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Metastable phases, in general, are unstable to nucleating droplets of the order defining the global free energy minima. However, whether such a droplet grows or shrinks relies on a competition between the surface tension and bulk energy density. In this talk I will discuss our recent work to study the role of coupling a topological fermionic field to a scalar field undergoing such nucleation processes. We find that existence of non-trivial fermionic boundary modes on the nucleating droplets leads to substantial quantum corrections to the surface tension thereby modifying the size of the critical nucleus beyond which unrestricted droplet growth happens. To illustrate the phenomena we devise a minimal model of fermions in a Chern insulating system coupled to a classical Ising field in two spatial dimensions. I will share some of the surprises and other questions we are trying to pose. |