  In recent years, Chebyshev polynomial expansions of tight-binding Green's
functions have been successfully applied to the study of a wide range of
spectral and transport properties of materials. However, the application of the
Chebyshev approach to the study of quantum transport properties of
noninteracting mesoscopic systems with leads has been hampered by the lack of a
suitable Chebyshev expansion of Landaeur's formula or one of its equivalent
formulations in terms of Green's functions in Keldysh's perturbation theory.
Here, we tackle this issue by means of a hybrid approach that combines the
efficiency of Chebyshev expansions with the convenience of complex absorbing
potentials to calculate the conductance of two-terminal devices in a
computationally expedient and accurate fashion. The versatility of the approach
is demonstrated for mesoscopic twisted bilayer graphene (TBG) devices with up
to $2.3\times10^6$ atomic sites. Our results highlight the importance of
moir\'e effects, interlayer scattering events and twist-angle disorder in
determining the conductance curves in devices with a small twist angle near the
TBG magic angle $\theta_m \approx 1.1^\circ$.
