Tunable non-integer high-harmonic generation in a topological insulator.

When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material1-11. Sub-optical-cycle dynamics-such as dynamical Bloch oscillations2-5, quasiparticle collisions6,12, valley pseudospin switching13 and heating of Dirac gases10-leave fingerprints in the HH spectra of conventional solids. Topologically non-trivial matter14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation16-20. Here we experimentally demonstrate HH generation in a three-dimensional topological insulator-bismuth telluride. The frequency of the terahertz driving field sharply discriminates between HH generation from the bulk and from the topological surface, where the unique combination of long scattering times owing to spin-momentum locking17 and the quasi-relativistic dispersion enables unusually efficient HH generation. Intriguingly, all observed orders can be continuously shifted to arbitrary non-integer multiples of the driving frequency by varying the carrier-envelope phase of the driving field-in line with quantum theory. The anomalous Berry curvature warranted by the non-trivial topology enforces meandering ballistic trajectories of the Dirac fermions, causing a hallmark polarization pattern of the HH emission. Our study provides a platform to explore topology and relativistic quantum physics in strong-field control, and could lead to non-dissipative topological electronics at infrared frequencies.

Quasi-Particle Self-Consistent GW for Molecules.

We present the formalism and implementation of quasi-particle self-consistent GW (qsGW) and eigenvalue only quasi-particle self-consistent GW (evGW) adapted to standard quantum chemistry packages. Our implementation is benchmarked against high-level quantum chemistry computations (coupled-cluster theory) and experimental results using a representative set of molecules. Furthermore, we compare the qsGW approach for five molecules relevant for organic photovoltaics to self-consistent GW results (scGW) and analyze the effects of the self-consistency on the ground state density by comparing calculated dipole moments to their experimental values. We show that qsGW makes a significant improvement over conventional G0W0 and that partially self-consistent flavors (in particular evGW) can be excellent alternatives.

Conductance saturation in a series of highly transmitting molecular junctions.

Revealing the mechanisms of electronic transport through metal-molecule interfaces is of central importance for a variety of molecule-based devices. A key method for understanding these mechanisms is based on the study of conductance versus molecule length in molecular junctions. However, previous works focused on transport governed either by coherent tunnelling or hopping, both at low conductance. Here, we study the upper limit of conductance across metal-molecule-metal interfaces. Using highly conducting single-molecule junctions based on oligoacenes with increasing length, we find that the conductance saturates at an upper limit where it is independent of molecule length. With the aid of two prototype systems, in which the molecules are contacted by either Ag or Pt electrodes, we find two different possible origins for conductance saturation. The results are explained by an intuitive model, backed by ab initio calculations. Our findings shed light on the mechanisms that constrain the conductance of metal-molecule interfaces at the high-transmission limit.

Off-Diagonal Self-Energy Terms and Partially Self-Consistency in GW Calculations for Single Molecules: Efficient Implementation and Quantitative Effects on Ionization Potentials.

The GW method in its most widespread variant takes, as an input, Kohn-Sham (KS) single particle energies and single particle states and yields results for the single-particle excitation energies that are significantly improved over the bare KS estimates. Fundamental shortcomings of density functional theory (DFT) when applied to excitation energies as well as artifacts introduced by approximate exchange-correlation (XC) functionals are thus reduced. At its heart lies the quasi-particle (qp) equation, whose solution yields the corrected excitation energies and qp-wave functions. We propose an efficient approximation scheme to treat this equation based on second-order perturbation theory and self-consistent iteration schemes. We thus avoid solving (large) eigenvalue problems at the expense of a residual error that is comparable to the intrinsic uncertainty of the GW truncation scheme and is, in this sense, insignificant.

Electron-vibration interaction in the presence of a switchable Kondo resonance realized in a molecular junction.

The interaction of individual electrons with vibrations has been extensively studied. However, the nature of electron-vibration interaction in the presence of many-body electron correlations such as a Kondo state has not been fully investigated. Here, we present transport measurements on a Copper-phthalocyanine molecule, suspended between two silver electrodes in a break-junction setup. Our measurements reveal both zero bias and satellite conductance peaks, which are identified as Kondo resonances with a similar Kondo temperature. The relation of the satellite peaks to electron-vibration interaction is corroborated using several independent spectroscopic indications, as well as ab initio calculations. Further analysis reveals that the contribution of vibration-induced inelastic current is significant in the presence of a Kondo resonance.

Density of states in graphene with vacancies: midgap power law and frozen multifractality.

