Isospin competitions and valley polarized correlated insulators in twisted double bilayer graphene.

New phase of matter usually emerges when a given symmetry breaks spontaneously, which can involve charge, spin, and valley degree of freedoms. Here, we report an observation of new correlated insulators evolved from spin-polarized states to valley-polarized states in twisted double bilayer graphene (TDBG) driven by the displacement field (D). At a high field |D | > 0.7 V/nm, we observe valley polarized correlated insulators with a big Zeeman g factor of ~10, both at v = 2 in the moiré conduction band and more surprisingly at v = -2 in the moiré valence band. Moreover, we observe a valley polarized Chern insulator with C = 2 emanating at v = 2 in the electron side and a valley polarized Fermi surface around v = -2 in the hole side. Our results demonstrate a feasible way to realize isospin control and to obtain new phases of matter in TDBG by the displacement field, and might benefit other twisted or non-twisted multilayer systems.