  Lattice reconstruction in twisted transition-metal dichalcogenide (TMD)
bilayers gives rise to piezo- and ferroelectric moir\'e potentials for
electrons and holes, as well as a modulation of the hybridisation across the
bilayer. Here, we develop hybrid $\mathbf{k}\cdot \mathbf{p}$ tight-binding
models to describe electrons and holes in the relevant valleys of twisted TMD
homobilayers with parallel (P) and anti-parallel (AP) orientations of the
monolayer unit cells. We apply these models to describe moir\'e superlattice
effects in twisted WSe${}_2$ bilayers, in conjunction with microscopic \emph{ab
initio} calculations, and considering the influence of encapsulation, pressure
and an electric displacement field. Our analysis takes into account mesoscale
lattice relaxation, interlayer hybridisation, piezopotentials, and a weak
ferroelectric charge transfer between the layers, and describes a multitude of
possibilities offered by this system, depending on the choices of P or AP
orientation, twist angle magnitude, and electron/hole valley.
