  We propose random tight-binding models that host macroscopically degenerate
zero energy modes and belong to the unitary class. Specifically, we employ the
molecular-orbital representation, where a Hamiltonian is constructed by a set
of non-orthogonal orbitals composed of linear combinations of atomic orbitals.
By setting the coefficients appearing in molecular orbitals to be random U(1)
variables, we can make the models belong to the unitary class. We find two
characteristic behaviors that are distinct from the random-real-valued
molecular-orbital model. Firstly, a finite energy gap opens on top of the
degenerate zero energy modes. Secondly, besides the zero energy modes, we also
argue that the band center of the finite energy modes is critical, which is
inherited from the dual counterpart, namely, the random-phase model on a
bipartite lattice. Furthermore, as a by-product of this model-construction
scheme, we also construct the random tight-binding model on a composite
lattice, where we also find a realization of critical states.
