Lambert C.J. Quantum Transport in Nanostructures and Molecules: An introduction to molecular electronics

IOP Publishing, 2021. — 447 p. — ISBN 978-0-7503-3637-6.Квантовый перенос в наноструктурах и молекулах: введение в молекулярную электронику
This reference text presents a conceptual framework for understanding room-temperature electron and phonon transport through molecules and other quantum objects. The flow of electricity through molecules is explained at the boundary of physics and chemistry, providing an authoritative introduction to molecular electronics for physicists, and quantum transport for chemists.
This book originated from a series of tutorials, which I have presented to new PhD students in my group for many years. Chapters 1 and 2 should be of interest to a novice wishing to be exposed to some of the terminology used to describe quantum transport at the molecular scale. Chapters 3–6 are intended to expose the reader to basic theoretical tools and by chapter 8, the reader should have enough knowledge to write their own code to solve for transport properties of arbitrary structures connected to 1d leads. Chapters 6 and 7 provide an introduction to the Landauer formula for electrical conductance and to thermoelectricity in nanostructures.
Table 8.1 of chapter 8 summarises analytic formulae for various model Green’s functions derived in later chapters. Chapter 8 also presents a new ‘magic ratio theory’ for intra-molecular bond currents. Chapters 9 and 11 generalise the discussion to structures with many leads or finite-width leads, while chapter 10 provides useful analytic results for Green’s functions of linear chains and rings. Analytic solutions for transport properties containing linear chains, pendant group and multiple paths are presented in chapters 11–13. Chapter 14 discusses relationships to time dependent states created by sources, while chapter 15 discusses densities of states and orbital product rules. Finally chapters 16 and 17 discuss technical details needed to describe transport in material specific structures.Preface
1 Introduction to molecular-scale electronics
2 Connectivity theory and noisy neighbour equations for quantum transport
3 A beginner’s guide to solving the Schrödinger equation
4 Quantum properties of linear chains and simple molecules
5 Quantum properties of electrodes in higher dimensions
6 Scattering theory of electrical conductance and thermopower
7 Thermoelectricity in nanostructures and molecules
8 A very useful formula (VUF) for the transmission coefficient of an arbitrary scatterer connected to one-dimensional leads and a magic ratio theory for intra-molecular currents
9 A quantum system connected to many scattering channels
10 Relationship between Green’s functions, wave functions and scattering amplitudes
11 Connectivity theory revisited: heteroatom substitution, decimation and the Breit–Wigner formula
12 Linear molecules
13 Quantum interference in molecules with parallel paths and pendant groups
14 Connectivity theory and equations of motion
15 Relationship between Green’s functions, molecular orbitals and densities of states
16 Solving the time-dependent Schrödinger equation and the theory of representations
17 Scattering theory in the presence of material-specific leads