Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)

TL;DR

This study uses density-functional theory to analyze how the Cu(111) Shockley surface state responds to external electric fields, revealing linear shifts, charge transfer effects, and detailed dispersion characteristics.

Contribution

It provides a detailed DFT-based analysis of the surface state's response to electric fields, including dispersion, energy shifts, and charge transfer mechanisms.

Findings

Surface state dispersion is isotropic and quadratic, with significant quartic contributions.

Energy position and effective mass shift linearly with electric field.

Charge transfer beyond outermost atoms accounts for a quarter of screening.

Abstract

The response of the Cu(111) Shockley surface state to an external electrical field is characterized by combining a density-functional theory calculation for a slab geometry with an analysis of the Kohn-Sham wavefunctions. Our analysis is facilitated by a decoupling of the Kohn-Sham states via a rotation in Hilbert space. We find that the surface state displays isotropic dispersion, quadratic until the Fermi wave vector but with a significant quartic contribution beyond. We calculate the shift in energetic position and effective mass of the surface state for an electrical field perpendicular to the Cu(111) surface; the response is linear over a broad range of field strengths. We find that charge transfer occurs beyond the outermost copper atoms and that accumulation of electrons is responsible for a quarter of the screening of the electrical field. This allows us to provide well-converged determinations of the field-induced changes in the surface state for a moderate number of layers in the slab geometry.