Dry-granular material flowing on rough inclines can experience a self-induced Rayleigh-Taylor (RT) instability followed by the spontaneous emergence of convection cells. For this to happen, particles are different in size and density; the larger particles are denser but still segregate toward the surface. When the flow is initially made of two layers of particles (dense particles above), a RT instability develops during the flow. When the flow is initially made of one homogeneous layer mixture, the granular segregation leads to the formation of an unstable layer of large, dense particles at the surface, that subsequently destabilizes in a RT plume pattern. The unstable density gradient has been only induced by the motion of the granular matter. This self-induced Rayleigh-Taylor instability and the two-layer RT instability are studied using two different methods: experiments and simulations. At last, contrary to the usual fluid behavior where the RT instability relaxes into two superimposed stable layers of fluid, the granular flow evolves to a pattern of alternated bands corresponding to recirculation cells analogous to Rayleigh-Bénard convection cells where segregation sustains the convective motion.