The density of states ϱ(E) of graphene is investigated numerically and within the self-consistent T-matrix approximation in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies n(A) and n(B) in both sublattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The onlinear sigma model predicts for BDI a Gade-type singularity ϱ(E)∼|E|(-1)exp[-|log(E)|(-1/x)]. Our numerical data are comparable to this result in a preasymptotic regime that gives way, however, at even lower energies to ϱ(E)∼E(-1)|log(E)|(-x̃), 1≤x̃<2. We take this finding as evidence that, similar to the case of dirty d-wave superconductors, generic bipartite random hopping models may also exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems.

Transport properties of individual C60-molecules.

Electrical and thermal transport properties of C60 molecules are investigated with density-functional-theory based calculations. These calculations suggest that the optimum contact geometry for an electrode terminated with a single-Au atom is through binding to one or two C-atoms of C60 with a tendency to promote the sp(2)-hybridization into an sp(3)-type one. Transport in these junctions is primarily through an unoccupied molecular orbital that is partly hybridized with the Au, which results in splitting the degeneracy of the lowest unoccupied molecular orbital triplet. The transmission through these junctions, however, cannot be modeled by a single Lorentzian resonance, as our results show evidence of quantum interference between an occupied and an unoccupied orbital. The interference results in a suppression of conductance around the Fermi energy. Our numerical findings are readily analyzed analytically within a simple two-level model.

The GW-Method for Quantum Chemistry Applications: Theory and Implementation.

The GW-technology corrects the Kohn-Sham (KS) single particle energies and single particle states for artifacts of the exchange-correlation (XC) functional of the underlying density functional theory (DFT) calculation. We present the formalism and implementation of GW adapted for standard quantum chemistry packages. Our implementation is tested using a typical set of molecules. We find that already after the first iteration of the self-consistency cycle, G0W0, the deviations of quasi-particle energies from experimental ionization potentials and electron affinities can be reduced by an order of magnitude against those of KS-DFT using GGA or hybrid functionals. Also, we confirm that even on this level of approximation there is a considerably diminished dependency of the G0W0-results on the XC-functional of the underlying DFT.

Broadening of the derivative discontinuity in density functional theory.

We clarify an important aspect of density functional theories, the broadening of the derivative discontinuity (DD) in a quantum system, with fluctuating particle number. Our focus is on a correlated model system, the single level quantum dot in the regime of the Coulomb blockade. We find that the DD-broadening is controlled by the small parameter Γ/U, where Γ is the level broadening due to contacting and U is a measure of the charging energy. Our analysis suggests that Kondoesque fluctuations have a tendency to increase the DD-broadening in our model by a factor of two.

Multifractality at the quantum Hall transition: beyond the parabolic paradigm.

We present an ultrahigh-precision numerical study of the spectrum of multifractal exponents Deltaq characterizing anomalous scaling of wave function moments |psi|2q at the quantum Hall transition. The result reads Deltaq=2q(1-q)[b0+b1(q-1/2)2+cdots, three dots, centered], with b0=0.1291+/-0.0002 and b1=0.0029+/-0.0003. The central finding is that the spectrum is not exactly parabolic: b1 not equal0. This rules out a class of theories of the Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.

Electrochemical gate-controlled electron transport of redox-active single perylene bisimide molecular junctions.

We report a scanning tunneling microscopy (STM) experiment in an electrochemical environment which studies a prototype molecular switch. The target molecules were perylene tetracarboxylic acid bisimides modified with pyridine (P-PBI) and methylthiol (T-PBI) linker groups and with bulky tert-butyl-phenoxy substituents in the bay area. At a fixed bias voltage, we can control the transport current through a symmetric molecular wire Au|P-PBI(T-PBI)|Au by variation of the electrochemical 'gate' potential. The current increases by up to two orders of magnitude. The conductances of the P-PBI junctions are typically a factor 3 larger than those of T-PBI. A theoretical analysis explains this effect as a consequence of shifting the lowest unoccupied perylene level (LUMO) in or out of the bias window when tuning the electrochemical gate potential VG. The difference in on/off ratios reflects the variation of hybridization of the LUMO with the electrode states with the anchor groups. I(T)-E(S(T)) curves of asymmetric molecular junctions formed between a bare Au STM tip and a T-PBI (P-PBI) modified Au(111) electrode in an aqueous electrolyte exhibit a pronounced maximum in the tunneling current at -0.740, which is close to the formal potential of the surface-confined molecules. The experimental data were explained by a sequential two-step electron transfer process.

