Electron correlation and non-Fermi-liquid behavior in minimally twisted bilayer graphene

We study the phenomena driven by electron-electron interactions in 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 linearly dispersing one-dimensional spin-1/2 fermions. We show that the interaction can realize a spin-gapped inter-channel charge density wave state at generic fillings. Moreover, we demonstrate that the finite-temperature resistivity features a non-Fermi-liquid behavior due to the (linearly dispersing) electrons scattering off the incoherent charge fluctuations in the domain-wall states. Our predictions are robust against the twist-angle disorder and can apply to other moir\'e systems that manifest topological domain-wall structures.