Interactions and Disorder in One-, Two-, and Three-Dimensional Systems

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The common theme of this theoretical research is the interplay between electron-electron interactions and the disorder in one-, two-, and three-dimensional systems. Such an interplay is at the core of many, if not all, phenomena that define the current agenda in the fields of strongly-correlated and mesoscopic systems including high-Tc materials, new phases in two-dimensional systems with and without magnetic field, quantum dots, carbon nanotubes, etc.A combination of strong interactions, disorder and reduced dimensionality may result in a significant deviation from or even a complete breakdown of the Fermi-liquid state. Non-Fermi-liquid metals are the subject of intensive studies in many subfields of condensed matter physics. An important, and in many cases only, tool for studying the Fermi-liquid state of a metal or its breakdown are the magneto-oscillations in thermodynamic and transport properties. For a Fermi liquid, the pattern of these oscillations encodes the principal parameters of the state, such as the effective mass and spin susceptibility. The first part of this project is devoted to the reconsideration of the theory of magneto-oscillations in a two-dimensional disordered, interacting system. Such a study is particularly relevant in view of recent experiments aimed at characterizing the state of electrons in semiconductor heterostructures which exhibit an unexpected metal-insulator transition, and is also of fundamental importance on its own footing. Although it is known that the conventional description of magneto-oscillations breaks down in two-dimensions, a comprehensive theory which replaces the conventional one and allows detailed comparison with experiment will be very useful.The peculiarity of a two-dimensional, interacting system is that even a relatively weak magnetic field leads to a non-perturbative reconstruction of the ground state. The theme of a magnetic-field induced reconstruction of the ground state is continued in the second part of the project that deals with three-dimensional metals in a strong magnetic field. In the extreme limit, when only the lowest Landau level remains populated, the magnetic field is known to induce instabilities of the ground state with respect to, e.g., spin-and charge-ordering or exciton pairing. It has recently been shown that the excitations of such a system behave similarly to those of a one-dimensional Luttinger liquid. This research aims at constructing a theory of transport in the "magnetic-field-induced Luttinger liquid." Also, there is a pressing need to develop the theory of dephasing in a strong magnetic field. The last part of the project is on Anderson localization and dephasing on one-dimensional systems and is related to the second part of the research project.Graduate students will be involved the project and will receive training in both solving the fundamental problems and applying them to understand experiments. Results will be incorporated into the graduate course on modern condensed matter physics that the PI teaches.%%%The common theme of this theoretical research is the interplay between electron-electron interactions and the disorder in one-, two-, and three-dimensional systems. Such an interplay is at the core of many, if not all, phenomena that define the current agenda in the fields of strongly-correlated and mesoscopic systems including high-Tc materials, new phases in two-dimensional systems with and without magnetic field, quantum dots, carbon nanotubes, etc. Graduate students will be involved the project and will receive training in both solving the fundamental problems and applying them to understand experiments. Results will be incorporated into the graduate course on modern condensed matter physics that the PI teaches.***