Theory of disorder-induced half-integer thermal Hall conductance*

Thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized non-integer value kappa=5/2, which indicates a non-Abelian phase of matter. Such exotic states have long been predicted to arise at this filling factor, but the measured value disagrees with numerical studies, which predict kappa=3/2 or 7/2. I will briefly review the contradictory experimental and theoretical findings and discuss how they may be reconciled. Specifically, I will describe a possible resolution based on disorder-induced formation of mesoscopic puddles. Interactions between these puddles can generate a coherent macroscopic state that exhibits a plateau with quantized kappa=5/2 and non-Abelian quasiparticles that are distinct from those of the microscopic puddles.