  The correlated insulator (CI) states and the recently discovered density wave
(DW) states in magic-angle twisted bilayer graphene (TBG) have stimulated
intense research interest. However, up to date, the nature of these
"featureless" correlated states with zero Chern numbers are still elusive, and
are lack of characteristic experimental signature. Thus, an experimental probe
to identify the characters of these featureless CI and DW states are urgently
needed. In this work, we theoretically study the correlated insulators and
density-wave states at different integer and fractional fillings of the flat
bands in magic-angle TBG based on extended unrestricted Hartree-Fock
calculations including the Coulomb screening effects from the remote bands. We
further investigate the nonlinear optical response of the various correlated
states, and find that the nonlinear optical conductivities can be used to
identify the nature of these CI and DW states at most of the fillings.
Therefore, we propose that nonlinear optical response can serve as a promising
experimental probe to unveil the nature of the CI and DW states observed in
magic-angle TBG.
