Variational approach to transport in quantum dots

We have derived a variational principle that defines the nonequilibrium steady-state transport across a correlated impurity mimicking, e.g., a quantum dot coupled to biased leads. This variational principle has been specialized to a Gutzwiller's variational space, and applied to the study of the simple single-orbital Anderson impurity model at half filling, finding a good qualitative accord with the observed behavior in quantum dots for the expected regime of values of the bias. Beyond the purely theoretical interest in the formal definition of a variational principle in a nonequilibrium problem, the particular methods proposed have the important advantage to be simple and flexible enough to deal with more complicated systems and variational spaces.Comment: 15 pages, 4 figure

Fano-Kondo effect in side-coupled double quantum dots at finite temperatures and the importance of the two-stage Kondo screening

We study the zero-bias conductance through the system of two quantum dots, one of which is embedded directly between the source and drain electrodes, while the second dot is side-coupled to the first one through a tunneling junction. Modeling the system using the two-impurity Anderson model, we compute the temperature-dependence of the conductance in various parameter regimes using the numerical renormalization group. We consider the non-interacting case, where we study the extent of the departure from the conventional Fano resonance line shape at finite temperatures, and the case where the embedded and/or the side-coupled quantum dot is interacting, where we study the consequences of the coexistence of the Kondo and Fano effects. If the side-coupled dot is very weakly interacting, the occupancy changes by two when the on-site energy crosses the Fermi level and a Fano-resonance-like shape is observed. If the interaction on the side-coupled dot is sizeable, the occupancy changes only by one and a very different line-shape results, which is strongly and characteristically temperature dependent. These results suggest an intriguing alternative interpretation of the recent experimental results study of the transport properties of the side-coupled double quantum dot [Sasaki et al., Phys. Rev. Lett. 103, 266806 (2009)]: the observed Fano-like conductance anti-resonance may, in fact, result from the two-stage Kondo effect in the regime where the experimental temperature is between the higher and the lower Kondo temperature.Comment: 9 pages, 11 figures. In V2: updated references, 3 new figures, additional discussio

Shifts in ownership toward high-powered motorcycles and its effects on public health

Objectives. We assessed whether policies designed to safeguard young motorcyclists would be effective given shifts in ownership toward high-powered motorcycles. Methods. We investigated population-wide motor vehicle driver and motorcyclist casualties (excluding passengers) recorded in Britain between 2002 and 2009. To adjust for exposure and measure individual risk, we used the estimated number of trips of motorcyclists and drivers, which had been collected as part of a national travel survey. Results. Motorcyclists were 76 times more likely to be killed than were drivers for every trip. Older motorcyclist age—strongly linked to experience, skill set,and riding behavior—did not abate the risks of high-powered motorcycles. Older motorcyclists made more trips on high-powered motorcycles. Conclusions: Tighter engine size restrictions would help reduce the use of high-powered motorcycles. Policymakers should introduce health warnings on the risks of high-powered motorcycles and the benefits of safety equipment

Mixed-state aspects of an out-of-equilibrium Kondo problem in a quantum dot

We reexamine basic aspects of a nonequilibrium steady state in the Kondo problem for a quantum dot under a bias voltage using a reduced density matrix, which is obtained in the Fock space by integrating out one of the two conduction channels. The integration has been carried out by discretizing the conduction channels preserving the two-fold degeneracy due to the left-going and right-going scattering states. The remaining subspace is described by a single-channel Anderson model, and the statistical weight is determined by the reduced density matrix. In the noninteracting case, it can be constructed as the mixed states that show a close similarity to the high-temperature distribution in equilibrium. Specifically, if the system has an inversion symmetry, the one-particle states in an energy window between the two chemical potentials \mu_R and \mu_L are occupied, or unoccupied, completely at random with an equal weight. The Coulomb interaction preserves these aspects, and the correlation functions can be expressed in a Lehmann-representation form using the mixed-state statistical weight.Comment: 8 pages, 3 figure

The Influence of Interference on the Kondo Effect in a Quantum Dot

We study the Kondo effect in a model system of a quantum dot embedded in an Aharanov-Bohm ring connected to two leads. By transforming to the scattering basis of the direct inter-lead tunneling, we are able to describe precisely how the Kondo screening of the dot spin occurs. We calculate the Kondo temperature and zero-temperature conductance and find that both are influenced by the Aharanov-Bohm ring as well as the electron density in the leads. We also calculate the form of an additional potential scattering term that arises at low energies due to the breaking of particle-hole symmetry. Many of our results are supported by numerical analysis using the numerical renormalization group.Comment: 24 pages, 18 figure

Do adverts increase the probability of finding online cognitive behavioural therapy for depression? Cross-sectional study

