By expressing the discrete Schrodinger equation as a second-order finite-difference equation with constant coefficients, the renormalization equations for substituted benzene dimers are derived via the c_n-coefficient elimination procedure. On subjecting the benzene molecule to a linear applied field, the resulting field-modified site energies are obtained, by projecting the site-energy locations onto a corresponding benzene dimer axis. Incorporating these modified site energies into the Lippmann-Schwinger scattering theory, enables the field effect to manifest itself in the substituted benzene electron transmission spectral function T(E). Variations in the T(E) energy spectra, arising from increases in the applied field gradient f, are described for each substituted benzene, and comparison made between their various patterns' behaviours. A common feature of the T(E) curves is their shifts to lower energies, as f increases to a calculated limiting value.
Transmission through a benzene ring, connected by sulfur contact atoms to gold leads, is calculated by a tight-binding model by means of the renormalization method. Attention is focused on the parameters associated with the contact atoms, namely their site energy and their bond energies with the ring and the leads. These parameters are found to have significant effects on the transmission probability function.
The Huckel molecular-orbital method (with overlap S) is used to derive the S-modified version of the renormalization equations, which are then employed to introduce overlap into the para-, meta- and ortho-benzene dimers' parameters. Invoking the Lippmann-Schwinger scattering theory enables the spectral energy transmission function T(E) to be found for each of the benzene types. The effect of overlap on the behaviour of the various T(E) curves is, indeed, marked, even for low values of S, where all the curves' symmetries become permanently broken. As S increases, the graphs become more distorte…
The renormalization method is applied to investigate the electron transmission properties of a circuit containing a benzene molecule, in which one of the carbon atoms has been modified so as to simulate displacement in position or replacement by another atom. Consideration of the different possible attachments of the leads, and the relative location of the modified atom, results in 9 distinct configurations to examine. For each configuration, the number and locations of anti-resonances, and whether they shift upon variation of the parameters, is seen to be the key to determining the shape of t…
The renormalization method has been previously used in conjunction with the Lippman-Schwinger equation to calculate transmission probabilities for benzene molecules, within the tight-binding approximation. Those results are extended here by presenting explicit formulas for the transmission probability functions, which are subsequently analysed for their anti-resonances, resonances and other maxima and minima.
Using the tight-binding model and the generalized Green's function formalism, the effect of quantum interference on the electron transport through the benzene molecule in a semiconductor/benzene/semiconductor junction is numerically investigated. We show how the quantum interference sources, different contact positions and local gate, can control the transmission characteristics of the electrode/molecule/electrode junction. We also study the occurrence of anti-resonant states in the transmission probability function using a simple graphical scheme (introduced in Ref.[Phys. Chem. Chem. Phys, 20…
The renormalization equations emerge from a Greenian-matrix solution of the discretized Schrodinger equation. A by-product of these equations is the decimation process, which enables substituted-benzenes to be mapped onto corresponding dimers, that are used to construct the series and parallel circuits of single-, double- and triple-dimers. The transmittivities of these circuits are calculated by the Lippmann-Schwinger theory, which yields the transmission-energy function T(E). The average value of T(E) provides a measure of the electron transport in the circuit in question. The undulating nat…
We present an alternative methodology for calculating the quasi-particle energy, energy loss, and optical spectra of a molecule deposited on graphene or a metallic substrate. To test the accuracy of the method it is first applied to the isolated benzene (C6H6) molecule. The quasiparticle energy levels and especially the energies of the benzene excitons (triplet, singlet, optically active and inactive) are in very good agreement with available experimental results. It is shown that the vicinity of the various substrates (pristine/doped graphene or (jellium) metal surface) reduces the quasiparti…
The transport through a quantum-scale device may be characterized by the transmission eigenvalues. These values constitute a junction PIN code where, for example, in single-atom metallic contacts the number of transmission channels is also the chemical valence of the atom. Recently, highly conductive single-molecule junctions (SMJ) with multiple transport channels have been formed from benzene molecules between Pt electrodes. Transport through these multi-channel SMJs is a probe of both the bonding properties at the lead-molecule interface and of the molecular symmetry. Here we utilize a many-…
While mesoscopic conducting loops are sensitive to external magnetic fields, as seen by observations of the Aharonov-Bohm (AB) effect in such structures, the field needed to observe the AB periodicity in small molecular rings is unrealistically large. The present study aims to identify conditions under which magnetic field dependence can be observed in electronic conduction through such molecules. We consider molecular ring structures modeled both within the tight-binding (Hückel) model and as continuous rings. In fact, much of the observed qualitative behavior can be rationalized in terms of …
We calculate transmission eigenvalue distributions for Pt-benzene-Pt and Pt-butadiene-Pt junctions using realistic state-of-the-art many-body techniques. An effective field theory of interacting $π$-electrons is used to include screening and van der Waals interactions with the metal electrodes. We find that the number of dominant transmission channels in a molecular junction is equal to the degeneracy of the molecular orbital closest to the metal Fermi level.
