The half-filled Landau level: The case for Dirac composite fermions

Abstract

In a two-dimensional electron gas under a strong magnetic field, correlations generate emergent excitations distinct from electrons. It has been predicted that "composite fermions"--bound states of an electron with two magnetic flux quanta--can experience zero net magnetic field and form a Fermi sea. Using infinite-cylinder density matrix renormalization group numerical simulations, we verify the existence of this exotic Fermi sea, but find that the phase exhibits particle-hole symmetry. This is self-consistent only if composite fermions are massless Dirac particles, similar to the surface of a topological insulator. Exploiting this analogy, we observe the suppression of 2k(F) backscattering, a characteristic of Dirac particles. Thus, the phenomenology of Dirac fermions is also relevant to two-dimensional electron gases in the quantum Hall regime.