The object of our investigation are layered and two-dimensional (2D) materials, such as cuprate and pnictide high-temperature superconductors, superconducting oxide interfaces, like LaAlO3/SrTiO3, disordered superconducting thin films, like InO, TiN, NbN, and transition metal dichalcogenides (TMDs), and graphene. Upon variation of the carrier density and/or disorder, these systems exhibit various novel phenomena, including a superconductor-to-insulator transition (SIT). Moreover, as a result of the competition between superconductivity and other phases (magnetic, charge-ordered, ...), many of these systems are characterized by a rich variety of intriguing behaviors, and their responses to different weak perturbations can be unusually sizable, opening the way to their exploitation in device engineering. In many cases, a major issue is the occurrence of an intrinsically inhomogeneous state: In cuprates, this state is characterized by dynamical or static charge ordering. The mechanism for the occurrence of CDWs and their role in determining the high critical temperature, the possible occurrence of filamentary superconductivity, and the anomalous properties of the metallic phase are central issues of this research field and will be investigated within the present project. The two-dimensional electron gas (2DEG) formed at oxide interfaces exhibits an inhomogeneous, likely rather filamentary, superconducting state, possibly realizing the long-sought quantum Griffiths phase, with rare regions affecting the properties of the system near the SIT. In oxide interfaces, TMDs, and disordered thin films, the inhomogeneity also affects the superfluid response, the current-voltage characteristics, and the properties of the magnetic-field-induced vortex lattice, calling for a systematic investigation of these effects. Finally, the investigation of the novel phenomena uncovered in field-effect-doped graphene adds a new chapter to the physics of 2D electron systems .
The present research project has both a fundamental character and relevant applicative implications. Superconductivity is nowadays experiencing a renewed interest. Recent experiments on cuprate superconductors unambiguously demonstrate the ubiquitous presence of CDWs, thereby boosting the theoretical debate about their interplay with superconductivity. In the more recent field of oxide interfaces, the relevance of inhomogeneity raised several questions and proposals. Also the field of 2D crystalline superconductors is attracting a renewed interest for the many unsolved fundamental issues and for the potential device applications. Our project is at the core of these crucial and intense activities, as it mainly deals with the interplay between superconductivity and inhomogeneities or charge ordering, giving rise to both dynamical or static density fluctuations, and investigates the inhomogeneity as an intrinsic emergent character in low-dimensional superconducting electron systems. The idea that inhomogeneity is not extrinsic, but may be a leading physical actor of low-dimensional superconductors, is a new perspective, which has emerged only recently and in various forms in the different systems mentioned above. The timeliness and relevance of the proposed research is naturally witnessed by the reference list below, which mostly contains very recent papers.
In cuprates, although the idea of fluctuating charge ordering as a particular form of electron softness was proposed by our group long ago, it found compelling experimental evidence only very recently [18]. The now well-established experimental collaborations (in RXS and transport) allow to make our theoretical scenario more detailed and rich. There is a huge activity in this field and our group is in a favourable position to answer and systematise the several open issues raised by experiments. This would bring important progress in a field that has always been broadly investigated. The field of oxide interfaces is instead more recent and it attracted great attention in the last decade. Also in this field our group played a relevant role pointing out the intrinsically inhomogeneous character of LaAlO3/SrTiO3 interfaces [6-11] and providing possible microscopic mechanisms to account for it. Again, the understanding of the electron softness mechanisms would entail the possibility of practical exploitation [19,20]. Within this respect, the vortex physics in thin superconducting films is also deeply connected to the superfluid response of a low-dimensional superconductor. In particular the identification of the hexatic phase, besides representing a challenge from the point of view of fundamental research, offers a new perspective on the possibility to tune a superconducting system to a very low-dissipative but resistive phase by means of the external magnetic field, with a plethora of possible applications.
For what concerns the graphene-based materials, our recent discovery of a large polar response in gapped graphene is a surprising result with several potential implications. First of all, the prediction of a piezoelectric coefficient per layer in mono- and bilayer graphene three times larger than that of a large-gap full polar insulator as hexagonal BN has several implications for transport properties of graphene-like systems. For example, the piezoelectric acoustic-phonons scattering can be relevant to model charge transport and charge-carrier relaxation in gated bilayer graphene. In addition, the link between the effective dynamical charge and the topological properties offers an alternative and yet completely unexplored way to investigate theoretically and experimentally the topological properties of Dirac-like systems, with a large impact for the physics of several 2D systems.
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