Many paths to interference: a journey between quantum dots and single molecule junctions

Recently, there are significant breakthrough in experimental demonstrations of Cooper pair splitting (CPS) using the double quantum dot system [1-3]. The next important step, after successful splitting of Cooper pairs, would be experimental demonstration that the split electrons remain entangled. It occurs significantly more challenging since eight years after the first demonstration of the splitting there is still lack of the entanglement detection in this system. Therefore, we explore a general model of the CPS coupled to two ferromagnetic detectors converting spin information into charge information. We use perturbation theory taking into account of the spin dynamics and the exchange interaction between quantum dots and the ferromagnetic detectors. Despite of the complex spin precession in quantum dots [4] it is still possible to determine spin correlation by dc current measurements in this system. We propose an entanglement test based on the Bell inequalities and the entanglement witness approach. 1. L. Hofstetter, S. Csonka, J. Nygard, and C. Schonenberger, Nature 461, 960 (2009). 2. J. Wei and V. Chandrasekhar, Nature Physics 6, 494 (2010). 3. Z. B. Tan, D. Cox, T. Nieminen, P. Lahteenmaki, D. Golubev, G. B. Lesovik, and P. J. Hakonen, Phys.Rev. Lett. 114, 096602 (2015). 4. A. D. Crisan, S. Datta, J. J. Viennot, M. R. Delbecq, A. Cottet, and T. Kontos, Nature Communications 7, 10451 (2016).

The interaction between electronic and vibrational degrees of freedom in single-molecule junctions results from a dependence of the electronic energies on the nuclear displacement, but also from the dependence of the electronic states of the molecular bridge on the nuclear coordinates. The latter mechanism leads to a direct coupling between different electronic states and is referred to as nonadiabatic electronic-vibrational coupling. Employing a perturbative non-equilibrium Green's function approach, we study the influence of nonadiabatic electronic-vibrational coupling on the transport properties of model molecular junctions. Furthermore, we investigate the influence of adiabatic and nonadiabatic electronic-vibrational coupling on interference effects in the electronic current as well as the interplay between adiabatic and nonadiabatic electronic-vibrational interactions. A. Erpenbeck, R. Härtle, M. Thoss - Phys. Rev. B 91, 195418 (2015)

Marc H. Garner (1), Haixing Li (2), Madhav Neupane (2), Zhichun Shangguan(3), Shengxiong Xiao (3), Colin Nuckolls (2), Latha Venkataraman (2), Gemma C. Solomon (1). 1) University of Copenhagen, Denmark. 2) Columbia University, USA. 3) Shanghai Normal University, China. Abstract Molecular forms of silicon hold great promise for future applications in electronics at the molecular scale. With the combination of the conformational flexibility of saturated molecules and electronic sigma-conjugation through the molecular backbone, functionalized silanes have shown a range of interesting properties. Unlike their linear counterparts, bicyclic silanes are constrained to well-defined conformations and are sterically crowded molecules. Consequently, notable through-bond and through-space signatures are measured in single-molecule junction experiments. These competing components of the single-molecule conductance are analyzed by calculating interatomic transmission pathways. Through-space coupling can both result in higher conductance as more transmission pathways become available, or in lower conductance as the transmission pathways can give rise to destructive quantum interference in the transmission. This insight into the structure-function relationships of molecular silicon provides a solid basis for continued efforts for designing silane-based single-molecule devices.

In this work, we investigate the decoherence effects which play an important role in the charge transport characteristics of quantum wires at room temperature. For molecular junctions and one-dimensional molecular wires we investigate the distinct dephasing models to calculate and compare the effective resistances and investigate the crossover from coherent Landauer transport to ohmic behavior in long wires. First, we consider the Momentum Relaxing Dephasing (MRD) and the Büttiker Probe (BP) models. These approaches rely on the empirical coupling strength of electronic states to the environment. Then we introduce the electron-phonon dephasing model and consider different approximations including the first Born approximation (BA) and the self-consistent Born approximation (SCBA). Besides, we consider the interplay of disorder and dissipation. Our theoretical method is based on the nonequilibrium Green function approach to quantum transport. To go towards the atomistic ab initio theory, we implemented the method in combination with the density functional based tight binding (DFTB) theory [1] within the DFTB+ code [2] and DFTB-NEGF transport method [3]. We will present the results on dephasing effects in resonant and off-resonant transport, in particular we investigated the effects of electron-phonon interaction and the robustness of quantum interference with respect to dephasing. [1] G. Penazzi et al., J. Phys. Chem. C {\bf 120}, 16383 (2016) [2] B. Aradi, B. Hourahine, Th. Frauenheim, J. Phys. Chem. A {\bf 111}, 5678 (2007) [3] A. Pecchia, L. Salvucci, G. Penazzi, A. Di Carlo, New J. Phys. {\bf 10}, 065022 (2008).

