Stability and Activation Gaps of the Parafermionic Hall States in the Second Landau Level

Analyzing the effective conformal field theory for the parafermionic Hall states, corresponding to filling fractions νk = 2 + k/(kM + 2), k = 2, 3, . . ., M odd, we show that the even k plateaux are expected to be more stable than their odd k neighbors. The reason is that the parafermion chiral algebra can be locally extended for k even. This reconciles the theoretical implication, that the bigger the k the less stable the fluid, with the experimental fact that, for M = 1, the k = 2 and k = 4 plateaux are already observed at electron temperature Te ≃ 8 mK, while the Hall resistance for k = 3 is not precisely quantized at that temperature in the sample of Pan et al. Using a heuristic gap ansatz we estimate the activation energy gap for ν3 = 13/5 to be approximately 0.015 K, which implies that the quantization of the Hall conductance could be observed for temperature below 1 mK in the same sample. We also find an appealing exact relation between the fractional electric charge and fractional statistics of the quasiholes. Finally, we argue that besides the Moore–Read phase for the ν2 = 5/2 state there is another relevant phase, in which the fundamental quasiholes obey abelian statistics and carry half-integer electric charge.