Optical conductivity of twisted bilayer graphene under heterostrain

Abstract

<sec>Twisted bilayer graphene (TBG) is a two-dimensional material composed of two layers stacked at a certain angle. When the twisted angle decreases, the lattice mismatch between two layers produces moiré pattern at a long wavelength which significantly modifies the low-energy band structure. In particular, when the twisted angle is close to the so-called “magic angle”, two moiré flat bands are formed near a charge neutral point due to the strong interlayer coupling. These flat bands with high density of states are essential in realizing superconductivity and correlated insulating states. More recently, the magic angle TBG combining an hBN system has exhibited spin-valley polarization when 3/4 of flat bands are filled, thereby providing an ideal platform to achieve quantum anomalous Hall states. Whether it is TBG system or TBG-hBN system, the flat band becomes a crucial condition for discovering so rich physical connotations. Besides the twisted angle, the strain gives an alternative way to modulate flat bands. It has been reported that applying heterostrain in magic angle TBG can makes flat moiré band tunable; strain can also generate flat bands in non-magic angle TBG. Moreover, the reconstruction of TBG due to the strain gives rise to a serial of novel physical phenomena such as topological protected soliton and photonic crystal. Another reason for studying strain effect is that the strain is ubiquitous in the fabrication progress. The strain can also be controlled via piezoelectric substrate which makes possible the in situ modulation of correlated states, topology and quantum effect. </sec><sec>Our work is to study the heterostrain effect in TBG band structure and optical conductivity by using a continuum model. Although the resulting conduction band and valence bands keep connected through Dirac points protected by the <i>C</i><sub>2</sub> symmetry, their separation increases significantly when heterostrain is applied while the Dirac point is also shifted. The optical conductivity is characterized by a series of peaks associated with van Hove singularities, and the peak energies are systematically shifted with the strain amplitude. These changes show that the heterostrain exerts a great influence on electron property of TBG.</sec>