  Here we present a theoretical analysis (applicable to all twist angles of
TBG) of band dispersion and density of states in TBG relating evolution of flat
band and Van-Hove singularities with evolution of interlayer coupling in TBG. A
simple tight binding Hamiltonian with environment dependent interlayer hopping
and incorporated with internal configuration of carbon atoms inside a supercell
is used to calculate band dispersion and density of states in TBG. Various
Hamiltonian parameters and functional form of interlayer hopping applicable to
a wide range of twist angles in TBG is estimated by fitting calculated
dispersion and density of states with available experimentally observed
dispersion and density of states in Graphene, AB-stacked bilayer graphene and
some TBG systems. Computationally obtained band dispersion reveal that flat
band in TBG occurs very close to Dirac point of graphene and only along linear
dimension of two-dimensional wave vector space connecting two closest Dirac
points of two graphene layers of TBG.
