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

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

2001-02-26

arxiv.org/abs/cond-mat/0102451v3

Nucl.Phys. B626 (2002) 415-434

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

25 pages, LaTeX2e (using ELSART), 1 figure, 2 tables; added discussion on a possible phase transition

Scientific paper

10.1016/S0550-3213(02)00069-X

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.

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