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Author: Lazarus Solomon Publisher: ISBN: Category : Electron transport Languages : en Pages :
Book Description
A general expression for quantum transmission of non-interacting spinless electrons through models of a fully connected network of sites that can be regarded as a nanoparticle is obtained using matrix algebra. This matrix algebra method leads to the same results given by the Green's function method without requiring the mathematical sophistication as required by the later. The model of the nanoparticle in this study comprises a single linear array of atoms that profile the input and output leads connected to a fully connected blob of atoms. A simple tight-binding Hamiltonian motivates the quantum transmission in the discrete lattice system. If there are n atoms in the nanoparticle, the methodology requires the inverse of a n x n matrix. The solution is obtained analytically for different cases: a single atom in the nanoparticle, a single dangle atom, n fully connected atoms in a mean-field type cluster with symmetric input and output connections, and the most general case where the n fully connected atoms can be connected arbitrarily to the input and output leads. A numerical solution is also provided for the case where the intra-bonds among the atoms in the nanoparticle are varied (a case with not-fully connected atoms). The expression for the transmission coefficient thus obtained using the matrix method is compared with the transmission coefficients derived using the real space Renormalization Group method and the Green's function method.
Author: Dmitry Ryndyk Publisher: Springer ISBN: 3319240889 Category : Science Languages : en Pages : 251
Book Description
This book is an introduction to a rapidly developing field of modern theoretical physics – the theory of quantum transport at nanoscale. The theoretical methods considered in the book are in the basis of our understanding of charge, spin and heat transport in nanostructures and nanostructured materials and are widely used in nanoelectronics, molecular electronics, spin-dependent electronics (spintronics) and bio-electronics. The book is based on lectures for graduate and post-graduate students at the University of Regensburg and the Technische Universität Dresden (TU Dresden). The first part is devoted to the basic concepts of quantum transport: Landauer-Büttiker method and matrix Green function formalism for coherent transport, Tunneling (Transfer) Hamiltonian and master equation methods for tunneling, Coulomb blockade, vibrons and polarons. The results in this part are obtained as possible without sophisticated techniques, such as nonequilibrium Green functions, which are considered in detail in the second part. A general introduction into the nonequilibrium Green function theory is given. The approach based on the equation-of-motion technique, as well as more sophisticated one based on the Dyson-Keldysh diagrammatic technique are presented. The main attention is paid to the theoretical methods able to describe the nonequilibrium (at finite voltage) electron transport through interacting nanosystems, specifically the correlation effects due to electron-electron and electron-vibron interactions.
Author: Massimo V. Fischetti Publisher: Springer ISBN: 3319011014 Category : Technology & Engineering Languages : en Pages : 481
Book Description
This textbook is aimed at second-year graduate students in Physics, Electrical Engineering, or Materials Science. It presents a rigorous introduction to electronic transport in solids, especially at the nanometer scale.Understanding electronic transport in solids requires some basic knowledge of Hamiltonian Classical Mechanics, Quantum Mechanics, Condensed Matter Theory, and Statistical Mechanics. Hence, this book discusses those sub-topics which are required to deal with electronic transport in a single, self-contained course. This will be useful for students who intend to work in academia or the nano/ micro-electronics industry.Further topics covered include: the theory of energy bands in crystals, of second quantization and elementary excitations in solids, of the dielectric properties of semiconductors with an emphasis on dielectric screening and coupled interfacial modes, of electron scattering with phonons, plasmons, electrons and photons, of the derivation of transport equations in semiconductors and semiconductor nanostructures somewhat at the quantum level, but mainly at the semi-classical level. The text presents examples relevant to current research, thus not only about Si, but also about III-V compound semiconductors, nanowires, graphene and graphene nanoribbons. In particular, the text gives major emphasis to plane-wave methods applied to the electronic structure of solids, both DFT and empirical pseudopotentials, always paying attention to their effects on electronic transport and its numerical treatment. The core of the text is electronic transport, with ample discussions of the transport equations derived both in the quantum picture (the Liouville-von Neumann equation) and semi-classically (the Boltzmann transport equation, BTE). An advanced chapter, Chapter 18, is strictly related to the ‘tricky’ transition from the time-reversible Liouville-von Neumann equation to the time-irreversible Green’s functions, to the density-matrix formalism and, classically, to the Boltzmann transport equation. Finally, several methods for solving the BTE are also reviewed, including the method of moments, iterative methods, direct matrix inversion, Cellular Automata and Monte Carlo. Four appendices complete the text.
