Technological progress made nowadays possible the design and patterning of new quantum materials with remarkable properties, and the investigation of known materials under unusual, yet controlled, conditions. One can gain control of crucial aspects, like the quantum confinement or the crystal strain, or endow a material with new characteristics. Within this context, we will investigate various systems that share some common properties, like being layered or nearly two-dimensional, hosting superconductivity, competing phenomena, the interplay of different bands, and/or disorder at different scales. We will study high-temperature cuprates and pnictide superconductors, oxide interfaces and transition metal dichalcogenides, hosting gate-tunable superconductivity, and disordered superconducting thin films. In these systems, the superconducting transition can be tuned changing the carrier density and/or the microscopic disorder. As a consequence of the competition of ordered phases with superconductivity, the electrons tend to be clumpy in these systems, and the charge density is modulated at the nanoscale. In cuprates, the competing phase is charge-ordered, and the related dynamical charge fluctuations may be responsible for superconducting pairing, and for the anomalies in the metallic phase, like a specific heath that seemingly diverges at low temperature, or a resistivity that is a linear function of the temperature down to very low temperature (the so-called Planckian behavior). We plan to improve our understanding of these intriguing phenomena. Moreover, cuprates, oxide interfaces, transition metal dichalcogenides, and disordered superconducting film, under some specific conditions, host an inhomogeneous, seemingly filamentary, superconducting state, whose equilibrium and non-equilibrium behavior will be thoroughly investigated. Some of these systems exhibit multi-band superconductivity, and the resulting variety of physical behaviors will be likewise investigated.
