Two-dimensional electrons at mirror and twistronic twin boundaries in van der Waals ferroelectrics

Semiconducting transition metal dichalcogenides (MX$_2$) occur in 2H and rhombohedral (3R) polytypes, respectively distinguished by anti-parallel and parallel orientation of consecutive monolayer lattices. In its bulk form, 3R-MX$_2$ is ferroelectric, hosting an out-of-plane electric polarisation, the direction of which is dictated by stacking. Here, we predict that twin boundaries, separating adjacent polarization domains with reversed built-in electric fields, are able to host two-dimensional electrons and holes with an areal density reaching $\sim 10^{13} {\rm cm}^{-2}$. Our modelling suggests that n-doped twin boundaries have a more promising binding energy than p-doped ones, whereas hole accumulation is stable at external surfaces of a twinned film. We also propose that assembling pairs of mono-twin films with a `magic' twist angle $\theta^*$ that provides commensurability between the moir\'e pattern at the interface and the accumulated carrier density, should promote a regime of strongly correlated states of electrons, such as Wigner crystals, and we specify the values of $\theta^*$ for homo- and heterostructures of various TMDs.