We predict an enormous order-dependent quantum enhancement of thermoelectric effects in the vicinity of a higher-order `supernode' in the transmission spectrum of a nanoscale junction. Single-molecule junctions based on 3,3'-biphenyl and polyphenyl ether (PPE) are investigated in detail. The nonequilibrium thermodynamic efficiency and power output of a thermoelectric heat engine based on a 1,3-benzene junction are calculated using many-body theory, and compared to the predictions of the figure-of-merit ZT.
We discuss the general form of the transmission spectrum through a molec- ular junction in terms of the Green function of the isolated molecule. By introducing a tight binding method, we are able to translate the Green func- tion properties into practical graphical rules for assessing beforehand the possible existence of antiresonances in an energy range for a given choice of connecting sites. The analysis is exemplified with a benzene molecule under a hypothetical local gate, which allows one to continuously tune the on-site energy of single atoms, for various connection topologies and gate p…
The effect of dephasing on electron transport through a benzene molecule is carefully examined using a phenomenological model introduced by Büttiker. Within a tight-binding framework all the calculations are performed based on the Green's function formalism. We investigate the influence of dephasing on transmission probability and current-voltage characteristics for three different configurations ({\em ortho}, {\em meta} and {\em para}) of the molecular system depending on the locations of two contacting leads. The presence of dephasing provides a significant change in the spectral properties …
The effects of water wetting conditions on the transport properties of molecular nano-junctions are investigated theoretically by using a combination of classical molecular dynamics and first principles electronic transport calculations. These are at the level of the non-equilibrium Green's function method implemented for self-interaction corrected density functional theory. We find that water effectively produces electrostatic gating to the molecular junction, with a gating potential determined by the time-averaged water dipole field. Such a field is large for the polar benzene-dithiol molecu…
Single-molecule biosensing, with a promise of being applied in protein and DNA sequencing, could be achieved using tunneling current approach. Electrode-molecule-electrode tunneling current critically depends on whether molecular levels contribute to electronic transport or not. Here we found employing DFT and Non-Equilibrium Green's Function formalism that energies of benzene molecular levels placed between graphene electrodes are strongly influenced by electrode termination. Termination-dependent dipoles formed at the electrode ends induce in-gap field effect that is responsible for shifting…
Interaction of graphene with a defect layer of a 1D defective photonic structure correspondingly could open a Dirac gap in its nonlinear energy dispersion. Also, an excitonic gap could be created upon applied strong magnetic fields at low temperatures. Now, the exact solution for the transmission of the allowed defective states under the influence of a homogeneous magnetic field requires providing a new scheme for the transfer matrix method to cover the circularly polarized propagation of the light in THz regime. In this paper, through an easy-to-follow framework for obtaining the distinct exp…
Klein tunneling refers to the absence of normal backscattering of electrons even under the case of high potential barriers. At the barrier interface, the perfect matching of electron and hole wavefunctions enables a unit transmission probability for normally incident electrons. It is theoretically and experimentally well understood in two-dimensional relativistic materials such as graphene. Here we investigate the Klein tunneling effect in Weyl semimetals under the influence of magnetic field induced by anti-symmetric ferromagnetic stripes placed at barrier boundaries. Our results show that th…
We study the conductance $g$ of an electron interferometer created in a two dimensional electron gas between a nanostructured contact and the depletion region induced by the charged tip of a scanning gate microscope. Using non-interacting models, we study the beating pattern of interference fringes exhibited by the images giving $g$ as a function of the tip position when a parallel magnetic field is applied. The analytical solution of a simplified model allows us to distinguish between two cases: (i) If the field is applied everywhere, the beating of Fabry-Pérot oscillations of opposite spins …
We report the one-electron spectrum and eigenstates of infinite achiral and chiral $(2m,m)$ carbon nanotubes found by using the analytic solution to the Schrödinger equation for the tight-binding Hückel-type Hamiltonian. With the help of matching the wave functions on the interfaces between the regions, where electrons have different site energies, we find and compare the transmission coefficients for zigzag, armchair and chiral nanotubes subjected to the action of an applied step-like potential. The correspondence between the nanotube band structure and the energy dependence of the transmissi…
Spin transport in thin-film materials can be studied by ferromagnetic resonantly (FMR) driven spin pumping of a charge-free spin current which induces an electromotive force through the inverse spin Hall effect (ISHE). For quantitative ISHE experiments, precise control of the FMR driving field amplitude $B_1$ is crucial. This study exploits in situ monitoring of $B_1$ by utilization of electron paramagnetic resonantly (EPR) induced transient nutation of paramagnetic molecules (a 1:1 complex of α,γ-bisdiphenylene-β-phenylallyl and benzene, BDPA) placed as $B_1$ probe in proximity of a NiFe/Pt-b…
We show that, on general theoretical grounds, transmission of light in graphene always presents a non-vanishing minimum value independently of any material and physical condition, the transmission coefficient being higher in the presence of a substrate, and getting increasing when QED corrections higher than alpha come into play. Explicit numerical calculations for typical cases are carried out when an external magnetic field is applied to the sample, showing that, in epitaxial graphene, a threshold effect exists leading to a non trivial minimum transmission, for a non vanishing light frequenc…
