Theory of disorder-induced half-integer thermal Hall conductance

The thermal Hall conductance in the half-filled first Landau level was recently measured to take the quantized noninteger value κ_{xy}=5/2 (in units of temperature times π^{2}k_{B}^{2}/3h), 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 κ_{xy}=3/2 or 7/2. We resolve this contradiction by invoking the disorder-induced formation of mesoscopic puddles with locally κ_{xy}=3/2 or 7/2. Interactions between these puddles generate a coherent macroscopic state that exhibits a plateau with quantized κ_{xy}=5/2. The non-Abelian quasiparticles characterizing this phase are distinct from those of the microscopic puddles and, by the same mechanism, could even emerge from a system comprised of microscopic Abelian puddles.