Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids

The properties of the isotropic incompressible fractional quantum Hall (FQH) state at filling 5/2 are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform px+ipy pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at filling 5/2. Motivated by these findings, I will discuss the properties of an inhomogeneous paired state – a px+ipy pair-density-wave (PDW) – whose melting could be the origin of the observed liquid-crystalline phases. This state can be viewed as an array of domain and anti-domain walls of the order parameter.

I will show that the nodes of the PDW order parameter, the location of the domain walls (and anti-domain walls) where the order parameter changes sign, support a pair of symmetry-protected counter-propagating Majorana modes. The coupling behavior of the domain wall Majorana modes crucially depends on the interplay of the Fermi energy and the PDW pairing energy. The analysis of this interplay yields a rich set of topological states. The pair-density-wave order state in paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases - as well as transitions thereof - tuned by the strength of the pairing liquid crystalline order.