  The recent observed anomalous Hall effect in magic angle twisted bilayer
graphene (TBG) aligned to hexagonal boron nitride (hBN) and unconventional
ferroelectricity in Bernal bilayer graphene sandwiched by hBN present a new
platform to tune the correlated properties in graphene systems. In these
graphene-based moir\'e superlattices, the aligned hBN substrate plays an
important role. In this paper, we analyze the effects of hBN substrate on the
band structure of the TBG. By means of an atomistic tight-binding model we
calculate the electronic properties of TBG suspended and encapsulated with hBN.
Interestingly, we found that the physical properties of TBG are extremely
sensitive to the presence of hBN and they may be completely different if TBG is
suspended or encapsulated. We quantify these differences by analysing their
electronic properties, optical conductivity and band topology. We found that
the narrow bandwidth, band gap, local density of states and optical
conductivity are significantly modified by the aligned hBN substrates.
Interestingly, these electronic properties can be used as a signature of the
alignment in experiment. Moreover, the TBG/hBN superlattices in the presence or
absence of the two-fold rotation symmetry response differently to the external
electric field. For the TBG suspended in the hBN, application of an electric
field results in the charge unevenly distributed between graphene layers, which
can be used to tune the strength of the valley Hall effect or the anomalous
Hall effect. Such rich topological phase diagram in these systems may be useful
for experiments.
