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.
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