First-Principles Nanocapacitor Simulations of the Optical Dielectric Constant in Water Ice

TL;DR

This paper presents a novel combined DFT and NEGF framework to accurately compute the dielectric response of nanometer-scale water ice capacitors, addressing challenges in charge partitioning and interfacial polarizability.

Contribution

It introduces a robust charge-separation protocol for nanocapacitors, enabling precise dielectric property extraction in low-dimensional dielectrics like water ice.

Findings

Confinement does not change ice's intrinsic electronic response.

The dielectric constant of ice remains insensitive to proton order.

The method provides unambiguous capacitance and polarizability measurements.

Abstract

We introduce a combined density functional theory (DFT) and non-equilibrium Green's function (NEGF) framework to compute the capacitance of nanocapacitors and directly extract the dielectric response of a sub-nanometer dielectric under bias. We identify that at the nanoscale conventional capacitance evaluations based on stored charge per unit voltage suffer from an ill-posed partitioning of electrode and dielectric charge. This partitioning directly impacts the geometric definition of capacitance through the capacitor width, which in turn makes the evaluation of dielectric response uncertain. This ambiguous separation further induces spurious interfacial polarizability when analyzed via maximally localized Wannier functions. Focusing on crystalline ice, we develop a robust charge-separation protocol that yields unique capacitance-derived polarizability and dielectric constants, unequivocally demonstrating that confinement neither alters ice's intrinsic electronic response nor its insensitivity to proton order. Our results lay the groundwork for rigorous interpretation of capacitor measurements in low-dimensional dielectric materials.