The enigma of the $\nu=2+\frac{3}{8}$ fractional quantum Hall effect
  The fractional quantum Hall effect at $\nu=2+3/8$, which has been definitively observed, is one of the last fractions for which no viable explanation has so far been demonstrated. Our detailed study suggests that it belongs to a new class of of exotic states described by the Bonderson-Slingerland wave function. Its excitations are non-Abelian anyons similar to those of the well studied Pfaffian state at 5/2, but its wave function has a more complex structure. Using the effective edge theory, we make predictions for various measurable quantities that should enable a confirmation of the underlying topological order of this state. 
Jimmy A. Hutasoit, Ajit C. Balram, Sutirtha Mukherjee, Ying-Hai Wu,   Sudhansu S. Mandal, A. Wojs, Vadim Cheianov and J. K. Jain
cond-mat.mes-hall cond-mat.str-el