  We study the non-Hermitian 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 postselcting special
measurement outcomes with the use of quantum-gas microscopy and can lead to
understanding the NH many-body physics triggered by exceptional manifolds in
open quantum systems.
