  We present a comprehensive discussion on nonunitary superconductivity in
complex quantum materials. Starting with a brief review of the notion of
nonunitary superconductivity, we discuss its spectral signatures in simple
models with only the spin as an internal degree of freedom. In complex
materials with multiple internal degrees of freedom, there are many more
possibilities for the development of nonunitary order parameters. We provide
examples focusing on d-electron systems with two orbitals, applicable to a
variety of materials. We discuss the consequences for the superconducting
spectra, highlighting that gap openings of band crossings at finite energies
can be attributed to a nonunitary order parameter if this is associated with a
finite superconducting fitness matrix $\hat{F}_C(\mathbf{k})$. We speculate
that nonunitary superconductivity in complex quantum materials is in fact very
common and can be associated with multiple cases of time-reversal symmetry
breaking superconductors.
