We present atomistic calculations of quantum coherent electron transport through fulleropyrrolidine terminated molecules bridging a graphene nanogap. We predict that three difficult problems in molecular electronics with single molecules can be solved by utilizing graphene contacts: (1) a back gate modulating the Fermi level in the graphene leads facilitates control of the device conductance in a transistor effect with high on-off current ratio; (2) the size mismatch between leads and molecule is avoided, in contrast to the traditional metal contacts; (3) as a consequence, distinct features in charge flow patterns throughout the device are directly detectable by scanning techniques. We show that moderate graphene edge disorder is unimportant for the transistor function.

We report a detailed investigation of the interplay between size quantization and local scattering centers in graphene nanoribbons, as seen in the local density of states. The spectral signatures, obtained after Fourier transformation of the local density of states, include characteristic peaks that can be related to the transverse modes of the nanoribbon. In armchair ribbons, the Fourier transformed density of states of one of the two inequivalent sublattices takes a form similar to that of a quantum channel in a two-dimensional electron gas, modified according to the differences in bandstructure. After addition of the second sublattice contribution, a characteristic modulation of the pattern due to superposition is obtained, similar to what has been obtained in spectra due to single impurity scattering in large-area graphene. We present analytic results for the electron propagator in armchair nanoribbons in the Dirac approximation, including a single scattering center within a T-matrix formulation. For comparison, we have extended the investigation with numerics obtained with an atomistic recursive Green's function approach. The spectral signatures of the atomistic approach include the effects of trigonal warping. The impurity induced oscillations in the local density of states are not decaying at large distance in few-mode nanoribbons.

The reason why the half-integer quantum Hall effect (QHE) is suppressed in graphene grown by chemical vapor deposition (CVD) is unclear. We propose that it might be connected to extended defects in the material and present results for the quantum Hall effect in graphene with [0001] tilt grain boundaries connecting opposite sides of Hall bar devices. Such grain boundaries contain 5-7 ring complexes that host defect states that hybridize to form bands with varying degree of metallicity depending on grain boundary defect density. In a magnetic field, edge states on opposite sides of the Hall bar can be connected by the defect states along the grain boundary. This destroys Hall resistance quantization and leads to non-zero longitudinal resistance. Anderson disorder can partly recover quantization, where current instead flows along returning paths along the grain boundary depending on defect density in the grain boundary and on disorder strength. Since grain sizes in graphene made by chemical vapor deposition are usually small, this may help explain why the quantum Hall effect is usually poorly developed in devices made of this material. The half-integer quantum Hall effect (QHE) [1,2] in monolayer graphene grown on silicon-carbide substrates has been observed to metrological accuracy [3][4][5]. Very high breakdown currents have been recorded, and quantization remains accurate also at elevated temperatures. This material may therefore be the next choice for an improved resistance standard. On the other hand, QHE plateaux have not been measured to the same level of accuracy on Hall bars made of graphene grown by chemical vapor deposition (CVD) [6,7]. The reason for this disparity is unclear, but it may be due to extrinsic effects, such as defects and inhomogeneity introduced in the process of graphene transfer from substrates used in the growth to other substrates used for devices, or due to defects in the material itself, such as grain boundaries that usually are found in graphene made by CVD [8].In a recent experiment [7], it was indeed argued that grain boundaries may be the source of reduced quantization in devices made of CVD graphene. A clear theoretical picture of how the QHE is destroyed in graphene with grain boundaries is however still lacking. One particular and very special type of grain boundary has been considered theoretically in the literature before [7,9]. The grain boundary consists of a perfect row of 5-8-5 ring complexes that separates two perfect armchair ribbons oriented along the same axis. To join the armchair ribbons to the grain boundary, the ribbons are cut at 90• to their armchair edges so that perfect zigzag edges are formed. These zigzag edges can be attached to the grain boundary. In a magnetic field, a picture appears of current flowing along an armchair edge in the ribbon and along a zigzag edge along the grain boundary over to the opposite edge of the ribbon where the current can flow back in the opposite direction. This special type of grain boundary is not the only or typical grain...

