of treating the origin, initial excitation and transport of electrons in advanced modelling of the attosecond response of solids, and our absolute data provide a benchmark. Starting from a robustly characterized surface, we then extend attosecond spectroscopy towards isolating the emission properties of atomic adsorbates on surfaces and demonstrate that these act as photoemitters with instantaneous response. We also find that the tungsten core-electron timing remains unchanged by the adsorption of less than one monolayer of dielectric atoms, providing a starting point for the exploration of excitation and charge migration in technologically and biologically relevant adsorbate systems.

Electron-Hole Crossover in Gate-Controlled Bilayer Graphene Quantum Dots.

Electron and hole Bloch states in bilayer graphene exhibit topological orbital magnetic moments with opposite signs, which allows for tunable valley-polarization in an out-of-plane magnetic field. This property makes electron and hole quantum dots (QDs) in bilayer graphene interesting for valley and spin-valley qubits. Here, we show measurements of the electron-hole crossover in a bilayer graphene QD, demonstrating opposite signs of the magnetic moments associated with the Berry curvature. Using three layers of top gates, we independently control the tunneling barriers while tuning the occupation from the few-hole regime to the few-electron regime, crossing the displacement-field-controlled band gap. The band gap is around 25 meV, while the charging energies of the electron and hole dots are between 3 and 5 meV. The extracted valley g-factor is around 17 and leads to opposite valley polarization for electrons and holes at moderate B-fields. Our measurements agree well with tight-binding calculations for our device.

Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic Transport.

We report on measurements of quantized conductance in gate-defined quantum point contacts in bilayer graphene that allow the observation of subband splittings due to spin-orbit coupling. The size of this splitting can be tuned from 40 to 80 µeV by the displacement field. We assign this gate-tunable subband splitting to a gap induced by spin-orbit coupling of Kane-Mele type, enhanced by proximity effects due to the substrate. We show that this spin-orbit coupling gives rise to a complex pattern in low perpendicular magnetic fields, increasing the Zeeman splitting in one valley and suppressing it in the other one. In addition, we observe a spin polarized channel of 6e^{2}/h at high in-plane magnetic field and signatures of interaction effects at the crossings of spin-split subbands of opposite spins at finite magnetic field.

Impact of Many-Body Effects on Landau Levels in Graphene.

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity v_{F}. In contrast to the logarithmic divergence of v_{F} at zero magnetic field, we find a piecewise linear scaling of v_{F} as a function of the charge carrier density, due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of ≈6 meV contained in the experimentally extracted Landau level transitions energies.

Embedding for bulk systems using localized atomic orbitals.

We extend projection-based embedding techniques to bulk systems to treat point defects in semiconductors and insulators. To avoid non-additive kinetic energy contributions, we construct the density partition using orthogonal subsets of orbitals. We have implemented our approach in the popular Vienna ab initio simulation package software package. We demonstrate its power for defect structures in silicon and polaron formation in titania, two challenging cases for conventional Kohn-Sham density functional theory.

Wave-function mapping of graphene quantum dots with soft confinement.

Using low-temperature scanning tunneling spectroscopy, we map the local density of states of graphene quantum dots supported on Ir(111). Because of a band gap in the projected Ir band structure around the graphene K point, the electronic properties of the QDs are dominantly graphenelike. Indeed, we compare the results favorably with tight binding calculations on the honeycomb lattice based on parameters derived from density functional theory. We find that the interaction with the substrate near the edge of the island gradually opens a gap in the Dirac cone, which implies soft-wall confinement. Interestingly, this confinement results in highly symmetric wave functions. Further influences of the substrate are given by the known moiré potential and a 10% penetration of an Ir surface resonance into the graphene layer.

The speed limit of optoelectronics.

Light-field driven charge motion links semiconductor technology to electric fields with attosecond temporal control. Motivated by ultimate-speed electron-based signal processing, strong-field excitation has been identified viable for the ultrafast manipulation of a solid's electronic properties but found to evoke perplexing post-excitation dynamics. Here, we report on single-photon-populating the conduction band of a wide-gap dielectric within approximately one femtosecond. We control the subsequent Bloch wavepacket motion with the electric field of visible light. The resulting current allows sampling optical fields and tracking charge motion driven by optical signals. Our approach utilizes a large fraction of the conduction-band bandwidth to maximize operating speed. We identify population transfer to adjacent bands and the associated group velocity inversion as the mechanism ultimately limiting how fast electric currents can be controlled in solids. Our results imply a fundamental limit for classical signal processing and suggest the feasibility of solid-state optoelectronics up to 1 PHz frequency.

Veselago lens and Klein collimator in disordered graphene.

We simulate electron transport through graphene nanoribbons of realistic size containing a p-n junction patterned by electrostatic gates. For a sharp p-n interface, Klein tunneling leads to refocusing of a divergent beam forming a Veselago lens. Wider transition regions allow only electrons with near-perpendicular incidence to pass the junction, forming a Klein collimator. Using a third nearest neighbor tight binding description we explore the influence of interface roughness and bulk disorder on guiding properties. We provide bounds on disorder amplitudes and p-n junction properties to be satisfied in order to experimentally observe the focusing effect and compare our predictions to very recent realizations.

Size quantization of Dirac fermions in graphene constrictions.

Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically defined graphene constrictions. At high carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity of ∼1.5 × 10(6) m s(-1) in our constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices.

Tunable Fano resonances in transport through microwave billiards.

We present a tunable microwave scattering device that allows the controlled variation of Fano line shape parameters in transmission through quantum billiards. Transport in this device is nearly fully coherent. By comparison with quantum calculations, employing the modular recursive Green's-function method, the scattering wave function and the degree of residual decoherence can be determined. The parametric variation of Fano line shapes in terms of interacting resonances is analyzed.

The single-channel regime of transport through random media.

The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a 'necklace state'. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

Electron-hole crossover in graphene quantum dots.

We investigate the addition spectrum of a graphene quantum-dot in the vicinity of the electron-hole crossover as a function of perpendicular magnetic field. Coulomb-blockade resonances of the 50 nm wide dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 50 states displays the unique complex evolution of the diamagnetic spectrum of a graphene dot from the low-field regime to the Landau regime with the n=0 Landau level situated in the center of the transport gap marking the electron-hole crossover. The average peak spacing in the energy region around the crossover decreases with increasing magnetic field. In the vicinity of the charge neutrality point we observe a well resolved and rich excited state spectrum.