Conjugated macrocycles, also known as annulenes, have been a focus of research over the last 50 years, particularly for their excellent optoelectronic properties. Recently, new strategies have been developed for the synthesis of monodisperse cyclic conjugated oligomers with porphyrin subunits having well-defined diameters between 3-10 nm via Vernier-templating.1 The conjugated cyclic nature of these compounds makes them ideal candidates for the study of quantum interference in single molecules. Placing two anchor points on opposing sides of a ring and subsequent attachment to a pair of gold electrodes should provide a system in which the electron wavefuntion can take two pathways and provide the basis for a Mach-Zehnder type of interferometer. In this work we present some preliminary experimental results on these systems. 1. J. K. Sprafke, D. V. Kondratuk, M. Wykes, A. L. Thompson, M. Hoffmann, R. Drevinskas, W.-H. Chen, C. K. Yong, J. Kärnbratt, J. E. Bullock, M. Malfois, M. R. Wasielewski, B. Albinsson, L. M. Herz, D. Zigmantas, D. Beljonne, H. L. Anderson. J. Am. Chem. Soc., 2011, 133 (43), pp 17262–17273

We study an entangled state of spatially separated electrons, in particular their spins, in a solid state electronic system. The ground state of conventional superconductors is a singlet state of electron Cooper pairs that can provide a natural source of entangled electrons. One of the proposals to obtain the nonlocal entanglement of electrons is to use the Cooper pairs split in the Double Quantum Dot (DQD) system using the Coulomb interaction between electrons [1]. We have analyzed an efficiency of the separation of Cooper pairs in systems, where the DQD is connected to the two superconducting leads [2,3], or to the superconducting and normal ferromagnetic leads [4-6]. Addressing the idea of quantum communication with entangled electrons in a solid state, where ferromagnetic detectors allow for spin correlation detection, we provide, using quantum information theory, a lower bond on the spin polarization of detectors. We find that lower bond for the spin polarization is p > 58 % for detection of entanglement using an optimal entanglement witness. It provides the minimal spin polarization of ferromagnetic materials that can be useful in quantum communication. [1] L. Hofstetter, S. Csonka, J. Nygård, and C. Schönenberger, Nature 461, 960 (2009). [2] R. S. Deacon, A. Oiwa, J. Sailer, S. Baba, Y. Kanai, K. Shibata, K. Hirakawa, and S. Tarucha, Nature Communications 6, 7446 (2015). [3] D. Tomaszewski, P. Busz, R. Lopez, R. Zitko, M. Lee, and J. Martinek, Phys. Rev. Lett. (submitted). [4] R. Zitko, J. Lim, R. Lopez, J. Martinek, P. Simon, Phys. Rev. Lett. 108, 166605 (2012). [5] W. Kłobus, A. Grudka, A. Baumgartner, D. Tomaszewski, C. Schönenberger, and J. Martinek, Phys. Rev. B 89, 125404 (2014). [6] P. Busz, D. Tomaszewski, J. Martinek, Phys. Rev. Lett. (submitted).

We present a method based on graph theory for evaluation of the inelastic propensity rules for molecules exhibiting complete destructive quantum interference in their elastic transmission. The method uses an extended adjacency matrix corresponding to the structural graph of the molecule for calculating the Green function between the sites with attached electrodes and consequently states the corresponding conditions the electron-vibration coupling matrix must meet for the observation of an inelastic signal between the terminals. The method can be fully automated and we provide a functional website running a code using Wolfram Mathematica, which returns a graphical depiction of destructive quantum interference configurations together with the associated inelastic propensity rules for a wide class of molecules.

