CAREER: Non-Equilibrium Transport and Disorder Effects in Quantum Wires and Related Systems

Brown University, Providence RI

Investigators

Abstract

This CAREER award combines research on low-dimensional conductors with educational activities for university and high-school students. Since future nano-devices will operate in the presence of time-dependent fields and in other far-from-equilibrium conditions, an understanding of non-equilibrium transport on the nanoscale is crucially important. Thus, a realistic description of quantum wires raises the difficult problem of non-equilibrium effects in the presence of electron interactions. Solids always contain impurities, and hence an understanding of mesoscopic transport is impossible without an understanding of the interplay of disorder and interaction. The research will employ a combination of systematic analytical and numerical methods to investigate interaction effects in far-from-equilibrium transport in quantum wires and the interplay of interaction and disorder in low-dimensional mesoscopic conductors. The research will focus on the following problems: 1. Non-equilibrium transport in Luttinger liquids. In the ratchet effect, a dc current is generated by an external ac field in a spatially asymmetric system. This effect is expected to help in the development of future nano-diodes, nano-switches, and nano-transistors. The existing theoretical studies of the ratchet effect have focused on Fermi-liquid systems and simplified models of non-interacting electrons. However, the electronic interaction is significant and results in the formation of a Luttinger liquid in quantum wires. The proposed research will include a systematic investigation of the ratchet effect in Luttinger liquids using the Keldysh technique, bosonisation, renormalization group, large-N mean-field approach, and numerical methods. 2. Spin transport far from equilibrium. There is growing interest in the physics of spin transport in mesoscopic systems. An important part of this development is the investigation of possible ways to produce a spin current. The proposed research will include a theoretical study of the spin ratchet effect in Luttinger liquids. 3. Transport in quantum Hall systems. Recent experiments on interference and tunneling of fractionally charged quasi-particles raise new fundamental questions concerning quasiparticle transport which cannot be answered by standard methods. The proposed research will combine an approach which treats a 2D electron gas as a system of interacting quantum wires with the bosonization procedure and with the methods developed in the theory of soft matter systems with quenched disorder. The approach can help to solve the problem of QHE plateau transition. Educational activities will include the development of an introductory course in nanoscience targeted primarily at freshmen; integration of recent developments in the fields related to the grant into the regular physics curriculum; participation of students and postdocs in research and related activities such as a journal club; and outreach to Providence inner-city high schools. An internet-based high-school-level tutorial will be prepared on the basis of the freshmen course. On intellectual grounds, the proposed research will advance the knowledge about strongly correlated electronic systems. The basic laws of quantum mechanics have been known for a long time, but emergent properties of many-body systems still constitute a field full of puzzles and surprises. Progress in this field is of fundamental importance. The proposed research will benefit the emergent field of far-from-equilibrium quantum many-body systems. The proposed work will employ analogies between low-dimensional electron systems and soft condensed matter and thus bridge the existing gap between hard and soft matter physics. The proposed research will also have broader impacts. A theoretical understanding of transport in quantum wires is critical for nanocircuitry. Thus, the results of this proposal will be important for the multi-disciplinary nanoscience community. The education component will advance discovery and understanding of nanoscience while promoting teaching, training and learning at different levels and broaden the participation of underrepresented groups. Non-technical abstract: The research focus is on the fundamental properties of materials in confined geometries as are found on the nanoscale. At these scales the theories we usually use have to be modified to account for confinement and this brings issues like disorder and interactions between electrons to the forefront. The research will study these fundamental issues that may form the basis for future nanoscale devices (nanoelectronics). The principal investigator will develop and teach an introductory course on nanoscience for college freshmen. He will also participate in outreach to high school students through the internet and in person. Research results will be integrated into course material.