Conductance quantization in graphene nanoconstrictions with mesoscopically smooth but atomically stepped boundaries

We present the results of million atom electronic quantum transport calculations for graphene nanoconstrictions with edges that are smooth apart from atomic scale steps. We find conductances quantized in integer multiples of 2e2/h and a plateau at ~0.5*2e2/h as in recent experiments [Tombros et al., Nature Physics 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/h occur even for strongly non-adiabatic electron backscattering at the stepped edges that lowers the conductance by one or more conductance quanta below the adiabatic value. We also show that conductance plateaus near 0.5*2e2/h can occur as a result of electron backscattering at stepped edges even in the absence of electron-electron interactions.Comment: 5 pages, 4 figure

Composite fermion edge states, fractional charge and current noise

A composite fermion edge state theory of current fluctuations, fractional quasiparticle charge and Johnson-Nyquist noise in the fractional quantum Hall regime is presented. It is shown that composite fermion current fluctuations and the charges of the associated quasiparticles are strongly renormalized by the interactions between composite fermions. The important interaction is that mediated by the fictitious electric field associated with composite fermion currents. The dressed current fluctuations and quasiparticle charges are calculated self-consistently in a mean field theory for smooth edges. Analytic results are obtained. The values of the fractional quasiparticle charges obtained agree with the predictions of previous theories in the incompressible regions of the 2DEG where those theories apply. In the compressible regions the magnitudes of the quasiparticle charges vary with position. Since Johnson-Nyquist noise arises from the compressible regions, it is due to quasiparticles whose charges differ from the simple fractions of $e$ that apply in the incompressible regions. Never the less, the Nyquist noise formula $S=4{k_B}T G$ is obeyed on fractional quantum Hall plateaus. Some implications for the interpretation of recent shot noise measurements in the fractional quantum Hall regime are briefly discussed.Comment: 15 pages Revtex + 2 postscript figure

Identification of the Atomic Scale Structures of the Gold-Thiol Interfaces of Molecular Nanowires by Inelastic Tunneling Spectroscopy

We examine theoretically the effects of the bonding geometries at the gold-thiol interfaces on the inelastic tunneling spectra of propanedithiolate (PDT) molecules bridging gold electrodes and show that inelastic tunneling spectroscopy combined with theory can be used to determine these bonding geometries experimentally. With the help of density functional theory, we calculate the relaxed geometries and vibrational modes of extended molecules each consisting of one or two PDT molecules connecting two gold nanoclusters. We formulate a perturbative theory of inelastic tunneling through molecules bridging metal contacts in terms of elastic transmission amplitudes, and use this theory to calculate the inelastic tunneling spectra of the gold-PDT-gold extended molecules. We consider PDT molecules with both trans and gauche conformations bound to the gold clusters at top, bridge and hollow bonding sites. Comparing our results with the experimental data of Hihath et al. [Nano Lett. 8, 1673 (2008)], we identify the most frequently realized conformation in the experiment as that of trans molecules top-site bonded to both electrodes. We find the switching from the 42 meV vibrational mode to the 46 meV mode observed in the experiment to be due to the transition of trans molecules from mixed top-bridge to pure top-site bonding geometries. Our results also indicate that gauche molecular conformations and hollow site bonding did not contribute significantly to the experimental inelastic tunneling spectra. For pairs of PDT molecules connecting the gold electrodes in parallel we find total elastic conductances close to twice those of single molecules bridging the contacts with similar bonding conformations and small splittings of the vibrational mode energies for the modes that are the most sensitive to the molecule-electrode bonding geometries.Comment: 14 pages, 8 figures, 1 table. arXiv admin note: significant text overlap with arXiv:1103.2378; http://jcp.aip.org/resource/1/jcpsa6/v136/i1/p014703_s

Theory of Interacting Parallel Quantum Wires

We present self-consistent numerical calculations of the electronic structure of parallel Coulomb-confined quantum wires, based on the Hohenberg-Kohn-Sham density functional theory of inhomogeneous electron systems. We find that the corresponding transverse energy levels of two parallel wires lock together when the wires' widths are similar and their separation is not too small. This energy level locking is an effect of Coulomb interactions and of the the density of states singularities that are characteristic of quasi- one-dimensional Fermionic systems. In dissimilar parallel wires level lockings are much less likely to occur. Energy level locking in similar wires persists to quite large wire separations, but is gradually suppressed by inter-wire tunneling when the separation becomes small. Experimental implications of these theoretical results are discussed.Comment: RevTeX, 23 papes, 8 compressed tar figures in a separate file, to be published in the Canadian Journal of Physics

Theoretical Study of Electrical Conduction Through a Molecule Connected to Metallic Nanocontacts

We present a theoretical study of electron transport through a molecule connected to two metallic nanocontacts. The system investigated is 1,4 benzene-dithiolate (BDT) chemically bonded to two Au contacts. The surface chemistry is modeled by representing the tips of the Au contacts as two atomic clusters and treating the molecule-cluster complex as a single entity in an extended Huckel tight binding scheme. We model the tips using several different cluster geometries. An ideal lead is attached to each cluster, and the lead to lead transmission is calculated. The role of the molecule-cluster interaction in transport is analyzed by using single channel leads. We then extend the calculations to multi-channel leads that are a more realistic model of the tip's environment. Using the finite-voltage, finite temperature Landauer formula, we calculate the differential conductance for the different systems studied. The similarities and differences between the predictions of the present class of models and recent experimental work are discussed.Comment: 23 pages, 11 figures, accepted PR