Long-range field-effect from gate tuning of non-local conductivity

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.