Twist angle, strain, corrugation and moire unit cell in twisted bi-layer graphene

Knowledge of the internal configuration of carbon atoms inside a moire unit cell of twisted bi-layer graphene (TBG) would enhance the accuracy of many-body quantum mechanical calculations related to TBG. This work put forward a comprehensive theoretical study of moire pattern in TBG, supported with computational analysis; which seek a mechanism to determine the internal configuration of carbon atoms inside a moire unit cell of TBG. This study first time establishes that all twist angles are commensurate twist angles which produce perfectly periodic commensurate moire patterns of TBG. It is also first time established that strain appearing in moire patterns of TBG can occur purely due to intrinsic reasons. Taking some insight from available experimental data related to TBG systems and conventional bi-layer graphene systems, a mathematical model is also presented for corrugation in TBG. Finally we present an universal algorithm to determine the internal configuration of carbon atoms inside a moire unit cell of TBG, which is first of its kind.