Making conventional unconventional and vice versa

Although superconductivity represents a rather common phenomenon in nature, the discovery of new promising superconducting materials often occurred in fortuitous situations. In recent years, the developing of advanced computational techniques allowed reliable predictions of the superconducting critical temperature of a real materials, starting de-facto a new era for the search of new superconductors. In this talk, we review the main theoretical and computational techniques developed to calculate the superconducting properties of conventional and unconventional superconductors by first-principles. Then, we show recent predictions of new superconductors, exploiting the potentialities of conventional superconductors in unconventional realization: two-dimensionality and high-pressure. We will describe the superconducting properties of graphene and phosphorene, prototype of two dimensional systems, and the high pressure superconducting phases of simple metals (sulfur and phosphorus) and a prototype topological crystalline insulator, like SnSe.