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

Abstract

Analyzing the effective conformal field theory for the parafermionic Hall states, corresponding to filling fractions nu_k=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 T_e~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 nu_3=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 nu_2=5/2 state there is another relevant phase, in which the fundamental quasiholes obey abelian statistics and carry half-integer electric charge.