Author: Kang Luo Publisher: ISBN: Category : Electrodes Languages : en Pages : 198
Book Description
Electron transport in nanoparticle single-electron transistors (SETs) is a fruitful method to explore a wide range of physical phenomena at the nanometer scale. In this thesis, we investigate electron transport in SETs incorporating various nanoparticles, including gold nanoparticles in both classical and quantum regimes and Pb nanoparticle in both superconducting and normal states. SETs have been successfully fabricated by incorporating individual gold nanoparticles into the gaps between two electrodes. Although single-electron tunneling behavior is prominent, quantized energy levels cannot be resolved in these SETs due to their relatively large particle sizes. A novel method has been developed to achieve SETs incorporating gold nanoparticles whose sizes are small enough to resolve discrete quantum energy levels. The devices consist of spontaneously-formed ultrasmall gold nanoparticles linked by alkanedithiols to gold electrodes. The devices reproducibly exhibit addition energies of a few hundred meV, which enables the observation of single electron tunneling at room temperature. At low temperatures, resonant tunneling through discrete energy levels in the Au nanoparticles is observed, which is accompanied by the excitations of molecular vibrations at large bias voltage. Having explored the SETs in normal state, we have extended the experiments to superconducting single-electron transistors (SSETs). We first fabricated and characterized Pb superconducting electrodes with nanometer-sized separation. Our observation clearly shows that conventional Barden-Cooper-Schrieffer theory remains valid to interpret the tunneling behavior between two nanometer-spaced Pb electrodes. Furthermore, by incorporating Pb nanoparticles between the two Pb electrodes, we have fabricated SSETs and investigated the transport properties of these devices. In the superconducting state, the conductance is suppressed by a combination of the single electron tunneling effect and the absence of density of states within the superconducting gap. In the suppression regime, the tunneling spectroscopy shows current features that arise from quasiparticle tunneling caused by singularity matching. At low temperature, the features can only be observed for odd charge states in SSETs. At high temperature, the odd-even parity effect is smeared out. Upon application of a magnetic field, the superconducting state is suppressed and single-electron tunneling behavior for normal metallic nanoparticles is recovered.
Author: Felix A Buot Publisher: World Scientific ISBN: 9814472972 Category : Technology & Engineering Languages : en Pages : 838
Book Description
This book presents the first comprehensive treatment of discrete phase-space quantum mechanics and the lattice Weyl-Wigner formulation of energy band dynamics, by the originator of these theoretical techniques. The author's quantum superfield theoretical formulation of nonequilibrium quantum physics is given in real time, without the awkward use of artificial time contour employed in previous formulations. These two main quantum theoretical techniques combine to yield general (including quasiparticle-pairing dynamics) and exact quantum transport equations in phase-space, appropriate for nanodevices. The derivation of transport formulas in mesoscopic physics from the general quantum transport equations is also treated. Pioneering nanodevices are discussed in the light of the quantum-transport physics equations, and an in-depth treatment of the physics of resonant tunneling devices is given. Operator Hilbert-space methods and quantum tomography are discussed. Discrete phase-space quantum mechanics on finite fields is treated for completeness and by virtue of its relevance to quantum computing. The phenomenological treatment of evolution superoperator and measurements is given to help clarify the general quantum transport theory. Quantum computing and information theory is covered to demonstrate the foundational aspects of discrete quantum dynamics, particularly in deriving a complete set of multiparticle entangled basis states.
Author: Kenji Hirose Publisher: CRC Press ISBN: 9814267597 Category : Science Languages : en Pages : 532
Book Description
As electric devices become smaller and smaller, transport simulations based on the quantum mechanics become more and more important. There are currently numerous textbooks on the basic concepts of quantum transport, but few present calculation methods in detail. This book provides various quantum transport simulation methods and shows applications
Author: Massimiliano Di Ventra Publisher: Cambridge University Press ISBN: 1139475029 Category : Science Languages : en Pages : 477
Book Description
In recent years there has been a huge increase in the research and development of nanoscale science and technology. Central to the understanding of the properties of nanoscale structures is the modeling of electronic conduction through these systems. This graduate textbook provides an in-depth description of the transport phenomena relevant to systems of nanoscale dimensions. In this textbook the different theoretical approaches are critically discussed, with emphasis on their basic assumptions and approximations. The book also covers information content in the measurement of currents, the role of initial conditions in establishing a steady state, and the modern use of density-functional theory. Topics are introduced by simple physical arguments, with particular attention to the non-equilibrium statistical nature of electrical conduction, and followed by a detailed formal derivation. This textbook is ideal for graduate students in physics, chemistry, and electrical engineering.
Author: Janez Bonca
Author: Janez Bonca
Author: Lazarus Solomon
Author: Dmitry Ryndyk
Author: Massimo V. Fischetti
Author: Kang Luo
Author: Felix A Buot
Author: Kenji Hirose
Author: Olga Trichtchenko
Author: Massimiliano Di Ventra
Author: