The moiré distortion effect on the flat band in twisted bilayer graphene.

We theoretically investigated the effect of non-uniform distortion on the electronic structure of twisted bilayer graphene (TBG). Usually, the flat bands of TBG can be understood by the moiré band theory based on a regular periodicity of the moiré superlattice.

In the recent experiments, however, it was observed that the moiré pattern of the actual TBG is not perfectly regular but exhibits super-moiré random structure caused by the local strain.

Here, we studied the effect of such a non-uniform distortion of the moiré pattern on the flat band of TBG. We find that the distortion splits the two degenerate flat bands into two separate portions in the energy axis, rather than simply broadening the band. We also show that the splitting width mainly depends on the interlayer-difference in the effective vector potential caused by the lattice distortion.