Two-dimensional (2D) electron systems are important both for fundamental and applicative reasons: they not only are more compact (an obvious advantage for applications), but their properties (like, e.g., superconductivity, SC) can be tuned by varying density and/or disorder. Specifically, we focus on high-temperature superconductors (HTSC), like cuprates and pnictides, oxide interfaces like LaAlO3/SrTiO3 (LAO/STO), and thin disordered superconducting films (TDSCF) like InO, TiN, NbN, and transition metal dichalcogenides, which all show a superconductor-to-insulator transition (SIT) when their electron density is varied. In these systems SC often competes with other phases (insulating, magnetic, charge-ordered, ¿) giving rise to rich phase diagrams, new phenomena and possible device engineering with strongly different responses to small stimuli.
A major issue in these systems is the common formation of an intrinsically inhomogeneous state: In HTSC this takes the form of (dynamical or static) charge ordering, which is ubiquitously found at low and moderate doping. Its formation mechanism and role in determining the high critical temperature and the anomalous properties is a central issue of this field and will be addressed here. The two-dimensional electron gas formed at oxide interfaces gives rise to an inhomogeneous superconducting state with possible applicative consequences, like spin-Hall and spin-Galvanic effects. Regarding the SIT in thin films, the role of inhomogeneity on the optical properties of collective phase and amplitude excitations of the superconducting order parameter will be studied, comparing the results with the outcomes in structurally inhomogeneous systems, like arrays of Al nanograins.