Session P14: Focus Session: Transport Properties of Nanostructures V: Theory and Computation II

Electron dynamics and the approach to steady state in molecular junctions

The description of transport through a molecular junction typically invokes the idea of a steady state - the system is driven out of equilibrium, and it is assumed that on the experimental timescale it will relax to a steady state distribution. In this talk we critically examine the approach toward steady state and address the question of whether or not there might be realistic situations where steady state never obtains. The tool we use for this study is real-time dependent density functional theory. We find that while the simulations can often show systematic deviations from reality, yet our calculations suggest that non-steady-state behavior could be relevant on ultrafast timescales.   

Correlated transport in molecular junctions with novel contact configurations

The effect on quantum transport of the geometry and connectivity of single-molecule junctions is investigated using a many-body nonequilibrium Green's function approach.$^1$ The variation of intramolecular interactions due to changes in screening over an ensemble of contact geometries is found to lead to significant variations of the linear transport coefficients of the junction. The transmission phase(s) and their evolution as a function of energy are found to depend strongly on the connectivity of the junction, despite being constrained by the Friedel sum-rule. For multi-channel junctions, the channel transmissions are found to deviate significantly from the predictions of mean-field approaches due to strong Coulomb correlations.\\ $^1$J. P. Bergfield and C. A. Stafford, Phys.\ Rev.\ B {\bf 79}, 245125 (2009).   

Many body effects on energy dissipations accompanying charge transport through single molecular bridge junction

Local heating due to inelastic electron-phonon (e-ph) scatterings accompanying charge transport through single molecular bridge junction [1-3] has been theoretically discussed. [4] Here, in this talk, electron-electron collision effect on the local heating, energy dissipation and thermoelectric energy conversion will be discussed. Because the Hartree-Fock electron-electron self-energy is energy independent and it covers most of electron-electron interaction energy, the collision is mostly elastic. Inelastic contribution from electron-electron collision is limited beyond Hartree-Fock (HF) approximation. Electron correlation effect (beyond HF approximation) on the local heating and energy dissipation will be discussed using the screened Coulomb RPA (GW) approximation and beyond. Some electromagnetic problems will be addressed.\\[4pt] [1] Y. Asai, Phys. Rev. Lett. 93, 246102 (2004); 94, 099901 (2005).\\[0pt] [2] T. Shimazaki and Y. Asai, Phys. Rev. B77, 075110 (2008).\\[0pt] [3] T. Shimazaki and Y. Asai, Phys. Rev. B77, 115428 (2008).\\[0pt] [4] Y. Asai, Phys. Rev. B78, 045434 (2008) and in preparation.   

Density matrix description of non-equilibrium quantum transport

Interacting quantum systems and non-equilibrium phenomena both embody fundamental challenges in theoretical physics. Phenomena at the confluence of the two are in general not very well understood and suffer from a lack of a unifying theoretical description. In this work we focus on the nonlinear transport through a quantum dot maintained at a finite bias. Non-equilibrium quantum impurity models are reformulated in terms of the Lippmann-Schwinger operators which are used to construct a steady state density matrix and hence define an effective equilibrium. This facilitates the implementation of standard many-body techniques. We expand upon the work of Hershfield \footnote{S. Hershfield, Phys. Rev. Lett. 70, 2134 - 2137 (1993)} and show the equivalence of observables computed in the Keldysh approach and the density matrix formalism. We also show how to implement systematic perturbative as well as non-perturbative techniques using this scheme for the Anderson model far from equilibrium, in the limits of weak and large Coulomb interaction. This allows us to rigorously compute transport quantities such as the I-V characteristics and the spectral function, taking into account the full-bias dependence.   

Time-Dependent Methods for Studying Wave Packet Behavior in Graphene

Recent work on the quantum hall effect in graphene has promoted the use of time-dependent methods for studying wave packet behavior in graphene. Here we develop a framework to calculate the propagation of wave packets in finite graphene systems, permitting us to examine their interaction with cuts along the major symmetry lines as well as irregular edges. This work is supported by the U.S. Dept. of Energy Computer Science Graduate Fellowship under grant DE-FG02-97ER25308.   

