Contents -- Preface -- Acknowledgments -- Brief history of the field and experimental techniques -- 1. The birth of molecular electronics -- 1.1 Why molecular electronics? -- 1.2 A brief history of molecular electronics -- 1.3 Scope and structure of the book -- 2. Fabrication of metallic atomic-size contacts -- 2.1 Introduction -- 2.2 Techniques involving the scanning electron microscope (STM) -- 2.3 Methods using atomic force microscopes (AFM) -- 2.4 Contacts between macroscopic wires -- 2.5 Transmission electron microscope -- 2.6 Mechanically controllable break-junctions (MCBJ) -- 2.7 Electromigration technique -- 2.8 Electrochemical methods -- 2.9 Recent developments -- 2.10 Electronic transport measurements -- 2.11 Exercises -- 3. Contacting single molecules: Experimental techniques -- 3.1 Introduction -- 3.2 Molecules for molecular electronics -- 3.2.1 Hydrocarbons -- 3.2.2 All carbon materials -- 3.2.3 DNA and DNA derivatives -- 3.2.4 Metal-molecule contacts: anchoring groups -- 3.2.5 Conclusions: molecular functionalities -- 3.3 Deposition of molecules -- 3.4 Contacting single molecules -- 3.4.1 Electromigration technique -- 3.4.2 Molecular contacts using the transmission electron microscope -- 3.4.3 Gold nanoparticle dumbbells -- 3.4.4 Scanning probe techniques -- 3.4.4.1 Direct contact -- 3.4.4.2 Contacting rod-like molecules -- 3.4.4.3 STM in liquid environment -- 3.4.5 Mechanically controllable break-junctions (MCBJs) -- 3.5 Contacting molecular ensembles -- 3.5.1 Nanopores -- 3.5.2 Shadow masks -- 3.5.3 Conductive polymer electrodes -- 3.5.4 Microtransfer printing -- 3.5.5 Gold nanoparticle arrays -- 3.6 Exercises -- Theoretical background -- 4. The scattering approach to phase-coherent transport in nanocontacts -- 4.1 Introduction -- 4.2 From mesoscopic conductors to atomic-scale junctions.

4.3 Conductance is transmission: Heuristic derivation of the Landauer formula -- 4.4 Penetration of a potential barrier: Tunnel e ect -- 4.5 The scattering matrix -- 4.5.1 Definition and properties of the scattering matrix -- 4.5.2 Combining scattering matrices -- 4.6 Multichannel Landauer formula -- 4.6.1 Conductance quantization in 2DEG: Landauer formula at work -- 4.7 Shot noise -- 4.8 Thermal transport and thermoelectric phenomena -- 4.9 Limitations of the scattering approach -- 4.10 Exercises -- 5. Introduction to Green's function techniques for systems in equilibrium -- 5.1 The Schrodinger and Heisenberg pictures -- 5.2 Green's functions of a noninteracting electron system -- 5.3 Application to tight-binding Hamiltonians -- 5.3.1 Example 1: A hydrogen molecule -- 5.3.2 Example 2: Semi-infinite linear chain -- 5.3.3 Example 3: A single level coupled to electrodes -- 5.4 Green's functions in time domain -- 5.4.1 The Lehmann representation -- 5.4.2 Relation to observables -- 5.4.3 Equation of motion method -- 5.5 Exercises -- 6. Green's functions and Feynman diagrams -- 6.1 The interaction picture -- 6.2 The time-evolution operator -- 6.3 Perturbative expansion of causal Green's functions -- 6.4 Wick's theorem -- 6.5 Feynman diagrams -- 6.5.1 Feynman diagrams for the electron-electron interaction -- 6.5.2 Feynman diagrams for an external potential -- 6.6 Feynman diagrams in energy space -- 6.7 Electronic self-energy and Dyson's equation -- 6.8 Self-consistent diagrammatic theory: The Hartree-Fock approximation -- 6.9 The Anderson model and the Kondo effect -- 6.9.1 Friedel sum rule -- 6.9.2 Perturbative analysis -- 6.10 Final remarks -- 6.11 Exercises -- 7. Nonequilibrium Green's functions formalism -- 7.1 The Keldysh formalism -- 7.2 Diagrammatic expansion in the Keldysh formalism -- 7.3 Basic relations and equations in the Keldysh formalism.

