  We study phenomena driven by electron-electron interactions in the minimally
twisted bilayer graphene (mTBLG) with a perpendicular electric field. The
low-energy degrees of freedom in mTBLG are governed by a network of
one-dimensional domain-wall states, described by two channels of
one-dimensional linearly dispersing spin-1/2 fermions. We show that the
interaction can realize a spin-gapped inter-channel charge density wave (CDW)
state at low temperatures, forming a "Coulomb drag" between the channels and
leaving only one charge conducting mode. For sufficiently high temperatures,
power-law-in-temperature resistivity emerges from the charge umklapp
scatterings within a domain wall. Remarkably, the presence of the CDW states
can strengthen the charge umklapp scattering and induce a resistivity minimum
at an intermediate temperature corresponding to the CDW correlation energy. We
further discuss the conditions that resistivity of the network is dominated by
the domain walls. In particular, the power-law-in-temperature resistivity
results can apply to other systems that manifest topological domain-wall
structures.
