Band geometry induced high angular momentum excitonic superfluid in gapped chiral fermion systems

We study the exciton condensation in the heterostructures where the electron layer and the hole layer formed by gapped chiral fermion (GCF) systems are separately gated. High angular momentum such as p - and d -wavelike excitonic pairing may emerge when the gap of the GCF systems is small compared to the Fermi energy, and the chiral winding numbers of the electrons and holes are the same. This is a result of the nontrivial band geometry and can be linked to the Berry curvature when projected onto the Fermi surface. In realistic systems, we propose that staggered graphene and surface states of magnetically doped topological insulators or intrinsic axion insulators are promising candidates for realizing p -wave exciton superfluid, and anomalous Hall conductivity can be used as a signature in experiments.