  We report an order-N approach to compute the Kubo Hall conductivity for
disorderd two-dimensional systems reaching tens of millions of orbitals, and
realistic values of the applied external magnetic fields (as low as a few
Tesla). A time-evolution scheme is employed to evaluate the Hall conductivity
$\sigma_{xy}$ using a wavepacket propagation method and a continued fraction
expansion for the computation of diagonal and off-diagonal matrix elements of
the Green functions. The validity of the method is demonstrated by comparison
of results with brute-force diagonalization of the Kubo formula, using
(disordered) graphene as system of study. This approach to mesoscopic system
sizes is opening an unprecedented perspective for so-called reverse engineering
in which the available experimental transport data are used to get a deeper
understanding of the microscopic structure of the samples. Besides, this will
not only allow addressing subtle issues in terms of resistance standardization
of large scale materials (such as wafer scale polycrystalline graphene), but
will also enable the discovery of new quantum transport phenomena in complex
two-dimensional materials, out of reach with classical methods.
