  We study tunnel junctions consisting of a two-dimensional ferroelectric (FE)
material sandwiched between graphene electrodes. We formulate a theory for the
interplay of the FE polarization and induced free charges in such devices,
taking into account quantum capacitance effects. We predict a gate-sensitive FE
voltage difference across the device, which can be measured using electrostatic
force microscopy. Incorporating this electrostatic theory in the tunneling
current-voltage characteristics, we identify a resonance peak associated with
aligned Dirac cones as a highly sensitive probe of the FE polarization of the
junction. This opens the way for device applications with few atom-thick FE
layers acting as readable ultra-high-density memory.
