Spontaneous polarization of composite fermions in the n = 1 Landau level of graphene

Motivated by recent experiments that reveal expansive fractional quantum Hall states in the n=1 graphene Landau level and suggest a nontrivial role of the spin degree of freedom [F. Amet, A. J. Bestwick, J. R. Williams, L. Balicas, K. Watanabe, T. Taniguchi, and D. Goldhaber-Gordon, Nat. Commun. 6. 5838 (2015) (/process.php?-d=ioV9v1bWGIdbvcTNUhiC3ooXZvhYxWVxoci603zT76o%3D&b= 1 )], we perform an accurate quantitative study of the competition between fractional quantum Hall states with different spin polarizations in the n=1 graphene Landau level. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the n=0 Landau level. In particular, for the states at filling factors v=s/(2s+ or -1), s positive integer, a combination of exact diagonalization and the composite fermion theory shows that the ground state is fully spin polarized and supports a robust spin-wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean-field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin-polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the n=1 graphene Landau level, indicating an absence of composite fermion pairing at half filling in the n=1 graphene Landau level.