  Mirror-symmetric magic-angle twisted trilayer graphene (MATTG) hosts flat
electronic bands close to zero energy, and has been recently shown to exhibit
abundant correlated quantum phases with flexible electrical tunability. However
studying these phases proved challenging as these are obscured by intertwined
Dirac bands. In this work, we demonstrate a novel spectroscopy technique, that
allows to quantify the energy gaps and Chern numbers of the correlated states
in MATTG by driving band crossings between Dirac cone Landau levels and the
energy gaps in the flat bands. We uncover hard correlated gaps with Chern
numbers of C = 0 at integer moire unit cell fillings of nu = 2 and 3 and reveal
novel charge density wave states originating from van Hove singularities at
fractional fillings of nu = 5/3 and 11/3. In addition, we demonstrate the
existence of displacement field driven first-order phase transitions at charge
neutrality and half fillings of the moire unit cell nu = 2, which is consistent
with a theoretical strong-coupling analysis, implying the breaking of the C2T
symmetry. Overall these properties establish the diverse and electrically
tunable phase diagram of MATTG and provide an avenue for investigating
electronic quantum phases and strong correlations in multiple-band moire
systems.
