  This work put forward a comprehensive study of moire pattern in commensurate
twisted bilayer graphene (TBG) to determine the connection of moire period with
corresponding twist angle. Using the understanding of moire pattern,
computational codes are developed to simulate the planar positions of carbon
atoms lying in a large specimen of commensurate twisted bilayer graphene (CTBG)
with any commensurate twist angle. With the help of simulated moire patterns of
CTBG it is demonstrated that for many commensurate twist angles the apparent
moire period may be quite different from the actual moire period, and the same
moire pattern may have multiple slightly different values of the apparent moire
period. These multiple slightly different values of the apparent moire period
show that strain and broken rotational symmetry in moire pattern of CTBG are
intrinsic. From various values of apparent moire period, the apparent strain in
moire pattern of CTBG is calculated for many commensurate twist angles; the
calculated values of apparent strain are in good agreement with experimentally
reported values. Taking some insight from available experimental data related
to twisted bilayer graphene systems and conventional bilayer graphene systems,
corrugation in CTBG is modelled and incorporated with the simulated positions
of carbon atoms.
