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``Electron-Electron Interactions in Disordered Systems'' deals with the interplay of disorder and the Coulomb interaction. Prominent experts give state-of-the-art reviews of the theoretical and experimental work in this field and make it clear that the interplay of the two effects is essential, especially in low-dimensional systems.
Advances in semiconductor technology have made possible the fabrication of structures whose dimensions are much smaller than the mean free path of an electron. This book gives a thorough account of the theory of electronic transport in such mesoscopic systems. After an initial chapter covering fundamental concepts, the transmission function formalism is presented, and used to describe three key topics in mesoscopic physics: the quantum Hall effect; localisation; and double-barrier tunnelling. Other sections include a discussion of optical analogies to mesoscopic phenomena, and the book concludes with a description of the non-equilibrium Green's function formalism and its relation to the transmission formalism. Complete with problems and solutions, the book will be of great interest to graduate students of mesoscopic physics and nanoelectronic device engineering, as well as to established researchers in these fields.
This book surveys advances in the study of electron behavior in systems without periodicity--one of the most fascinating areas in solid state physics. The first half of the book covers impurity bands in three dimensions, focusing on the regime in which the electrons are spatially localized, so that an interesting interplay of localization and interaction arises. The second part of the book covers the outstanding features of two-dimensional electron systems, explaining the remarkable effects of magnetic fields, including the normal and fractional quantum Hall effect. As a whole, the book draws together findings from an enormous amount of research into the electronic properties of disordered systems, while the separate chapters may be read as self-contained units.
A thorough account of the theory of electronic transport in semiconductor nanostructures.
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.
Electron-electron interactions (EEIs) are one of the few unsolved mysteries in condensed matter physics. When these interactions are strong enough, they can lead to fascinating physics like high-Tc superconductivity, Wigner solids and many other exotic quantum phases for which there is no complete theoretical description. Fermi Liquid (FL) theory, which has emerged as the pre-eminent theory for describing EEIs, fails in these cases where interactions are strong. However, the limits of the validity of Fermi Liquid theory in an interacting electronic system has not yet been experimentally tested in a systematic way. 2D electron/hole systems (2DES/2DHS) are an ideal system for this purpose due to the wide tunability of EEI strength through changing carrier density, and the clear signatures of EEIs in 2D magneto-transport. In this thesis, we first explore magneto-transport signatures of EEIs for a weakly interacting 2DES in van der Waals (vdW) layered semiconductor InSe. We analyse these in the framework of FL theory and extract the FL parameter which quantifies electron spin-exchange interaction strength. Next, we investigate similar magneto-transport signatures of EEIs observed in a strongly interacting 2DHS in a GaAs/AlGaAs heterostructure over the temperature range 0.1-1 K. We find that, in this case, the conventional perturbative approach of treating EEIs in FL theory does not account for transport behavior in this system. We further find a resolution of this fact at higher temperatures within the range of study through the observed signatures of collective viscous transport of the 2D hole fluid, thus lending a direction to fully understand transport behavior in this strongly correlated regime. Finally, we explore the possiblity of building new nanostructures for 2D transport, by investigating the transport properties of a vdW semiconductor heterostructure InSe/GaSe. We find that this heterostructure has interesting properties like large gate-transfer hysteresis and a time-dependent conductance decay, which can be explained by considering the gate electric field induced interfacial charge transfer from InSe to GaSe enforced by the band alignment between InSe and GaSe. This work highlights important effects to consider while building new heterostructure systems to explore interesting physics and build novel devices. Overall, this thesis explores EEI effects in 2DES/2DHS over a wide range of carrier densities and in different material systems, and provides a direction for understanding these effects in the strongly correlated regime, and proposes a direction to discover new systems to explore such effects.
This volume proceeds from a description of a disordered electron liquid via effective functional or diffusion modes to a theory of interacting electrons in disordered conductors that is of the Fermi-liquid type but with renormalizable parameters. The influence of disorder on the temperature of the superconducting transition in homogeneous amorphous films is analyzed theoretically. Critical properties in the vicinity of metal-insulator transitions are discussed and spin instability is considered: the latter shows the great importance of spin fluctuation in the region of the transition.