Seminar/ Colloquium

January 23, 2023: Prof. Ravindra Bhatt, Princeton University

Title: Composite fermions and Fermi surfaces

Abstract: The Nobel prize winning discoveries of the integer and fractional quantum Hall effects (IQHE/FQHE) triggered intensive research on electrons in two dimensions in a strong perpendicular magnetic field. Detailed investigations uncovered a rich phase diagram of a seemingly very simple system and led to a comprehensive understanding of various phases, and exotic phenomena associated with them. These include charge fractionalization, Abelian and nonAbelian quantum states, topological spin excitations, and 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 are known to 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.