ABSTRACT

            Following the initial discovery of the fractional quantum Hall effect (FQHE) in two-dimensional electrons in a strong perpendicular magnetic field (the Landau level regime) for an electron density corresponding to a one-third filled Landau level, and its subsequent explanation in terms of variational wavefunctions for fillings equal to inverse odd integers, the FQHE was discovered for a much larger set of fractions.

            The composite fermion picture due to Jain provides a natural way to understand these phases. The theory also naturally predicts the existence of certain gapless phases in the midst of much larger set of gapped FQH phases, corresponding to filling fractions that are inverse even integers. 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.

            In this talk, we briefly review the arguments for various fractional quantum Hall phases following the picture of composite fermions, and then go a step further – what is the nature of the Fermi surface describing the n = 1/2 state? How sensitive is it 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 (B = 0)? What is the relationship between the Fermi surface of electrons at B = 0 (which depends sensitively on the electronic structure of the material), and the composite fermion Fermi surface? Using a combination of analytic and numerical techniques, we show that the answer is both surprising, and amenable to a parameter free experimental test.