Understanding the low dielectric constant of nanoconfined water capacitors*

The relative out of plane dielectric constant of nano confined water in graphene capacitors 

was shown to be as low as 2.1 for capacitor thickness below 1 nm by Fumagalli et al. (Science 360, 2018). This

study motivated a plethora of theoretical studies aiming to explain this surprising behavior. It is surprising because such low

measured value is even lower than the high frequency dielectric constant of ice.

In this work we show that both experimental and theoretical studies suffer from intrinsic arbitrariness

associated to the ill defined concept of a macroscopic  dielectric constant in a microscopic 2D limit. 

We show that the two-dimensional transverse polarizability is the natural choice to characterize the

response of a nanoconfined dielectric in a capacitor. This polarizability can also be connected to

the actual experimental measurements of differential capacitance, providing a clean way of comparing

both experimental and theoretical results, eliminating the need for intermediate arbitrary choices needed

for the computation of the dielectric constant.