CMSA Topological Quantum Matter Seminar: Chern Mosaic and ideal bands in helical trilayer graphene

In this talk I will present helical trilayer graphene (hTTG) which is characterized an emergent real-space Chern mosaic pattern resulting from the interface of two incommensurate moiré lattices [1]. This pattern shows distinct regions with finite integer Chern numbers separated by domain walls where the spectrum is gapless and connected at all energy scales [2]. After introducing the Hamiltonian describing hTTG I will focus my attention 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 bands features the superposition of a Chern -1 and a Chern 2 bands described by the superposition of two lowest Landau level [2,3]. The origin of the flat bands can be explained using a combination of geometrical relations and symmetry arguments [3]. Building on this knowledge, I will discuss the properties of the zero-modes at higher magic angles.

[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)