Effects of Strain on the Flat Band in Twisted Bilayer Graphene

Based on the effective continuum model,we systematically study the electronic band structures and density of states of twisted bilayer graphene near the magic angle under the influence of different types of strain,including shear strain,volume-preserving strain and biaxial strain.We find that the flat bands behave very differently under various types of strain.Volume-preserving strain generically leads to broader van Hove singularities associated with the flat bands compared with those under shear strain,with dissimilar strain direction dependence.The band structures and density of states under shear and volume-preserving strains change with the strain direction,while those under biaxial strain are independent of the direction of strain.In particular,the effect of biaxial strain on twisted bilayer graphene is geometrically and electronically similar to the influence of the twisted angle.Our results reveal the characteristic structures in the band structures and density of states under various types of strain,which can serve as fingerprints for exploring the effects of strain on the novel physics of this system.