Troels Markussen

The Relation between Structure and Quantum Interference in Single Molecule Junctions

Quantum interference (QI) of electron pathways has recently attracted increased interest as an enabling tool for single-molecule electronic devices. Although various molecular systems have been shown to exhibit QI effects and a number of methods have been proposed for its analysis, simple guidelines linking the molecular structure to QI effects in the phase-coherent transport regime have until now been lacking. In the present work we demonstrate that QI in aromatic molecules is intimately related to the topology of the molecules π system and establish a simple graphical scheme to predict the existence of QI-induced transmission antiresonances. The generality of the scheme, which is exact for a certain class of tight-binding models, is proved by a comparison to first-principles transport calculations for 10 different configurations of anthraquinone as well as a set of cross-conjugated molecular wires.

Electron and phonon transport in silicon nanowires: Atomistic approach to thermoelectric properties

We compute both electron- and phonon transmissions in thin disordered silicon nanowires. Our atomistic approach is based on tight-binding and empirical potential descriptions of the electronic and phononic systems, respectively. Surface disorder is modeled by including surface silicon vacancies. It is shown that the average phonon- and electron transmissions through long SiNWs containing many vacancies can be accurately estimated from the scattering properties of the isolated vacancies using a recently proposed averaging method [Phys. Rev. Lett. 99, 076803 (2007)]. We apply this averaging method to surface disordered SiNWs in the diameter range 1 − 3 nm to compute the thermoelectric figure of merit, ZT. It is found that the phonon transmission is affected more by the vacancies than the electronic transmission leading to an increased thermoelectric performance of disordered wires, in qualitative agreement with recent experiments. The largest ZT > 3 is found in strongly disordered h 111i oriented wires with a diameter of 2 nm.

Thermoelectric properties of finite graphene antidot lattices

We present calculations of the electronic and thermal transport properties of graphene antidot lattices with a finite length along the transport direction. The calculations are based on a single orbital tight-binding model and the Brenner potential. We show that both electronic and thermal transport properties converge fast toward the bulk limit with increasing length of the lattice: only a few repetitions (~6) of the fundamental unit cell are required to recover the electronic band gap of the infinite lattice as a transport gap for the finite lattice. We investigate how different antidot shapes and sizes affect the thermoelectric properties. The resulting thermoelectric figure of merit, ZT, can exceed 0.25, and it is highly sensitive to the atomic arrangement of the antidot edges. Specifically, hexagonal holes with pure zigzag edges lead to an order-of-magnitude smaller ZT as compared to pure armchair edges. We explain this behavior as a consequence of the localization of states, which predominantly occurs for zigzag edges, and of an increased splitting of the electronic minibands, which reduces the power factor.

Electrochemical control of quantum interference in anthraquinone-based molecular switches

Using first-principles calculations we analyze the electronic transport properties of a recently proposed anthraquinone-based electrochemical switch. Robust conductance on/off ratios of several orders of magnitude are observed due to destructive quantum interference present in the anthraquinone but absent in the hydroquinone molecular bridge. A simple explanation of the interference effect is achieved by transforming the frontier molecular orbitals into localized molecular orbitals thereby obtaining a minimal tight-binding model describing the transport in the relevant energy range in terms of hopping via the localized orbitals. The topology of the tight-binding model, which is dictated by the symmetries of the molecular orbitals, determines the amount of quantum interference.

Heat conductance is strongly anisotropic for pristine silicon nanowires.

We compute atomistically the heat conductance for ultrathin pristine silicon nanowires (SiNWs) with diameters ranging from 1 to 5 nm. The room temperature thermal conductance is found to be highly anisotropic: wires oriented along the <110> direction have 50-75% larger conductance than wires oriented along the <100> and <111> directions. We show that the anisotropies can be qualitatively understood and reproduced from the bulk phonon band structure. Ab initio density functional theory (DFT) is used to study the thinnest wires, but becomes computationally prohibitive for larger diameters, where we instead use the Tersoff empirical potential model (TEP). For the smallest wires, the thermal conductances obtained from DFT and TEP calculations agree within 10%. The presented results could be relevant for future phonon-engineering of nanowire devices.

Scaling theory put into practice: first-principles modeling of transport in doped silicon nanowires.

