Composite Fermions and their Fermi Surfaces

Synopsis

The decades following the initial discovery of the integer and fractional quantum Hall effects (IQHE/FQHE) in two-dimensional electrons in a strong perpendicular magnetic field led to a detailed understanding of the rich phase diagram and exotic phenomena characterizing various phases. These include charge fractionalization, Abelian and non-Abelian quantum states, topological spin excitations, charge-density-wave phases, to name a few. This body of work paved the way for the new field of topological materials in the 21st century. The composite fermion picture developed by Jain provides a natural way to understand the sequence of FQH phases. It also naturally predicts the existence of certain gapless phases at even denominator filling fractions of a Landau level in the midst of the more common gapped FQH phases with odd denominator filling fractions and quantized Hall conductance. In particular, the phase for a half-filled lowest Landau level (filling factor n = 1/2) is seen as a Fermi liquid of composite fermions formed out of electrons bound to two vortices, in the absence of a magnetic field. After briefly reviewing the arguments for various fractional quantum Hall phases following the picture of composite fermions, we concentrate on the gapless phase at filling factor n = 1/2 and explore the nature of its Fermi surface. We will compare its behavior with that of Fermi surfaces of familiar metals with weak electron-electron interactions which depend sensitively on the electronic structure of the material. We ask questions such as - What is the relationship between the Fermi surface of electrons at zero magnetic field and the composite fermion Fermi surface? How sensitive is the latter to perturbations of the zerofield Hamiltonian? What happens when the system does not have rotational symmetry with a circular Fermi surface at zero magnetic field? Using a combination of analytic and numerical techniques, we show that the answer is both surprising, and amenable to a parameter free experimental test, which it passes with surprising accuracy.

RAVINDRA BHATT

Ravindra Bhatt is Professor of Electrical Engineering and Associated Professor in Physics at Princeton University, and currently a Member of the School of Natural Sciences at the Institute for Advanced Study, Princeton. After obtaining his Ph.D. in Physics from the University of Illinois under the mentorship of William McMillan and John Bardeen, Bhatt joined the Theoretical Physics Research Department at Bell Laboratories as Member of Technical Staff in 1976, and later became Department Head. In 1990, he moved to Princeton University as Professor, where he also served as Director of the Princeton Center for Complex Materials, and Faculty Fellow and Associate Director, Princeton Center for Theoretical Science. He has held visiting appointments at several institutions including MIT, Institute for Advanced Study (Princeton), Institute for Theoretical Physics (Santa Barbara), Newton Institute (Cambridge), Ecole Normale Superieure (Paris), Imperial College (London), and Indian Institute of Science (Bangalore). Bhatt is a Fellow of the American Physical Society and American Association for the Advancement of Science, and is a recipient of a Guggenheim Fellowship. Bhatt’s research has covered diverse areas in condensed matter, such as disordered and correlated electronic systems, quantum Hall effect, quantum phase transitions, quantum and classical spin glasses, doped semiconductors, diluted magnetic semiconductors, structural phase transitions, high temperature superconductors, and quantum fluids and solids. In recent years, his research has focused on fractional quantum Hall physics-archive and the interplay of disorder and topology.