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The effect of the warping term on the fractional quantum Hall states in topological insulators

The warping effect on the fractional quantum Hall (FQH) states in topological insulators is studied theoretically. Based on the perturbed wavefunctions, which include contributions from the warping term, analytical expressions for Haldane's pseudopotentials are obtained. We show that the warping term does not break the symmetry of the pseudopotentials for $n$=$\pm1$ Landau levels (LLs). With increasing the warping strength of the Fermi surface, our results indicate that the stability of the FQH states for LL $n=0$ (LLs $n$=$\pm1$) becomes stronger (weaker), and the excitation gap at $ν=1/3$ FQH state for LL $n$=0 also increases while the gaps for LLs $n$=$\pm1$ are unchanged.