We combine the ideas of scaling theory and universal conductance fluctuations with density-functional theory to analyze the conductance properties of doped silicon nanowires. Specifically, we study the crossover from ballistic to diffusive transport in boron or phosphorus doped Si nanowires by computing the mean free path, sample-averaged conductance G, and sample-to-sample variations std(G) as a function of energy, doping density, wire length, and the radial dopant profile. Our main findings are (i) the main trends can be predicted quantitatively based on the scattering properties of single dopants, (ii) the sample-to-sample fluctuations depend on energy but not on doping density, thereby displaying a degree of universality, and (iii) in the diffusive regime the analytical predictions of the Dorokhov-Mello-Pereyra-Kumar theory are in good agreement with our ab initio calculations.

Quantifying transition voltage spectroscopy of molecular junctions: Ab initio calculations

Transition voltage spectroscopy (TVS) has recently been introduced as a spectroscopic tool for molecular junctions where it offers the possibility to probe molecular level energies at relatively low bias voltages. In this work we perform extensive ab-initio calculations of the non-linear current voltage relations for a broad class of single-molecule transport junctions in order to assess the applicability and limitations of TVS. We find, that in order to fully utilize TVS as a quantitative spectroscopic tool, it is important to consider asymmetries in the coupling of the molecule to the two electrodes. When this is taken properly into account, the relation between the transition voltage and the energy of the molecular orbital closest to the Fermi level closely follows the trend expected from a simple, analytical model.

Surface Disordered Ge–Si Core–Shell Nanowires as Efficient Thermoelectric Materials

Ge-Si core-shell nanowires with surface disorder are shown to be very promising candidates for thermoelectric applications. In atomistic calculations we find that surface roughness decreases the phonon thermal conductance significantly. On the contrary, the hole states are confined to the Ge core and are thereby shielded from the surface disorder, resulting in large electronic conductance values even in the presence of surface disorder. This decoupling of the electronic and phonon transport is very favorable for thermoelectric purposes, giving rise to promising room temperature figure of merits ZT > 2. It is also found that the Ge-Si core-shell wires perform better than pure Si nanowires.

Cross-conjugation and quantum interference: a general correlation?

We discuss the relationship between the π-conjugation pattern, molecular length, and charge transport properties of molecular wires, both from an experimental and a theoretical viewpoint. Specifically, we focus on the role of quantum interference in the conductance properties of cross-conjugated molecules. For this, we compare experiments on two series of dithiolated wires. The first set we synthesized consists of three dithiolated oligo(phenylene ethynylene) (OPE) benchmark compounds with increasing length. The second series synthesized comprises three molecules with different π-conjugation patterns, but identical lengths, i.e. an anthracene (linear conjugation), an anthraquinone (cross-conjugation), and a dihydroanthracene (broken conjugation) derivative. To benchmark reliable trends, conductance experiments on these series have been performed by various techniques. Here, we compare data obtained by conductive-probe atomic force microscopy (CP-AFM) for self-assembled monolayers (SAMs) with single-molecule break junction and multi-molecule EGaIn data from other groups. For the benchmark OPE-series, we consistently find an exponential decay of the conductance with molecular length characterized by β = 0.37 ± 0.03 Å(-1) (CP-AFM). Remarkably, for the second series, we do not only find that the linearly conjugated anthracene-containing wire is the most conductive, but also that the cross-conjugated anthraquinone-containing wire is less conductive than the broken-conjugated derivative. We attribute the low conductance values for the cross-conjugated species to quantum interference effects. Moreover, by theoretical modeling, we show that destructive quantum interference is a robust feature for cross-conjugated structures and that the energy at which complete destructive interference occurs can be tuned by the choice of side group. The latter provides an outlook for future devices in this fascinating field connecting chemistry and physics.

Electronic transport through Si nanowires : Role of bulk and surface disorder

Received 13 June 2006; revised manuscript received 15 September 2006; published 15 December 2006We calculate the resistance and mean free path in long metallic and semiconducting silicon nanowires SiNW’s using two different numerical approaches: a real-space Kubo method and a recursive Green’s-function method. We compare the two approaches and find that they are complementary: depending on thesituation a preferable method can be identified. Several numerical results are presented to illustrate the relativemerits of the two methods. Our calculations of relaxed atomic structures and their conductance properties arebased on density functional theory without introducing adjustable parameters. Two specific models of disorderare considered: Unpassivated, surface reconstructed SiNW’s are perturbed by random on-site Andersondisorder whereas defects in hydrogen passivated wires are introduced by randomly removed H atoms. Theunpassivated wires are very sensitive to disorder in the surface whereas bulk disorder has almost no influence.For the passivated wires, the scattering by the hydrogen vacancies is strongly energy dependent and forrelatively long SiNW’s