Rationalizing and reconciling energy gaps and quantum confinement in narrow atomically precise armchair graphene nanoribbons

Abstract

Recent advances in bottom-up production of atomically precise armchair graphene nanoribbons (AGNRs) and their structural and electronic characterization through scanning tunneling microscopy (STM) and spectroscopy (STS) present an opportunity and a challenge for their interpretation and inter-correlation, especially in view of several seemingly conflicting results for their electron distribution and gap size, sometimes by more than 300%. Such large discrepancies, which threaten to undermine the extraordinary achievements of their synthesis, are threefold: Experiment vs. theory; experiment vs. experiment; and theory vs. theory. Here we illustrate that by using many-body corrections through time-dependent (TD) density functional theory (DFT), and proper identification of the STS gap, we can reproduce all known, and predict new as yet unknown, experimental data for such AGNRs. Furthermore, we can rationalize and suggest ways to reconcile practically all known discrepancies. We demonstrate that besides the width measured by the number N of carbon atoms across, the length and the length-variation of the gap properties, which reveal a semiconductor-metal transition, is an important factor which is usually overlooked in the literature. This, together with inherent problems of DFT for accurate gap determination, on top of experimental STS difficulties, are the main sources of such discrepancies.