Electronic properties of twisted bilayer graphene with biaxial heterostrain

Abstract Twisted bilayer graphene (TBG), celebrated for its flat bands at the magic angle, has garnered significant attention in condensed matter physics. Interestingly, environmental differences on both sides may lead to different strain effects (heterostrain), forming periodic moiré potentials between two graphene layers with unequal numbers of atoms. Using tight-binding calculations, we systematically study the electronic properties of TBG with biaxial heterostrain. The results reveal two distinct regimes based on the Dirac valley locations: (1) Dirac valleys remain at the K point, similar to unstrained TBG, but valley separation occurs near charge neutrality due to unequal strain; (2) a twofold degenerate Dirac valley emerges at the K point, accompanied by a fourfold degenerate valley at the Γ point, and their low-energy bands near the Fermi level are hybridized. Moreover, biaxial heterostrain weakens interlayer coupling, increases the Dirac velocity, broadens the bandwidth of the subbands near the Fermi level and modulates the bandgap at the superlattice band edge. These results may provide insights into experimental observations and motivate further research into TBG.