Exact Theory of Fermi-Energy Response at Metallic Interfaces

TL;DR

This paper introduces an exact linear-response theory for calculating Fermi-energy shifts at metallic interfaces using finite electric fields, achieving high accuracy and validating with experimental data.

Contribution

It provides a rigorous, local theoretical framework for Fermi-energy response at metallic interfaces, overcoming previous approximation limitations.

Findings

Quadratic error scaling of Fermi-level shifts with sub-meV accuracy

Reproduces work-function changes under molecular perturbations

Provides electrode potential estimates consistent with experiments

Abstract

The response of the Fermi energy to external perturbations governs key physical observables at metallic interfaces. Although this response admits a local formulation in terms of the Fukui function, its evaluation has traditionally been limited by inherent approximations, fundamentally rooted in the difficulty of adding a finite charge in a periodic system. We present an exact resolution to this problem that leverages the screening properties of electronic conductors to compute Fukui functions via a finite electric field. The resulting linear-response theory yields strictly quadratic error scaling of Fermi-level shifts across representative platinum surfaces, achieving sub-meV accuracy up to fields of 0.1 V/\AA. The approach is further validated by reproducing work-function changes under molecular perturbations, and by providing mean-field estimates of electrode potentials that yield capacitance--voltage curves consistent with experiment. Our findings establish a rigorous foundation for a local theory relating electrostatic screening and Fermi-energy variations at metallic interfaces.