Title: Theory of Disorder-Induced Half-Integer Thermal Hall Conductance,
Abstract: Electrons that are confined to a single Landau level in a two dimensional
electron gas realize the effects of strong electron-electron repulsion in its
purest form. The kinetic energy of individual electrons is completely quenched
and all physical properties are dictated solely by many-body effects. A
remarkable consequence is the emergence of new quasiparticles with fractional
charge and exotic quantum statistics of which the most exciting ones are
non-Abelian quasiparticles. A non-integer quantized thermal Hall conductance
$\kappa_{xy}$ (in units of temperature times the universal constant $\pi^2
k_B^2 /3 h$; $h$ is the Planck constant and $k_B$ the Boltzmann constant)
necessitates the existence of such quasiparticles. It has been predicted, and
verified numerically, that such states are realized in the clean half-filled
first Landau level of electrons with Coulomb repulsion, with $\kappa_{xy}$
being either $3/2$ or $7/2$. Excitingly, a recent experiment has indeed
observed a half-integer value, which was measured, however, to be
$\kappa_{xy}=5/2$. We resolve this contradiction within a picture where smooth
disorder results in the formation of mesoscopic puddles with locally
$\kappa_{xy}=3/2$ or $7/2$. Interactions between these puddles generate a
coherent macroscopic state, which is reflected in an extended plateau with
quantized $\kappa_{xy}=5/2$. The topological properties of quasiparticles at
large distances are determined by the macroscopic phase, and not by the
microscopic puddle where they reside. In principle, the same mechanism might
also allow non-Abelian quasiparticles to emerge from a system comprised of
microscopic Abelian puddles.