Low-energy Electron Reflectivity from Graphene: First-Principles Computations and Approximate Models

TL;DR

This paper introduces a first-principles computational method to analyze low-energy electron reflectivity from graphene surfaces, revealing multiple reflectivity minima and associated states, and develops a tight-binding model that aligns well with the detailed calculations.

Contribution

It presents a novel computational approach for electron reflectivity analysis and a simplified tight-binding model that accurately reproduces first-principles results for multilayer graphene.

Findings

Two bands of reflectivity minima identified at 0-8 eV and 14-22 eV.

Number of minima in each band correlates with the number of graphene layers.

Tight-binding model matches first-principles reflectivity spectra.

Abstract

A computational method is developed whereby the reflectivity of low-energy electrons from a surface can be obtained from a first-principles solution of the electronic structure of the system. The method is applied to multilayer graphene. Two bands of reflectivity minima are found, one at 0 - 8 eV and the other at 14 - 22 eV above the vacuum level. For a free-standing slab with n layers of graphene, each band contains n-1 zeroes in the reflectivity. Two additional image-potential type states form at the ends of the graphene slab, with energies just below the vacuum level, hence producing a total of 2n states. A tight-binding model is developed, with basis functions localized in the spaces between the graphene planes (and at the ends of the slab). The spectrum of states produced by the tight-binding model is found to be in good agreement with the zeros of reflectivity (i.e. transmission resonances) of the first-principles results.