  We developed an efficient numerical approach to compute the different
components of the orbital Hall responses in disordered materials from the Berry
phase theory of magnetization. We propose a theoretical framework based on the
Chebyshev expansion of Green's functions and the position operator for systems
under arbitrary boundary conditions. The capability of this scheme is
illustrated by computing the orbital Hall conductivity for gapped graphene and
Haldane model in the presence of nonperturbative disorder effects. This
methodology opens the door to realistic simulations of orbital Hall responses
in arbitrary complex models of disordered materials.