C. Salhani†, M. L. Della Rocca†, C. Bessis†, R. Bonnet†, A. Chevillot§, P. Martin§, J.-C. Lacroix§, C. Barraud†, Philippe Lafarge† †Université Paris Diderot, Sorbonne Paris Cité, Laboratoire MPQ, UMR 7162, CNRS, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France. §Université Paris Diderot, Sorbonne Paris Cité, ITODYS, UMR 7086, CNRS, 15 rue J.-A. de Baïf, 75205 Paris Cedex 13, France. We present inelastic electron tunneling spectroscopy of large area molecular junction showing quantum interference effects. We have fabricated vertical molecular junctions based on a cross-conjugated anthraquinone thin layer (~8 nm), on which low-noise transport measurements are performed, by acquiring simultaneously the current-voltage characteristic, its second derivative, and the differential conductance. Signatures of vibrational modes excited by inelastic events are present in the whole measured voltage range. In the low bias voltage regime (0 – 200 meV), where destructive quantum interference suppresses elastic charge transport, such signatures are improved in amplitude. Inelastic electron transport spectroscopy data are compared to infrared attenuated total reflection spectroscopy on Au/anthraquinone thin films. Common vibrational modes can be clearly identified, but transport measurements reveal the existence of vibrational modes in a wider range (0 – 400 meV) where infrared spectroscopy is lacking. In particular, different azo-based bonds, difficult to see by infrared spectroscopy, are clearly unveiled.

In recent years, there is substantial progress in creation of specially separated spin entangled electrons in solid state using the splitting of Cooper pairs, which is necessary ingredient of quantum communication and computing. It is also possible to generate a Josephson supercurrent form by split nonlocal Cooper pairs [1]. This new Josephson current required further studies especially its interference properties. While the behavior of single electrons under the influence of Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects is well understood, it raises the question of the impact of these effects on nonlocal superconducting Cooper pairs that for s-wave superconductors are in spin singlet state. We analyze a normal ring, where a single electron interference is possible and two parallel nanowires connected to two superconducting electrodes, where a single-electron interference can be absent but a cross Andreeev reflection is possible. At low transmission, we can link the AB effect only to local Cooper pairs and the AC effect to nonlocal Cooper pair transport. We demonstrate that by using two quantum dots we can obtain different AC phases for the nonspin-flip and spin-flip transport processes that leads to a beating in the AC effect. 1. R. S. Deacon, A. Oiwa, J. Sailer, S. Baba, Y. Kanai, K. Shibata, K. Hirakawa, and S. Tarucha, Nature Communications 6, 7446 (2015).

Quantum interference (QI) effects have received a lot of recent attention as a potential enabling tool for the implementation of logic gates or data storage in single molecule junctions. In this context branched molecules are of particular interest because they can cause either constructive or destructive QI in the electron transport through the junction depending on whether the two branches are symmetry equivalent or this symmetry is disturbed by structural variations or local charging. In our theoretical study where we combine a nonequilibrium Green's function (NEGF) approach with density functional theory (DFT) we investigate branched compounds containing ferrocene moieties in both branches which due to their metal centers are designed to allow for such asymmetry induced by local charging. In these compounds the ferroecene moieties are connected to pyridil anchor groups either directly or via acetylene spacers in a meta-connection where we also compare our results with those obtained for the respective single-branched molecules with both meta- and para-connections between the metal center and the anchors. We find two destructive QI features, one slightly above the highest occupied (HOMO) and one slightly below the lowest unoccupied molecular orbital (LUMO), even for the uncharged branched compound with spacer groups inserted. In principle these features can result from a variety of structural aspects of this molecule, namely i) the two paths provided by the two branches, ii) the existence of several nearly degenerate states on the ferrocene and iii) the meta-connections between the anchor groups and the redox-active moiety. In an analysis based on a decomposition of MOs into fragment orbitals (FOs) which we focus on the QI feature near the LUMO because it dominates the conductance, we find the meta-connections to be its main cause and the presence of the acetylene spacers also a necessary requirement while local charging on one of the branches does not have a significant influence on the conductance.