  Moir\'e systems displaying flat bands have emerged as novel platforms to
study correlated electron phenomena. Insulating and superconducting states
appear upon doping magic angle twisted bilayer graphene (TBG), and there is
evidence of correlation induced effects at the charge neutrality point (CNP)
which could originate from spontaneous symmetry breaking. Our theoretical
calculations show how optical conductivity measurements can distinguish
different symmetry breaking states, and reveal the nature of the correlated
states. In the specific case of nematic order, which breaks the discrete
rotational symmetry of the lattice, we find that the Dirac cones are displaced,
not only in momentum space but also in energy, inducing finite Drude weight at
the CNP. We also show that the sign of the dc conductivity anisotropy induced
by a nematic order depends on the degree of lattice relaxation, the doping and
the nature of the symmetry breaking.
