Scaling of the energy gap in pattern-hydrogenated graphene

TL;DR

This paper demonstrates that the energy gap in pattern-hydrogenated graphene scales with the square root of hydrogen concentration relative to carbon, aligning with experimental observations and affecting electronic transport properties.

Contribution

The study provides a theoretical model linking the energy gap to hydrogenation patterns and confirms it with electronic structure and transport simulations.

Findings

Energy gap scales with √N_H/N_C considering disorder.

Calculated dispersion matches ARPES results.

Transport simulations show a gap up to 1 eV.

Abstract

Recent experiments show that a substantial energy gap in graphene can be induced via patterned hydrogenation on an iridium substrate. Here, we show that the energy gap is roughly proportional to $\sqrt{N_{H}}/N_{C}$ when disorder is accounted for, where $N_H$ and $N_C$ denote concentration of hydrogen and carbon atoms, respectively. The dispersion relation, obtained through calculation of the momentum-energy resolved density of states, is shown to agree with previous angle-resolved photoemission spectroscopy results. Simulations of electronic transport in finite size samples also reveal a similar transport gap, up to 1eV within experimentally achievable $\sqrt{N_{H}}/N_{C}$ value.