Strongly Correlated Low-Dimensional Systems

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New growth and fabrication techniques, together with chemical and electrostatic doping, are enabling an unprecedented control and manipulation of electrons in solids. Examples range from chemically synthesized semiconductor nanowires to doped buckeyball crystals. In many cases of interest the motion of itinerant electrons is intentionally restricted by sample geometry or by strong lattice commensurability effects. Under these conditions, correlation effects are strongly enhanced and transitions into "localized" Mott or Wigner crystal states are possible. Itinerant electrons proximate to such localized phases often exhibit unusual behavior, in apparent conflict with standard Fermi liquid theory. Disentangling the subtle correlation effects and identifying the underlying physics in such technologically important systems presents a formidable challenge.In this theoretical award, the quantum physics of correlated electrons will be explored by focusing on the behavior near, or even in, the localized regime. Specifically, the following will be studied:Transport in carbon nanotubes proximate to superconductors, studying the interplay between Luttinger liquid correlations and superconducting proximity effects;Studying unidirectional charge density waves (stripe phases) in single- and bi-layer quantum Hall systems at higher Landau levels. The goal is to describe the interstripe quasi-particle dynamics in such phases by exploiting the connections between chiral Luttinger liquid and composite Fermion approaches;Continuing to develop a theoretical framework for describing the pseudogap regime of the cuprates - and Mott insulators more generally - by quantum disordering a superconductor via a proliferation of vortices. In particular, the physics and implications of the 2D Bose metal," a normal (non-super) fluid of 2D quantum bosons, will be explored;Obtaining and analyzing microscopic models of 2D electrons with large ring exchange interactions which exhibit fractionalized quantum phases. O finterest are the statistics of the particles and the experimental implications of the topological order.%%%New growth and fabrication techniques, together with chemical and electrostatic doping, are enabling an unprecedented control and manipulation of electrons in solids. Examples range from chemically synthesized semiconductor nanowires to doped buckeyball crystals. In many cases of interest the motion of itinerant electrons is intentionally restricted by sample geometry or by strong lattice commensurability effects. Under these conditions, correlation effects are strongly enhanced and transitions into "localized" Mott or Wigner crystal states are possible. Itinerant electrons proximate to such localized phases often exhibit unusual behavior, in apparent conflict with standard Fermi liquid theory. Disentangling the subtle correlation effects and identifying the underlying physics in such technologically important systems presents a formidable challenge.In this theoretical award, the quantum physics of correlated electrons will be explored by focusing on the behavior near, or even in, the localized regime. The results will be of great fundamental interest and will also influence the development of devices based on these phenomena.***