Dipolar Bogolons: From Superfluids to Pfaffians

We study neutral fermionic `Bogolons' which are quasiparticle excitations of gapped phases that arise due to fermion (BCS) pairing, such as superfluids, superconductors, and paired quantum Hall states. As we demonstrate, a na\"{i}ve construction of a quasiparticle wavepacket by solving the mean-field BCS equations leads to a contradiction: there is a net electrical current {\it even when the group velocity vanishes}. Resolution of this paradox requires the computation of supercurrents in the wavepacket state, typically a complicated exercise in self-consistency. In this Letter we demonstrate that these corrections may be approximately calculated from correlations in the mean-field ground state, and lead to a divergence-free, dipolar current pattern associated with the quasiparticle. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar {\it charge} distribution, paralleling Read's observation that composite fermions are neutral dipoles.