Effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene

We present a theoretical study of the effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene (TBG) at small twist angle, based on the band structures obtained from a continuum model. We find that heterostrain, lattice relaxation, and their combination give rise to very distinctive spectroscopic features in the optical conductivity, which can be used to probe and distinguish these effects. From the spectrum at various Fermi energies, important features in the strain- and relaxation-modified band structure, such as the band gap, bandwidth, and van Hove singularities, can be directly measured. The peak associated with the transition between the flat bands in the optical conductivity with twist angle $\ensuremath{\theta}=1.{05}^{\ensuremath{\circ}}$ are highly sensitive to the direction of the strain, which can provide direct information on the strain-modified flat bands. Moreover, discussing $\ensuremath{\theta}=1.{47}^{\ensuremath{\circ}}$ and $1.{81}^{\ensuremath{\circ}}$ as two more examples, we show that the qualitative changes of optical conductivity under the influence of strain and lattice relaxation are quite general in small-angle TBG.