  Electron-electron interactions play an important role in graphene and related
systems and can induce exotic quantum states, especially in a stacked bilayer
with a small twist angle. For bilayer graphene where the two layers are twisted
by a "magic angle", flat band and strong many-body effects lead to correlated
insulating states and superconductivity. In contrast to monolayer graphene, the
band structure of untwisted bilayer graphene can be further tuned by a
displacement field, providing an extra degree of freedom to control the flat
band that should appear when two bilayers are stacked on top of each other.
Here, we report the discovery and characterization of such displacement-field
tunable electronic phases in twisted double bilayer graphene. We observe
insulating states at a half-filled conduction band in an intermediate range of
displacement fields. Furthermore, the resistance gap in the correlated
insulator increases with respect to the in-plane magnetic fields and we find
that the g factor according to spin Zeeman effect is ~2, indicating spin
polarization at half filling. These results establish the twisted double
bilayer graphene as an easily tunable platform for exploring quantum many-body
states.
