▎ 摘　　要

Magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands, and exhibits correlated quantum phases with electrical tunability. In this work, we demonstrate a spectroscopy technique that allows for dissociation of intertwined bands and quantification of the energy gaps and Chern numbers C of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and energy gaps in the flat bands. We uncover hard correlated gaps with C = 0 at integer moir & eacute; unit cell fillings of v = 2 and 3 and reveal charge density wave states originating from van Hove singularities at fractional fillings v = 5/3 and 11/3. In addition, we demonstrate displacement-field-driven first-order phase transitions at charge neutrality and v = 2, which are consistent with a theoretical strong-coupling analysis, implying C(2)Tsymmetry breaking. Overall, these properties establish a diverse electrically tunable phase diagram of MATTG and provide an avenue for investigating other related systems hosting both steep and flat bands.