  Ferroelectric van der Waals heterostructures provide a natural platform to
design a variety of electrically controllable devices. In this work, we
demonstrate that AB bilayer graphene encapsulated in MoTe$_2$ acts as a valley
valve that displays a switchable built-in topological gap, leading to
ferroelectrically driven topological channels. Using a combination of ab initio
calculations and low energy models, we show that the ferroelectric order of
MoTe$_2$ allows the control of the gap opening in bilayer graphene and leads to
topological channels between different ferroelectric domains. Moreover, we
analyze the effect that the moir\'e modulation between MoTe$_2$ and graphene
layers has in the topological modes, demonstrating that the edge states are
robust against moir\'e modulations of the ferroelectrically-induced electric
potential. Our results put forward ferroelectric/graphene heterostructures as
versatile platforms to engineer switchable built-in topological channels
without requiring an external electric bias.
