Quantum Phenomena in Low-dimensional Systems
نویسنده
چکیده
A low-dimensional system is one where the motion of microscopic degrees-of-freedom, such as electrons, phonons, or photons, is restricted from exploring the full three dimensions of our world. There has been tremendous interest in low-dimensional quantum systems during the past twenty years, fueled by a constant stream of striking discoveries and also by the potential for, and realization of, new state-of-the-art electronic device architectures. The paradigm and workhorse of low-dimensional systems is the nanometer-scale semiconductor structure, or semiconductor “nanostructure,” which consists of a compositionally varying semiconductor alloy engineered at the atomic scale [1]. Traditionally one would not include naturally occurring low-dimensional entities such as atoms and molecules in the subject of this article, but some of the most exciting recent developments in the field have involved the use of molecules and even biologically important materials and has blurred the boundaries between the subject and other physical and life sciences. In addition, there are systems of great interest in physics, such as high-temperature superconductors, where the effects of reduced dimensionality are believed to be essential, and these too will be regarded as low dimensional. Many of the subjects covered here are central to the currently fashionable fields of nanoscience and nanotechnology [2,3]. The study of low-dimensional quantum phenomena has led to entirely new fields of research, such as the physics of mesoscopic systems, which will be discussed below. And low-dimensional systems have shed new light on the difficult questions of how disorder (impurities, for example) and electron-electron interaction affect a quantum system. In fact, understanding the combined effects of disorder and interactions in condensed matter systems is currently a problem of enormous interest. How are electrons, say, restricted from moving in three dimensions? The answer is confinement. Take, for example, an electron inside a long wire: The positively charged ions in the wire produce an electric field that prevents the electrons from escaping. Often, in fact, one can regard the electrons as being subjected to a hard-wall potential at the wire’s surface. The electronic eigenstates are given by a plane wave running along the wire multiplied by a localized function in the transverse directions. For a range of low energies the eigenstates have the same transverse eigenfunction and only the plane wave factor changes. This means that motion in those transverse directions is “frozen out,” leaving only motion along the wire. This article will provide a very brief introduction to the physics of low-dimensional quantum systems. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible. The fabrication of low-dimensional structures is introduced in Section II. In Section III some general features of quantum phenomena in low dimensions are discussed. The remainder of the article is devoted to particular low-dimensional quantum systems, organized by their “dimension.”
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This review article is about the role of electron-electron interactions in low dimensional systems and its transport properties in nano-structures. It begins with a review of the pair-distribution function theory of electron liquid systems taking into account the electron-electron interactions. We extend the theory for highly correlated system such two- and one-dimensional electron liquids. We...
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