  Unconventional superconductors represent one of the most intriguing quantum
states of matter. In particular, multiorbital systems have the potential to
host exotic non-unitary superconducting states. While the microscopic origin of
non-unitarity is not yet fully solved, competing interactions are suggested to
play a crucial role in stabilizing such states. The interplay between charge
order and superconductivity has been a recurring theme in unconventionally
superconducting systems, ranging from cuprate-based superconductors to
dichalcogenide systems and even to twisted van der Waals materials. Here, we
demonstrate that the existence of competing interactions gives rise to a
non-unitary superconducting state. We show that the non-unitarity stems from a
competing charge-ordered state whose interplay with superconductivity promotes
a non-trivial multiorbital order. We establish this mechanism both from a
Ginzburg-Landau perspective, and also from a fully microscopic selfconsistent
solution of a multiorbital Dirac material. Our results put forward competing
interactions as a powerful mechanism for driving non-unitary multiorbital
superconductivity.
