  We study the electron and spin transport in a van der Waals system formed by
one layer with strong spin-orbit coupling and a second layer without spin-orbit
coupling, in the regime when the interlayer tunneling is random. We find that
in the layer without intrinsic spin-orbit coupling spin-charge coupled
transport can be induced by two distinct mechanisms. First, the gapless
diffusion modes of the two isolated layers hybridize in the presence of
tunneling, which constitutes a source of spin-charge coupled transport in the
second layer. Second, the random tunneling introduces spin-orbit coupling in
the effective disorder-averaged single-particle Hamiltonian of the second
layer. This results in non-trivial spin transport and, for sufficiently strong
tunneling, in spin-charge coupling. As an example, we consider a van der Waals
system formed by a two-dimensional electron gas (2DEG)--such as graphene--and
the surface of a topological insulator (TI) and show that the proximity of the
TI induces a coupling of the spin and charge transport in the 2DEG. In
addition, we show that such coupling can be tuned by varying the doping of the
TI's surface. We then obtain, for a simple geometry, the current-induced
non-equilibrium spin accumulation (Edelstein effect) caused in the 2DEG by the
coupling of charge and spin transport.