Bloch-Redfield equation is a common tool for studying evolution of qubit systems weakly coupled to environment. We investigate the accuracy of the Born approximation underlying this equation. We find that the high order terms in the perturbative expansion contain accumulating divergences that make straightforward Born approximation inappropriate. We develop diagrammatic technique to formulate, and solve the improved self-consistent Born approximation. This more accurate treatment reveals an exponential time dependent prefactor in the non-Markovian contribution dominating the qubit long-time relaxation found in Phys. Rev. B 71, 035318 (2005). At the same time, the associated dephasing is not affected and is described by the Born-Markov approximation.Introduction. A quantum two-level system coupled to a bath of harmonic oscillators is a prominent model widely employed for describing dissipation in quantum physics. The spin-boson model is outlined in several textbooks [1-3], the advances are covered by the review articles (e.g. [4-6] and references therein). Immense literature is devoted to applications of the model to virtually all physics areas ranging from atomic physics and quantum optics to chemical physics and solid state physics.With the advent of quantum information the model regained increased attention, particularly within the field of quantum superconducting circuits [7].For the qubit applications, the most interesting is the weak coupling regime when the two-level system slowly looses coherence and relaxes to the equilibrium state. The Bloch-Redfield equation [8,9] is a common tool for describing this process. It is valid in the lowest, second order approximation with respect to the coupling to the bath, and employs the Markov approximation [3]. Several schemes beyond these approximations have been worked out based on the projection [2], path integral [1,5], diagrammatic [10] and renormalization group [11] techniques. Lifting constraints of the spin-boson model, such as a linear coupling to the bath [12], or equilibrium state of the bath [13,14], have been discussed in literature. However, in the qubit research, the Bloch-Redfield equation remains the basic theoretical model, whose prediction about an exponential in time qubit evolution is considered to be qualitatively correct. To what extent is this true? The negative answer was obtained in [15], where it was found that the qubit long-time relaxation is governed, within the Born approximation, by a power-law time dependent non-Markovian term. This phenomenon is of a fundamental origin being related to a bounded energy spectrum of the bath that generates singular branching points of the qubit Green function [16].In this paper we revisit the problem of long-time decoherence in the spin-boson model in the weak coupling limit. We analyze the perturbation expansion and find that the high-order corrections to the Born approximation contain accumulating divergences, which

By using Fourier-transform scanning tunneling spectroscopy we measure the interference patterns produced by the impurity scattering of confined Dirac quasiparticles in epitaxial graphene nanoflakes. Upon comparison of the experimental results with tight-binding calculations of realistic model flakes, we show that the characteristic features observed in the Fourier-transformed local density of states are related to scattering between different transverse modes (subbands) of a graphene nanoflake and allow direct insight into the gapped electronic spectrum of graphene. We also observe a strong reduction of quasiparticle lifetime which is attributed to the interaction with the underlying substrate. In addition, we show that the distribution of the on-site energies at flower defects leads to an effectively broken pseudospin selection rule, where intravalley backscattering is allowed. [17,18]. With regard to the electronic transport through graphene nanoribbons, the effect of impurity scattering and edge disorder becomes an important issue. A powerful tool to examine the quasiparticle interference (QPI) effects in graphene due to scattering at defects and edges is scanning tunneling microscopy and spectroscopy [19][20][21][22]. The observed QPI is directly related to modulations in the local density of states (LDOS) [23,24] and provides access to the present scattering vectors and thus to the electronic structure of graphene [25][26][27][28]. Recently, the influence of local scattering centers on the local density of states in graphene nanoribbons has been studied theoretically [29]. The interplay between single impurity scattering and size quantization was shown to generate characteristic spectral features in the Fourier transform (FT) LDOS that can be related to the transverse modes of the nanoribbon.Here we present a comprehensive study of size quantization in epitaxial graphene nanoflakes (GNFs) on Ag(111) upon analysis of QPI by STM and tight-binding simulations of realistic model flakes. We indeed find the characteristic features in the FT-LDOS related to scattering between different transverse modes of a GNF as predicted by theory. Detailed analysis of the scattering features allows one to gain a profound insight into the behavior of charge carriers in graphene flakes, including discrete electronic spectrum and quasiparticle lifetimes, as well as effects of pseudospin.Graphene nanoflakes were initially grown on Ir(111) and decoupled by noble metal intercalation as described elsewhere [13,30]. STM and STS measurements were carried out in an Omicron cryogenic STM setup in ultrahigh vacuum at T = 5−10 K. Differential conductance (dI/dV ) maps were * mikhail.fonin@uni-konstanz.de obtained using a standard lock-in technique with modulation voltages V mod = 3 mV(rms) and at frequencies f mod = 600−800 Hz. Tight-binding calculations were performed using an atomistic recursive Green's function formalism including the effects of trigonal warping in order to account for the relatively large doping level of graphene on A...

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