First Principles Investigations Of Electronic Structure And Transport Properties Of Graphitic Structures And Single Molecular Junctions

The focus of this dissertation is the determination of the electronic structure and trans- port properties of solids. We first review some of the theory and computational methodology used in the calculation of electronic structure and materials properties. Throughout the dis- sertation, we make extensive use of state-of-the-art software packages that implement den- sity functional theory, density functional perturbation theory, and the GW approximation, in addition to specialized methods for interpolating matrix elements for extremely accurate results. The first application of the computational framework introduced is the determi- nation of band offsets in semiconductor heterojunctions using a theory of quantum dipoles at the interface. This method is applied to the case of heterojunction formed between a new metastable phase of silicon, with a rhombohedral structure, and cubic silicon. Next, we introduce a novel method for the construction of localized Wannier functions, which we have named the optimized projection functions method (OPFM). We illustrate the method on a variety of systems and find that it can reliably construct localized Wannier functions with minimal user intervention. We further develop the OPFM to investigate a class of materials called topological insulators, which are insulating in the bulk but have conductive surface states. These properties are a result of a nontrivial topology in their band structure, which has interesting effects on the character of the Wannier functions. In the last sections of the main text, the noble metals are studied in great detail, including their electronic properties and carrier dynamics. In particular, we investigate, the Fermi surface properties of the no- ble metals, specifically electron-phonon scattering lifetimes, and subsequently the transport properties determined by carriers on the Fermi surface. To achieve this, a novel sampling technique is developed, with wide applicability to transport calculations. Additionally, the generation and transport of hot carriers is studied extensively. The distribution of hot carri- ers generated from the decay of plasmons is explored over a range of energy, and the transport properties, particularly the lifetimes and mean-free-paths, of the hot carriers are determined. Lastly, appendices detailing the implementation of the algorithms developed in the work is presented, along with a useful derivation of the electron-plasmon matrix elements.

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. 3.3. Deposition of molecules. 3.4. Contacting single molecules. 3.5. Contacting molecular ensembles. 3.6. Exercises -- 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 effect. 4.5. The scattering matrix. 4.6. Multichannel Landauer formula. 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. 5.4. Green's functions in time domain. 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. 6.6. 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. 6.10. 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. 7.4. Application of Keldysh formalism to simple transport problems. 7.5. Exercises -- 8. Formulas of the electrical current : exploiting the Keldysh formalism. 8.1. Elastic current : microscopic derivation of the Landauer formula. 8.2. Current through an interacting atomic-scale junction. 8.3. Time-dependent transport in nanoscale junctions. 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. 9.4. Slater-Koster two-center approximation. 9.5. Some illustrative examples. 9.6. The NRL tight-binding method. 9.7. The tight-binding approach in molecular electronics. 9.8. Exercises -- 10. Electronic structure II : density functional theory. 10.1. Elementary quantum mechanics. 10.2. Early density functional theories. 10.3. The Hohenberg-Kohn theorems. 10.4. The Kohn-Sham approach. 10.5. The exchange-correlation functionals. 10.6. The basic machinery of DFT. 10.7. DFT performance. 10.8. DFT in molecular electronics. 10.9. Exercises -- 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 -- 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. 13.3. A two-level model. 13.4. Length dependence of the conductance. 13.5. Role of conjugation in [symbol]-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. 14.2. 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. 15.5. Towards a theory of Coulomb blockade in molecular transistors. 15.6. Intermediate coupling : cotunneling and 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). 16.4. Crossover between PCS and IETS. 16.5. Resonant inelastic electron tunneling spectroscopy (RIETS). 16.6. Summary of vibrational signatures -- 17. Vibrationally-induced inelastic current II : theory. 17.1. Weak electron-phonon coupling regime. 17.2. Intermediate electron-phonon coupling regime. 17.3. Strong electron-phonon coupling regime. 17.4. Concluding remarks and open problems. 17.5. Exercises -- 18. The hopping regime and transport through DNA molecules. 18.1. Signatures of the hopping regime. 18.2. Hopping transport in molecular junctions : experimental examples. 18.3. DNA-based molecular junctions. 18.4. Exercises -- 19. Beyond electrical conductance : shot noise and thermal transport. 19.1. Shot noise in atomic and molecular junctions. 19.2. Heating and heat conduction. 19.3. Thermoelectricity in molecular junctions -- 20. Optical properties of current-carrying molecular junctions. 20.1. Surface-enhanced Raman spectroscopy of molecular junctions. 20.2. Transport mechanisms in irradiated molecular junctions. 20.3. Theory of photon-assisted tunneling. 20.4. Experiments on radiation-induced transport in atomic and molecular junctions. 20.5. Resonant current amplification and other transport phenomena in ac driven molecular junctions. 20.6. Fluorescence from current-carrying molecular junctions. 20.7. Molecular optoelectronic devices. 20.8. Final remarks. 20.9. Exercises -- 21. What is missing in this book?

