Christophe Mora

Topology and perfect metal in trilayer moiré graphene Christophe Mora Laboratoire Matériaux et Phénomènes Quantiques (MPQ) Université Paris Diderot The past decade has witnessed remarkable experimental achievements in the study of two-dimensional materials such as graphene, graphene-like compounds[1] or transition metal dichalcogenide (TMD) with the long-term goal of tailoring arbitrary heterostructures with desired properties. An inherent advantage of two-dimensional structures is the possibility of electrical doping to tune the Fermi level in different regimes of transport. Stacking monolayers with a small twist angle forming moiré patterns has been demonstrated to dramatically change the band structure, generating gaps and band flattening in a controllable manner, forming in certain cases topological phases of matter. The discovery in 2018 of Mott physics and unconventional superconductivity[2,3] in twisted bilayer graphene has given a very strong boost to the field. It clearly offers a versatile platform to explore strongly correlated matter in a relatively simple system. We will discuss the electronic structure of twisted graphene with three layers. After a general introduction to the topic, we will show how the band structure can be obtained in a continuum approximation valid for large moiré superlattices. We have identified “magic angles” as well as flat band regions relevant for many-body physics. Our main result[4], obtained through a symmetry analysis of the band model, is to prove that the trilayer geometry is a perfect metal in the sense that it is gapless at all energies. This remarkable property is a consequence of the number of topologically protected Dirac cones in the system. It is protected by an emergent particle-hole symmetry. Bibliography: [1] Elemental Analogues of Graphene: Silicene, Germanene, Stanene, and Phosphorene, S. Balendhran et al. small 2015, 11, 640 [2] Correlated insulator behaviour at half-filling in magic-angle graphne superlattices, Cao et al., Nature 556, 43 (2018) [3] Unconventional superconductivity in magic-angle graphene superlattices, Cao et al., Nature 556, 80 (2018) [4] Flat bands and perfect metal in trilayer moiré graphene, C. Mora, N. Regnault, B. A. Bernevig, Phys. Rev. Lett. 123, 026402 (2019)