The origin of planetary systems, including our solar system, has been one of the fundamental questions in astronomy. Despite of immense progress over last few decades, how planets are formed within the cradles of protoplanetary disks is still an open question. In this presentation, I will talk about our latest findings which point towards a new paradigm of planetary system formation. The dust grains present in the early disk can adsorb the charged particles and reduce the gas conductivity in their vicinity. This in turn can weaken the magnetorotational instability, which is considered to be the primary source of turbulence. With the help of numerical hydrodynamic simulations, which include the dust evolution as well as dust-dependent viscosity, we found that a dusty protoplanetary disk can develop a cascade of self-sustaining Rossby vortices. These small-scale vortices collect large amounts of dust and are secularly stable. The local conditions within the vortices offer favorable sites for overcoming traditional barriers to dust growth. The phenomenon of self-sustaining vortices can explain rapid formation of planetary cores via both streaming instability and direct gravitational collapse, while also being consistent with several constraints put forward by recent observations.