Isospin polarized Chern insulator state of C=4 in twisted double bilayer graphene

Flat band with nearly zero dispersion can be engineered by twisting van der Waals materials relative to each other, and lead to a series of strongly correlated states, for example unconventional superconductivity, correlated insulating state, orbital magnetism. The bandwidth and topological property of electronic band structure in twisted double bilayer graphene is tunable by an external displacement field. This system could be an excellent quantum simulator to study the interplay between topological phase transition and strong electron correlation. Theoretical calculation shows that the broken of C2x symmetry in TDBG by an electric displacement field leads to finite Chern numbers at the lowest conduction and valence band near charge neutrality. Hence Chern insulator may emergent from this topological non-trivial flat band under strong electron interaction. Here, we observe Chern insulator state with Chern number 4 at filling factor v=1 under small magnetic fields on twisted double bilayer graphene with twist angle 1.48°. Moreover, the longitudinal resistance shows a peak under a parallel magnetic field and increases temperature and field, that is analogous to the Pomeranchuk effect in 3He. This phenomenon indicates that Chern insulator at v=1 may originate from isospin polarization.