Theory of non-Hermitian fermionic superfluidity on a honeycomb lattice: Interplay between exceptional manifolds and Van Hove singularity

We study non-Hermitian (NH) fermionic superfluidity subject to dissipation of Cooper pairs on a honeycomb lattice, for which we analyze the attractive Hubbard model with a complex-valued interaction. Remarkably, we demonstrate the emergence of the dissipation-induced superfluid phase that is anomalously enlarged by a cusp on the phase boundary. We find that this unconventional phase transition originates from the interplay between exceptional lines and Van Hove singularity, which has no counterpart in equilibrium. Moreover, we demonstrate that the infinitesimal dissipation induces the nontrivial superfluid solution at the critical point. Our results can be tested in ultracold atoms with photoassociation techniques by postselecting special measurement outcomes with the use of quantum-gas microscopy, and they can lead to an understanding of the NH many-body physics triggered by exceptional manifolds in open quantum systems.