  The ability in experiments to control the relative twist angle between
successive layers in two-dimensional (2D) materials offers a new approach to
manipulating their electronic properties; we refer to this approach as
"twistronics". A major challenge to theory is that, for arbitrary twist angles,
the resulting structure involves incommensurate (aperiodic) 2D lattices. Here,
we present a general method for the calculation of the electronic density of
states of aperiodic 2D layered materials, using parameter-free hamiltonians
derived from ab initio density-functional theory. We use graphene, a semimetal,
and MoS$_2$, a representative of the transition metal dichalcogenide (TMDC)
family of 2D semiconductors, to illustrate the application of our method, which
enables fast and efficient simulation of multi-layered stacks in the presence
of local disorder and external fields. We comment on the interesting features
of their Density of States (DoS) as a function of twist-angle and local
configuration and on how these features can be experimentally observed.
