  Graphene/hexagonal boron nitride (G/$h$-BN) heterostructures offer an
excellent platform for developing nanoelectronic devices and for exploring
correlated states in graphene under modulation by a periodic superlattice
potential. Here, we report on transport measurements of nearly
$0^{\circ}$-twisted G/$h$-BN heterostructures. The heterostructures
investigated are prepared by dry transfer and thermally annealing processes and
are in the low mobility regime (approximately
$3000~\mathrm{cm}^{2}\mathrm{V}^{-1}\mathrm{s}^{-1}$ at 1.9 K). The replica
Dirac spectra and Hofstadter butterfly spectra are observed on the hole
transport side, but not on the electron transport side, of the
heterostructures. We associate the observed electron-hole asymmetry to the
presences of a large difference between the opened gaps in the conduction and
valence bands and a strong enhancement in the interband contribution to the
conductivity on the electron transport side in the low-mobility G/$h$-BN
heterostructures. We also show that the gaps opened at the central Dirac point
and the hole-branch secondary Dirac point are large, suggesting the presence of
strong graphene-substrate interaction and electron-electron interaction in our
G/$h$-BN heterostructures. Our results provide additional helpful insight into
the transport mechanism in G/$h$-BN heterostructures.
