I will present helical trilayer graphene (hTTG), which is characterized by an emergent real-space Chern mosaic pattern resulting from the interface of two incommensurate moiré lattices [1]. This pattern shows macroscopic regions with finite Chern number separated by domain walls where the spectrum is gapless [2]. After introducing the Hamiltonian describing hTTG, I will focus on the macroscopic domains, that host isolated flat bands with intriguing properties. Upon investigating the chiral limit, where analytical expressions can be derived, we found that the flat-band zero-energy manifold features a Chern-1 and a Chern-2 band described by the superposition of two lowest Landau levels [2,3]. The origin of the flat bands can be explained using a combination of geometrical relations and symmetry arguments [2,3]. The comparison with the recent experimental findings from reference [4] is discussed.
In the second part, I shift focus to a mechanism for inducing superconductivity in heterobilayer transition metal dichalcogenides (TMDs) from a repulsive electron model [5]. Notably, the interplay of symmetries and geometrical properties leads to the emergence of a p-wave Z2 topological superconductivity. This phenomenon persists even at low doping levels, paving the way for exploring the long-sought p-wave BEC-BCS topological transition.
[1] Y.Mao, D.Guerci, C.Mora, PRB 107, 125423 (2023) [Editors' Suggestion] [2] D.Guerci, Y.Mao, C.Mora, arXiv:2305.03702 (2023)
[3] D.Guerci, Y.Mao, C.Mora, arXiv:2308.02638 (2023)
[4] L.Xia, P.Jarillo-Herrero et al., arXiv:2310.12204 (2023)
[5] V.Crépel*, D. Guerci* et al., PRL 131, 056001 (2023) [Editors' Suggestion] [* equally contributing authors]