7.3.1 Relations between the Green's functions -- 7.3.2 The triangular representation -- 7.3.3 Unperturbed Keldysh-Green's functions -- 7.3.4 Some comments on the notation -- 7.4 Application of Keldysh formalism to simple transport problems -- 7.4.1 Electrical current through a metallic atomic contact -- 7.4.2 Shot noise in an atomic contact -- 7.4.3 Current through a resonant level -- 7.5 Exercises -- 8. Formulas of the electrical current: Exploiting the Keldysh formalism -- 8.1 Elastic current: Microscopic derivation of the Landauer formula -- 8.1.1 An example: back to the resonant tunneling model -- 8.1.2 Nonorthogonal basis sets -- 8.1.3 Spin-dependent elastic transport -- 8.2 Current through an interacting atomic-scale junction -- 8.2.1 Electron-phonon interaction in the resonant tunneling model -- 8.2.2 The Meir-Wingreen formula -- 8.3 Time-dependent transport in nanoscale junctions -- 8.3.1 Photon-assisted resonant tunneling -- 8.4 Exercises -- 9. Electronic structure I: Tight-binding approach -- 9.1 Basics of the tight-binding approach -- 9.2 The extended Huckel method -- 9.3 Matrix elements in solid state approaches -- 9.3.1 Two-center matrix elements -- 9.4 Slater-Koster two-center approximation -- 9.5 Some illustrative examples -- 9.5.1 Example 1: A benzene molecule -- 9.5.2 Example 2: Energy bands in line, square and cubic Bravais lattices -- 9.5.3 Example 3: Energy bands of graphene -- 9.6 The NRL tight-binding method -- 9.7 The tight-binding approach in molecular electronics -- 9.7.1 Some comments on the practical implementation of the tight-binding approach -- 9.7.2 Tight-binding simulations of atomic-scale transport junctions -- 9.8 Exercises -- 10. Electronic structure II: Density functional theory -- 10.1 Elementary quantum mechanics -- 10.1.1 The Schrodinger equation -- 10.1.2 The variational principle for the ground state.

10.1.3 The Hartree-Fock approximation -- 10.2 Early density functional theories -- 10.3 The Hohenberg-Kohn theorems -- 10.4 The Kohn-Sham approach -- 10.5 The exchange-correlation functionals -- 10.5.1 LDA approximation -- 10.5.2 The generalized gradient approximation -- 10.5.3 Hybrid functionals -- 10.6 The basic machinery of DFT -- 10.6.1 The LCAO Ansatz in the Kohn-Sham equations -- 10.6.2 Basis sets -- 10.7 DFT performance -- 10.8 DFT in molecular electronics -- 10.8.1 Combining DFT with NEGF techniques -- 10.8.2 Pluses and minuses of DFT-NEGF-based methods -- 10.9 Exercises -- Metallic atomic-size contacts -- 11. The conductance of a single atom -- 11.1 Landauer approach to conductance: brief reminder -- 11.2 Conductance of atomic-scale contacts -- 11.3 Conductance histograms -- 11.4 Determining the conduction channels -- 11.5 The chemical nature of the conduction channels of oneatom contacts -- 11.6 Some further issues -- 11.7 Conductance fluctuations -- 11.8 Atomic chains: Parity oscillations in the conductance -- 11.9 Concluding remarks -- 11.10 Exercises -- 12. Spin-dependent transport in ferromagnetic atomic contacts -- 12.1 Conductance of ferromagnetic atomic contacts -- 12.2 Magnetoresistance of ferromagnetic atomic contacts -- 12.3 Anisotropic magnetoresistance in atomic contacts -- 12.4 Concluding remarks and open problems -- Transport through molecular junctions -- 13. Coherent transport through molecular junctions I: Basic concepts -- 13.1 Identifying the transport mechanism in single-molecule junctions -- 13.2 Some lessons from the resonant tunneling model -- 13.2.1 Shape of the I-V curves -- 13.2.2 Molecular contacts as tunnel junctions -- 13.2.3 Temperature dependence of the current -- 13.2.4 Symmetry of the I-V curves -- 13.2.5 The resonant tunneling model at work -- 13.3 A two-level model.

13.4 Length dependence of the conductance -- 13.5 Role of conjugation in -electron systems -- 13.6 Fano resonances -- 13.7 Negative differential resistance -- 13.8 Final remarks -- 13.9 Exercises -- 14. Coherent transport through molecular junctions II: Test-bed molecules -- 14.1 Coherent transport through some test-bed molecules -- 14.1.1 Benzenedithiol: how everything started -- 14.1.2 Conductance of alkanedithiol molecular junctions: A reference system -- 14.1.3 The smallest molecular junction: Hydrogen bridges -- 14.1.4 Highly conductive benzene junctions -- 14.2 Metal-molecule contact: The role of anchoring groups -- 14.3 Tuning chemically the conductance: The role of side-groups -- 14.4 Controlled STM-based single-molecule experiments -- 14.5 Conclusions and open problems -- 15. Single-molecule transistors: Coulomb blockade and Kondo physics -- 15.1 Introduction -- 15.2 Charging effects in transport through nanoscale devices -- 15.3 Single-molecule three-terminal devices -- 15.4 Coulomb blockade theory: Constant interaction model -- 15.4.1 Formulation of the problem -- 15.4.2 Periodicity of the Coulomb blockade oscillations -- 15.4.3 Qualitative discussion of the transport characteristics -- 15.4.4 Amplitudes and line shapes: Rate equations -- 15.4.4.1 Linear response -- 15.4.4.2 Non-linear transport: A simple example -- 15.5 Towards a theory of Coulomb blockade in molecular transistors -- 15.5.1 Many-body master equations -- 15.5.2 A simple example: The Anderson model . -- 15.6 Intermediate coupling: Cotunneling and Kondo effect -- 15.6.1 Elastic and inelastic cotunneling -- 15.6.2 Kondo effect -- 15.7 Single-molecule transistors: Experimental results -- 15.8 Exercises -- 16. Vibrationally-induced inelastic current I: Experiment -- 16.1 Introduction -- 16.2 Inelastic electron tunneling spectroscopy (IETS).

16.3 Highly conductive junctions: Point-contact spectroscopy (PCS).