Research on graphene traditionally strives for highest-quality, minimal impurities and disorder in order to achieve ideal clean Dirac physics. On the other hand, the Superconductor to insulator transition (SIT) hinges on strong disorder to suppress superconductivity and enter the quantum critical regime that is dominated by quantum fluctuations. Disorder, defects and impurities are usually viewed upon as a nuisance. We propose to utilize the inhomogeneity in order to bring about novel quantum phases. There has been much effort in creating proximity structures between graphene and a superconductor, mainly in a quest to detect Majorana fermions. Another innovating aspect is the use of superconducting fluctuations in an insulator. Obviously, a good superconductor as an over-layer would short-circuit the graphene. Using a highly disordered superconductor opens a novel way to study the proximity effect in graphene. The suggested experiments offer unique access to a number of fundamental issues that have never been investigated before or have not been resolved so far: (1) How do superconducting fluctuations affect the graphene electronic properties?  (2) Where is the proximity effect most effective, at the Dirac Point or far from it? This will have significant implications on graphene-based devices. (3) Comparison between disordered CVD grown graphene and stacked flakes of hBN/SLG with a disordered superconductor over-layer. (4) Quantum hall as an over-layer is pushed through the SIT. This promises to reveal unique and interesting quantum phenomena.

A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically protected gapless surface states (TSS). BiSbTeSe2 is such a prototype 3D TI. It shows the Quantum Spin Hall Effect because of strong spin-orbit coupling which preserves the time reversal symmetry. It has been predicted/realized that TIs with their characteristic spin-helical Dirac Fermion TSS, attracted intense interest in fundamental physics and application point of view (e.g., topological quantum computing). We propose to study proximity induced superconductivity in few layer BiSbTeSe2 in contact with disordered InO film while driving the disordered systems through the superconductor to insulator transition. The surface carrier density of this TI has been shown to be small (1015/cm3) similar to low density superconductor (Indium oxide films). So, within the gate voltage range which controls the Fermi energy, one can tune it through the charge neutrality point of TSS (global Dirac point) and proximity coupled region (Superconducting Dirac point, SDP) and may realize the novel quantum phases at SDP. 

The relationship between superconductivity, dimensionality, and disorder remains a vibrant area of research. It is well-established that s-wave superconductivity can endure weak disorder without significant degradation. However, under strong disorder, the behavior changes dramatically. In 2D films, superconductivity can be disrupted by factors such as extreme disorder or non-thermal parameters, including magnetic fields, reduced thickness, altered chemical composition, or applied gate voltages. This suppression leads to a transition from a superconducting to an insulating state, termed the superconductor-insulator transition (SIT). Occurring at absolute zero temperature (T = 0), the SIT exemplifies a quantum phase transition, driven by quantum fluctuations rather than thermal effects. Despite extensive theoretical and experimental efforts, the SIT continues to provoke intense investigation and debate. A key question involves the nature of the insulating phase. Evidence suggests intriguing phenomena, such as Cooper pairing and an energy gap persisting in the insulating state. Theoretical models propose scenarios like preformed pairs or emergent electronic granularity, leading to superconducting islands within an insulating matrix. This state, termed a ‘Bosonic insulator,’ is associated with a pseudogap above the superconducting transition temperature or in the insulating phase.

The potential emergence of exotic quantum phases in strongly disordered superconductors underscores the complexity of superconductivity near the transition. Understanding these systems requires innovative theoretical approaches and advanced experimental techniques. This ongoing research highlights the rich and intricate physics of disordered superconducting films.

Complex oxides have attracted interest in condensed matter physics due to the strong correlation between their electronic structure, magnetic properties and structural transitions. Depending on their correlation, oxides can show superconductivity, ferromagneticity, ferroelasticity or a co-existance of these phases. The beauty of this system is that one can induce transformation of one phase into another by changing temperature, pressure, doping or magnetic field. When two oxides are brought together to form heterostructure, a host of phenomena can happen. An obvious advantage of oxide heterostructures over their bulk counterparts is gate voltage tunability of the interfacial charge carrier density. The mutual interplay of point group symmetry, charge inversion symmetry, U(1) gauge symmetry and spin rotation symmetry in heterostructures of these complex perovskite oxides lead to the coexistence of a host of intriguing properties - ferroelasticity, ferroelectricity, superconductivity and ferromagnetism. We want to probe the physics of the interplay of these phases by studying resistance and resistance fluctuations measurement (1/f noise).