Stripe Pairing Order in the 5/2-filling Fractional Quantum Hall State

The nu=5/2 fractional quantum Hall (FQH) state can be effectively described by a paired state of composite fermions with a chiral p-wave order parameter. Motivated by recent works showing an instability of this FQH state towards a phase with broken rotation symmetry, we study the properties of a p-wave pair density wave (PDW) state. We show that the domain walls (DWs) of the PDW order parameter support a pair of counter-propagating Majorana modes whose properties depend on the competition between the Fermi energy and the strength of the PDW order parameter. At weak coupling, the hybridization of DWs generically gives rise to a Majorana Fermi surface (MFS) that is protected by inversion and particle-hole symmetries. A uniform p-wave component gaps the MFS causing the system to enter a striped non-Abelian state with a chiral edge Majorana. At strong coupling, on the other hand, the system is described by a gapped phase without chiral Majorana edge states, which we identify with an striped Abelian paired state. The striped paired FQH state is therefore a fertile arena to study transitions between different topological orders tunned by the strength of the PDW order parameter.