Spontaneous parity breaking of graphene in the quantum Hall regime
  We propose that the inversion symmetry of the graphene honeycomb lattice is spontaneously broken via a magnetic field dependent Peierls distortion. This leads to valley splitting of the $n=0$ Landau level but not of the other Landau levels. Compared to quantum Hall valley ferromagnetism recently discussed in the literature, lattice distortion provides an alternative explanation to all the currently observed quantum Hall plateaus in graphene. 
Jean-No\"el Fuchs (LPS), Pascal Lederer (LPS)