  We study a capacitor made of three monolayers of transition metal
dichalcogenide (TMD) separated by hexagonal Boron Nitride (hBN). We assume that
the structure is symmetric with respect to the central layer plane. The
symmetry includes the contacts: if the central layer is contacted by the
negative electrode, both external layers are contacted by the positive one. As
a result a strong enough voltage $V$ induces electron-hole dipoles (indirect
excitons) pointing towards one of the external layers. Antiparallel dipoles
attract each other at large distances. Thus, the dipoles alternate in the
central plane forming a 2D antiferroelectric with negative binding energy per
dipole. The charging of a three-layer device is a first order transition, and
we show that if $V_1$ is the critical voltage required to create a single
electron-hole pair and charge this capacitor by $e$, the macroscopic charge
$Q_c = eSn_c$ ($S$ is the device area) enters the three-layer capacitor at a
smaller critical voltage $V_{c} < V_{1}$. In other words, the differential
capacitance $C(V)$ is infinite at $V = V_{c}$. We also show that in a
contact-less three-layer device, where the chemically different central layer
has lower conduction and valence bands, optical excitation creates indirect
excitons which attract each other, and therefore form antiferroelectric exciton
droplets. Thus, the indirect exciton luminescence is red shifted compared to a
two-layer device.

Mesoscale and Nanoscale Physics