Quantum chemistry calculations for molecules coupled to reservoirs: formalism, implementation, and application to benzenedithiol.

Modern quantum chemistry calculations are usually implemented for isolated systems-big molecules or atom clusters; total energy and particle number are fixed. However, in many situations, like quantum transport calculations or molecules in a electrochemical environment, the molecule can exchange particles (and energy) with a reservoir. Calculations for such cases require to switch from the canonical to a grand canonical description, where one fixes the chemical potential rather than particle number. To achieve this goal, the authors propose an implementation in standard quantum chemistry packages. An application to the nonlinear charge transport through 1,4-benzenedithiol will be presented. They explain the leading finite bias effect on the transmission as a consequence of a nonequilibrium Stark effect and discuss the relation to earlier work.

Exact relations between multifractal exponents at the Anderson transition.

Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the exponents with indices q<1/2 to those with q>1/2. The second relation connects the wave-function multifractality to that of Wigner delay times in a system with a lead attached.

Surface criticality and multifractality at localization transitions.

We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at a LD transition is different from that in the bulk. We illustrate this point with a calculation of boundary critical and multifractal behavior at the 2D spin quantum Hall transition and in a 2D metal at scales below the localization length.

Universality of the edge-tunneling exponent of fractional quantum Hall liquids.

In a microscopic model of fractional quantum Hall liquids with electron-electron interactions and confinement, we calculate the edge Green's function via exact diagonalization. Our results for nu=1/3 and 2/3 suggest that, in the presence of Coulomb interaction, "external" parameters such as the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, may cause deviations from universality in the edge-tunneling I-V exponent. In particular, we do not find any direct dependence of this exponent on the range of the interaction potential as suggested by recent calculations in contradiction to the topological nature of the edge.

Quasiclassical negative magnetoresistance of a 2D electron gas: interplay of strong scatterers and smooth disorder.

We study the quasiclassical magnetotransport of noninteracting fermions in two dimensions moving in a random array of strong scatterers (antidots, impurities, or defects) on the background of a smooth random potential. We demonstrate that the combination of the two types of disorder induces a novel mechanism leading to a strong negative magnetoresistance, followed by the saturation of the magnetoresistivity rho(xx)(B) at a value determined solely by the smooth disorder. Experimental relevance to the transport in semiconductor heterostructures is discussed.

Fluctuations of the inverse participation ratio at the anderson transition

Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale invariant, with a power-law asymptotic "tail." This scale invariance implies that the fractal dimensions D(q) are nonfluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between D2 and the spectral compressibility chi is violated in the regime of strong multifractality, with chi-->1 in the limit D2-->0.

Job satisfaction of Canadian public health nutritionists.

This study investigated the job satisfaction of public health nutritionists employed in provincial and municipal/regional departments of health in Canada. 153 (78%) of all eligible Canadian public health nutritionists responded to a mailed questionnaire. 89% of respondents indicated that overall, they were very satisfied or satisfied with their jobs. Although only 5% were dissatisfied or very dissatisfied, 31% would have doubts about recommending the profession to young people today, and 30% would choose a different profession if they could start again. Nutritionists who would recommend the profession had significantly higher (p < .05) levels of overall job satisfaction. Analysis of 23 job dimensions showed that nutritionists were most satisfied with their professional independence and stimulation. They were least satisfied with financial rewards and opportunities for advancement. The study provides direction on actions that may be taken to increase job satisfaction among Canadian public health nutritionists.

Self-perceived competence of Canadian public health nutritionists.

This study investigated the self-perceived competence of public health nutritionists employed in provincial and municipal/regional departments of health in Canada. One hundred and fifty-three (78%) of all eligible Canadian public health nutritionists responded to a mailed questionnaire. Nutritionists were asked to rate their level of competence on 10 competency scales and to indicate sources of their knowledge and skill development. Respondents gave the highest ratings to their interpersonal and communication skills and the lowest ratings to their research and information management abilities. T-tests showed that nutritionists who had completed a postgraduate degree felt significantly more competent in their managerial and administrative (p less than .05), organizational (p less than .01), program planning/evaluation (p less than .001), research (p less than .001), and supervisory/leadership/facilitating skills (p less than .05) than those with only a bachelor's degree. One-way ANOVA revealed significant effects of geographical location for eight competency scales. The results of this study identify continuing education needs and have implications for the graduate education of public health nutritionists.