Emergent quantum states in novel 2D materials

The list of outstanding properties of graphene is long, but important items are still missing. These items include intrinsic
magnetism, superconductivity, and topological phases. The three states have been predicted to show up in graphene, but further
theoretical analysis and experimental results uncovered the difficulties to realize them.
1) Robust intrinsic magnetism
Predicted to be observed in many ways, for example ferromagnestim in bilayer graphene, the most promising way is based on
the zero energy states induced by vacancies. Only paramagnetic behavior has been observed so far associated to vacancies.
2) Superconductivity
Observed in intercalated graphite, its realization in graphene requires prohibitive doping levels.
3) Topological phases
One of the first predictions of a topological insulator was made for graphene. The effect is hampered by a negligible spin-orbit
coupling constant.The discovery of graphene has made us realize that Nature offers many other 2D materials. This is precisely the innovativecharacter of the present project, where we aim to explore whether the quantum states mentioned above, still elusive in graphene,are favoured in novel 2D materials. The study of 2D materials beyond graphene is key to enhance graphene's properties bycombining this material with monolayers of 2D crystals in superstructures, which will allow broadening of the range of functional
applications of graphene. We will focus on transition metal dechalcogenides, with emphasis on MoS2. Atomic layers of this material can be produced usingmechanical exfoliation or chemical vapor deposition. We will also explore silicene, which can be seen as the silicon equivalent of graphene. It has been produced epitaxially on the Ag(111) surface. The choice for these materials is based on the evidence that  they may realize in a robust way the quantum phases that complement the properties of graphene.
1) Magnetic quantum states
Ferromagnetism has recently been reported in proton irradiated multilayered MoS2. Using a tight-binding model for MoS2
recently developed by members of the team  we will explore the robustness and possible field-effect control of magnetic
moments induced by vacancies in monolayer MoS2 and other transition metal dechalcogenides. This tight-binding model is ideal not only for mean-field and perturbative treatments but also for studies using Quantum Monte Carlo (QMC) methods. The team
has an established experience in the treatment of vacancies in graphene and graphite and their role in magnetism.
2) Superconducting quantum states
Superconductivity has recently been reported in highly doped multilayered MoS2, and a gap compatible with a superconducting
state has been observed in silicene. For MoS2, team members have recently pointed out that electron-electron
interactions in a single-layer of MoS2 might be the origin of superconductivity in the conduction band. The hole doped regime,
however, has not been explored yet. The spin orbit coupling in MoS2 introduces a sizable spin-splitting in the valance band.
Topological superconductivity  in this regime is not ruled out and will be investigated. For silicene we will study the role of electron-electron interactions and spin-orbit coupling in the observed superconducting state, and explore possible superconducting
phases in bilayer silicene.
3) Topological quantum states
Due to the enhanced spin-orbit coupling, silicene is a candidate material to display the quantum spin Hall insulating state first
predicted for graphene. Moreover, similarly to bilayer graphene a perpendicular electric field induces a trivial gap insulator, making the system an unusual tunable topological insulator. Following recent work by members of the team we will explore the robustness of such topological state to electron-electron interactions. We will study whether topological states may
also be stabilized in multilayer silicene or transition metal dechalcogenides. We will also explore the realization of topological
quantum Hall states in these systems by applying a perpendicular magnetic field. Using the team experience in the optical
characterization of graphene  we will study the optical properties of these materials both in trivial and non-trivial phases.