Role of Disorder in Strongly Correlated Low-Dimensional Systems

Florida State University, Tallahassee FL

Investigators

Abstract

This award supports research and education that aims to elucidate the interplay between electron-electron interaction and disorder in low dimensional electronic systems. This remains a major and difficult problem in modern condensed matter physics. This award supports studies of: edge states of fractional quantum Hall liquids, especially in the presence of edge reconstruction; bulk fractional quantum Hall liquids in the presence of disorder, focusing on the effects of disorder and interaction on their transport properties and critical behavior near the quantum phase transitions between different quantum Hall phases; quasiparticle transport properties in two-dimensional non-s-wave superconductors in the absence of time-reversal symmetry, with the cuprates as the prototype; and magnetic and superconducting properties of quantum dots and nano-size metallic grains. The PI will combine numerical and analytical methods in these investigations. Specific methods include mapping to an effective field theory, exact diagonalization, and quantum Monte Carlo simulation. Numerical studies will elucidate the topological properties, such as Chern numbers, of many-electron wave functions and quasiparticle wave functions in the PI's investigations of bulk fractional quantum Hall liquids and quasiparticle transport properties in superconductors. Calculations will focus on physical quantities that can be directly measured experimentally, and compare our results with experiments whenever possible. The broader impacts of this award are primarily educational; the work involves training the next generation of condensed matter theorists. This award supports fundamental research and education that seeks to advance our understanding of strongly interacting electrons confined to one or two dimensions and disrupted by imperfections. The PI will study the combined effect of strong correlations and disorder in a variety of materials and systems including quantum Hall systems and nanoscale ferromagnets and superconducting grains. This basic research helps improve understanding of fundamental and novel electronic states and phenomena that occur in materials and contributes to the intellectual underpinnings of potential future electronic device technologies. This award also supports training the next generation of condensed matter theorists.