Electron transport described in terms of the Dirac equation

Starting from the H{\"u}ckel Hamiltonian of finite, unsaturated hydrocarbon chains (ethylene, allyl radical, butadiene, pentadienyl radical, hexatriene, etc.), we perform a simple unitary transformation and obtain a Dirac matrix Hamiltonian. Thus already these small systems are described exactly in terms of the Dirac equation, the continuum limit of which yields the one-dimensional Dirac Hamiltonian. Using the source-sink potential method [1,2], complex potentials are introduced into the Dirac Hamiltonian to model infinite metal contacts. The electron-transport properties are then calculated and interpreted in terms of the Dirac Hamiltonian. Furthermore, we illustrate how the findings for short carbon chains carry over to a certain class of square graphene sheets.\hfill \break \noindent [1] F. Goyer, M. Ernzerhof, M. Zhuang, J. Chem. Phys. 126, 144104 (2007).\hfill \break [2] M. Ernzerhof, J. Chem. Phys. 127, 204709 (2007).   

Effects of bonding type and interface geometry on coherent transport through the single-molecule magnet Mn12

We investigate coherent electron transport through the single-molecule magnet Mn12, connected to Au electrodes, using the nonequilibrium Green's function method and density-functional theory. We analyze the impact on the electronic properties, and charge and spin transport across the junction of (i) using different bonding mechanisms and linker molecules; (ii) letting the geometry of the junction relax; (iii) using different molecular orientations. We consider nine interface geometries leading to five different bonding mechanisms and two molecular orientations. The two molecular orientations of Mn12 considered correspond to the magnetic easy axis of Mn12 parallel or normal to the direction of the electron transport. The general trend among the different bonding types and molecular orientations obtained from this study may be applied to transport through other single-molecule magnets.   

Study of convergence in quantum transport calculations

Transport calculations based on the non-equilibrium Green's function approach are most often implemented using localized atomic orbitals. We have studied the convergence properties of these calculations with respect to the number of basis states. We have found that the accuracy can be increased by using more basis states, but the computational cost rapidly increases. We show that replacing the atomic orbitals by optimized nonlocalized basis functions can significantly improve accuracy, with a lower cost than using atomic orbital states.   

Extension of the Source-Sink Potential (SSP) approach for multi-channel conductance calculations

In molecular electronics, molecules are connected to macroscopic contacts and the current passing through is studied as a function of the applied voltage. We focus on modeling the transmission of electrons through such a molecular electronic device (MED). Based on a simple H\"{u}ckel Hamiltonian to describe the $\pi$ electrons in conjugated systems, the SSP method [1,2,3] employs complex potentials to replace the wavefunction of the infinite contacts in a rigorous way. The initial SSP approach [4] was limited to two one-dimensional contacts, here we extend the approach to multiple channels, i.e., to two-dimensional contacts including transverse modes. We describe the development of the method and illustrate it with applications. \\ \\ References:\\ $[1]$ F. Goyer, M. Ernzerhof and M. Zhuang, J. Chem. Phys., 126, (2007) 144104.\\ $[2]$ M. Ernzerhof, J. Chem. Phys., 127, (2007) 204709.\\ $[3]$ B.T. Pickup and P.W. Fowler, Chem. Phys. Lett., 459, (2008) 198-202.\\ $[4]$ P. Rocheleau and M. Ernzerhof, J. Chem. Phys., 130 (17) (2009).   

Numerical studies of variable-range hopping in one-dimensional systems

We report on our recent numerical study [1] of hopping transport in disordered one-dimensional systems. A fast new algorithm, based on Dijkstra shortest-path algorithm, is devised to find the lowest-resistance path through the hopping network at arbitrary electric field. Probability distribution functions of individual resistances on the path and the net resistance are calculated and fitted to compact analytic formulas. Qualitative differences between statistics of resistance fluctuations in Ohmic and non-Ohmic regimes are elucidated. The results are compared with prior theoretical and experimental work on the subject.\\[6pt] [1] A. S. Rodin and M. M. Fogler, Phys. Rev. B 80, 155435 (2009).   

Coulomb gap in one dimension

The density of states (DOS) of a disordered system with localized electrons is studied theoretically in one dimension. Using a renormalization-group method it is shown that in the absence of screening a suppression of the DOS --- the Coulomb gap --- appears near the Fermi level. The Coulomb gap is logarithmic, in agreement with previous work; however, the numerical coefficient differs by the factor of two. This resolves the lingering discrepancy between earlier analytical and numerical results for this problem. Manifestations of the Coulomb gap in transport, tunneling, and photoemission properties of (quasi) one-dimensional systems (nanotubes, nanowires, nanoribbons, etc) are discussed.