Physical Society Colloquium

Composite fermions and their fermi surfaces

Ravin Bhatt

Princeton University & Institute for Advanced Study

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 ν = 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 ν = 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 zero-field 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.