Seminarium Fizyki Materii Skondensowanej

I will present (some of) the recently accumulated evidence that the topological properties of the incompressible quantum liquid formed by the electrons in a half-filled second Landau level (i.e., at the LL “filling factor” 5/2) are described by the spin-polarized “Pfaffian” wave function of Moore and Read with non-Abelian quasiparticles. One interesting aspect of the 5/2 fractional quantum Hall effect is that the experiments are carried out at rather low magnetic fields, such that the characteristic Coulomb energy can even exceed the cyclotron energy gap. This makesinter-LL excitations a (potentially) important effect, with the following consequence that will be discussed in some detail: The particle-hole conjugate of the Pfaffian is a genuine many-body state (called the “anti-Pfaffian”) despite having the same LL filling fraction (of one-half). In the commonly used approximation of an isolated Landau level, Pf and anti-Pf are exactly degenerate, but in real systems the particle-hole symmetry responsible for this degeneracy is removed by the presence of cyclotron excitations, in favor of one phase over the other. Accurate modeling of these effects has proven challenging, and two different approaches (derivation of effective many-body interactions inside anisolated LL and direct inclusion of cyclotron excitations in theconfiguration interaction diagonalization) will be presented/compared.