  We report the observation of an unexpected, long-range field-effect in
WTe$_2$ devices, leading to large gate-induced changes of the transport
properties of crystals much thicker than the electrostatic screening length.
The phenomenon --which manifests itself very differently from the conventional
field-effect-- originates from the non-local nature of transport in the devices
that are thinner than the carrier mean free path, because of the dominant role
of surface scattering. We reproduce theoretically the gate dependence of the
measured classical and quantum magneto-transport in all detail, and show that
the phenomenon is caused by the gate-tuning of the bulk carrier mobility by
changing the scattering at the surface. Our results demonstrate the possibility
to gate tune the electronic properties deep in the interior of conducting
materials, avoiding limitations imposed by electrostatic screening.