Objective To estimate the effect of online adverts on the probability of finding online cognitive behavioural therapy (CBT) for depression. Design Exploratory online cross-sectional study of search experience of people in the UK with depression in 2011. (1) The authors identified the search terms over 6 months entered by users who subsequently clicked on the advert for online help for depression. (2) A panel of volunteers across the UK recorded websites presented by normal Google search for the term ‘depression’. (iii) The authors examined these websites to estimate probabilities of knowledgeable and naive internet users finding online CBT and the improved probability by addition of a Google advert. Participants (1) 3868 internet users entering search terms related to depression into Google. (2) Panel, recruited online, of 12 UK participants with an interest in depression. Main outcome measures Probability of finding online CBT for depression with/without an advert. Results The 3868 users entered 1748 different search terms but the single keyword ‘depression’ resulted in two-thirds of the presentations of, and over half the ‘clicks’ on, the advert. In total, 14 different websites were presented to our panel in the first page of Google results for ‘depression’. Four of the 14 websites had links enabling access to online CBT in three clicks for knowledgeable users. Extending this approach to the 10 most frequent search terms, the authors estimated probabilities of finding online CBT as 0.29 for knowledgeable users and 0.006 for naive users, making it unlikely CBT would be found. Adding adverts that linked directly to online CBT increased the probabilities to 0.31 (knowledgeable) and 0.02 (naive). Conclusions In this case, online CBT was not easy to find and online adverts substantially increased the chance for naive users. Others could use this approach to explore additional impact before committing to long-term Google AdWords advertising budgets

Photoluminiscence of a quantum dot hybridized with a continuum

We calculate the intensity of photon emission from a trion in a single quantum dot, as a function of energy and gate voltage, using the impurity Anderson model and variational wave functions. Assuming a flat density of conduction states and constant hybridization energy, the results agree with the main features observed in recent experiments: non-monotonic dependence of the energy on gate voltage, non-Lorentzian line shapes, and a line width that increases near the regions of instability of the single electron final state to occupations zero or two.Comment: 4 pages, 3 figures, Journal-ref adde

Kondo screening cloud in a one dimensional wire: Numerical renormalization group study

We study the Kondo model --a magnetic impurity coupled to a one dimensional wire via exchange coupling-- by using Wilson's numerical renormalization group (NRG) technique. By applying an approach similar to which was used to compute the two impurity problem we managed to improve the bad spatial resolution of the numerical renormalization group method. In this way we have calculated the impurity spin - conduction electron spin correlation function which is a measure of the Kondo compensation cloud whose existence has been a long standing problem in solid state physics. We also present results on the temperature dependence of the Kondo correlations.Comment: published versio

Suppression of Kondo-assisted co-tunneling in a spin-1 quantum dot with Spin-Orbit interaction

Kondo-type zero-bias anomalies have been frequently observed in quantum dots occupied by two electrons and attributed to a spin-triplet configuration that may become stable under particular circumstances. Conversely, zero-bias anomalies have been so far quite elusive when quantum dots are occupied by an even number of electrons greater than two, even though a spin-triplet configuration is more likely to be stabilized there than for two electrons. We propose as an origin of this phenomenon the spin-orbit interaction, and we show how it profoundly alters the conventional Kondo screening scenario in the simple case of a laterally confined quantum dot with four electrons.Comment: 5 pages, 3 figures, submitted 05May201

Numerical renormalization group study of two-channel three-impurity triangular clusters

We study triangular clusters of three spin-1/2 Kondo or Anderson impurities that are coupled to two conduction leads. In the case of Kondo impurities, the model takes the form of an antiferromagnetic Heisenberg ring with Kondo-like exchange coupling to continuum electrons. We show that this model exhibits many types of the behavior found in various simpler one and two-impurity models, thereby enabling the study of crossovers between a number of Fermi-liquid (FL) and non-Fermi-liquid (NFL) fixed points. In particular, we explore a direct crossover between the two-impurity Kondo-model NFL fixed point and the two-channel Kondo-model NFL fixed point. We show that the concept of the two-stage Kondo effect applies even in the case when the first-stage Kondo state is of NFL type. In the case of Anderson impurities, we consider the transport properties of three coupled quantum dots. This class of models includes as limiting cases the familiar serial double quantum dot and triple quantum dot nanostructures. By extracting the quasiparticle scattering phase shifts, we compute the low-temperature conductance as a function of the inter-impurity tunneling-coupling. We point out that due to the existence of exponentially low temperature scales, there is a parameter range where the stable "zero-temperature" fixed point is essentially never reached (not even in numerical renormalization group calculations). The "zero-temperature" conductance is then of no interest and it may only be meaningful to compute the conductance at finite temperature. This illustrates the perils of studying the conductance in the ground state and considering thermal fluctuations only as a small correction.Comment: 12 pages, 13 figure