A comprehensive overview of the physical mechanisms that control electron transport and the characteristics of metal-molecule-metal (MMM) junctions. As far as possible, methods and formalisms presented elsewhere to analyze electron transport through molecules are avoided. This title introduces basic concepts--a description of the electron transport through molecular junctions—and briefly describes relevant experimental methods. Theoretical methods commonly used to analyze the electron transport through molecules are presented. Various effects that manifest in the electron transport through MMMs, as well as the basics of density-functional theory and its applications to electronic structure calculations in molecules are presented. Nanoelectronic applications of molecular junctions and similar systems are discussed as well. Molecular electronics is a diverse and rapidly growing field. Transport Properties of Molecular Junctions presents an up-to-date survey of the field suitable for researchers and professionals.

We present electronic structure and electron transport studies of materials with defects and impurities using density-functional theory. We develop a plane wave transport method based on density-functional theory for low symmetry nonorthogonal lattices. This is achieved by generalizing Choi and Ihm's algorithm for high symmetry lattices which requires the transport direction along a lattice vector that must be perpendicular to the basal plane formed by two other lattice vectors. This restriction is overcome in our method, allowing solutions to problems in which the transport direction is not along any lattice vectors. We apply our generalized transport method to calculate interface resistivity of grain boundaries in copper. Other than surface defects, we also study point defects such as single atom vacancy and impurities. Using electronic structure methods, we investigate adsorption of gold and iron clusters on perfect and defected graphene with a single vacancy. We focus on the size dependence of the electronic properties such as binding energy, charge transfer, magnetization, and density of states. Perfect graphene is found to be doped for Au clusters with an odd number of atoms and undoped with an even number of atoms. An odd-even oscillation in the magnetic moments is observed in Au-perfect as well as defected graphene system. While Fen clusters remain to be magnetic for all n, the spin of a single Fe atom on a defect site is very small due to a covalent bonding to C atoms.

The purpose of this book is to provide the reader with essential keys to a unified understanding of the rapidly expanding field of molecular materials and devices: electronic structures and bonding, magnetic, electrical and photo-physical properties, and the mastering of electrons in molecular electronics. Chemists will discover how basic quantum concepts allow us to understand the relations between structures, electronic structures, and properties of molecular entities and assemblies, and to design new molecules and materials. Physicists and engineers will realize how the molecular world fits in with their need for systems flexible enough to check theories or provide original solutions to exciting new scientific and technological challenges. The non-specialist will find out how molecules behave in electronics at the most minute, sub-nanosize level. The comprehensive overview provided in this book is unique and will benefit undergraduate and graduate students in chemistry, materials science, and engineering, as well as researchers wanting a simple introduction to the world of molecular materials.

This book is the second volume in the Handbook of Surface Science series and deals with aspects of the electronic structure of surfaces as investigated by means of the experimental and theoretical methods of physics. The importance of understanding surface phenomena stems from the fact that for many physical and chemical phenomena, the surface plays a key role: in electronic, magnetic, and optical devices, in heterogenous catalysis, in epitaxial growth, and the application of protective coatings, for example. Therefore a better understanding and, ultimately, a predictive description of surface and interface properties is vital for the progress of modern technology. An investigation of surface electronic structure is also central to our understanding of all aspects of surfaces from a fundamental point of view. The chapters presented here review the goals achieved in the field and map out the challenges ahead, both in experiment and theory.

Intensive research on fullerenes, nanoparticles, and quantum dots in the 1990s led to interest in nanotubes and nanowires in subsequent years. Handbook of Nanophysics: Nanotubes and Nanowires focuses on the fundamental physics and latest applications of these important nanoscale materials and structures. Each peer-reviewed chapter contains a broad-

Molecular Electronics is self-contained and unified in its presentation. It can be used as a textbook on nanoelectronics by graduate students and advanced undergraduates studying physics and chemistry. In addition, included in this new edition are previously unpublished material that will help researchers gain a deeper understanding into the basic concepts involved in the field of molecular electronics.

This book addresses the problem of teaching the Electronic Structure and Chemical Bonding of atoms and molecules to high school and university students. It presents the outcomes of thorough investigations of some teaching methods as well as an unconventional didactical approach which were developed during a seminar for further training organized by the University of Bordeaux I for teachers of the physical sciences.The text is the result of a collective effort by eleven scientists and teachers: physicists and chemists doing research at the university or at the CRNS, university professors, and science teachers at high-school or university level.While remaining wide open to the latest discoveries of science, the text also offers a large number of problems along with their solutions and is illustrated by several pedagogic suggestions. It is intended for the use of teachers and students of physics, chemistry, and of the physical sciences in general.