RUI: Highly Correlated Systems of Reduced Dimensionality: Broken Symmetry Phases in Quantum Hall Systems

California State University-Los Angeles, Los Angeles CA

Investigators

Abstract

0086191 Rezayi This is a RUI (Research at Undergraduate Institution) award for theoretical reseach on highly correlated electrons in reduced dimensionality. Electrons confined to two-dimensional Landau levels exhibit a host of intriguing phenomena. The most notable of these is the fractional quantum Hall effect. An emerging area in quantum Hall systems is the physics of high Landau levels. Experiments show highly anisotropic and non-linear electronic transport coefficients, as well as a reentrant quantum Hall phase showing a conduction threshold. These unusual transport properties have been associated with translational symmetry-breaking phases of the two-dimensional electron gas as predicted by Koulakov, Fogler and Shklovskii and also by Moessner and Chalker. The anisotropic transport results from a striped phase and the reentrant behavior could be a signature of a pinned crystalline phase. These are different from Wigner solids in having more than one electron per unit cell. The research projects to be done here are extensive studies of these phases by numerical exact-diagonalization methods. This approach seems particularly promising as the broken-symmetry phases have already been detected using such techniques by the principal investigator, Duncan Haldane and Kun Yang. Another area of research is to study various excitations (particularly involving reversed spins) of the quantum Hall state observed at half-filling of the first excited Landau level. Recent numerical calculations by the principal investigator and Duncan Haldane favor a BCS-like spin-polarized ground state of p-wave pairing of composite fermions - a composite object made up of an electron and an attached magnetic flux carrying two units of flux quanta. Upon tilting the magnetic field towards the electron-layer, a transition to a striped phase with associated anisotropic transport has been seen experimentally. The nature of this transition, as well as the quantitative dependence of physical properties (such as the energy gap) on the tilt angle, will also be investigated. In addition, the relevance of recently proposed novel quantum Hall phases involving groupings (generalized pairings) of more than two electrons to states of the first excited Landau level will be investigated. Many of these projects involve three important phases of electronic matter: the Fermi liquid, BCS-type pairing, and charge-density wave states. The work is therefore likely to enhance and deepen our understanding of these important phases of matter and uncover important inter-relations among them. %%% This is a RUI (Research at Undergraduate Institution) award for theoretical reseach on highly correlated electrons in reduced dimensionality. Electrons confined to two-dimensional Landau levels exhibit a host of intriguing phenomena. The most notable of these is the fractional quantum Hall effect. A number of different projects will be undertaken in this field, primarily using numerical methods. Undergraduate students will participate in some phases of the research. ***