  It has been well established that particulate systems show the jamming
transition and critical scaling behaviors associated with it. However, our
knowledge is limited to (nearly) monodisperse systems. Recently, a binary
mixture of jammed particles with large size dispersity was studied, and it was
suggested that two distinct jammed phases appeared. Here, we conduct a thorough
numerical study on this system with a special focus on the statistics of and
finite-size effects on the fraction of small particles that participate in the
rigid network. We present strong evidence that two distinct jammed phases
appear depending on the pressure and composition of two species, which are
separated by the first-order phase transition. In one of two phases, only large
particles are jammed, whereas both small and large particles are jammed in the
other phase. We also describe the phase diagram in the pressure-composition
plane, where the first-order phase transition line terminates at a critical
point. In addition, we investigate the mechanical properties in terms of the
elastic moduli over the phase diagram and find that discontinuous changes in
elastic moduli emerge across the phase transition. Remarkably, despite the
discontinuities, the elastic moduli in each jammed phase exhibit identical
scaling laws to those in the monodisperse systems.
