Analytical and Laboratory

Mystery Behind the Electron Structure Defects in Graphene Finally Solved

19 December 2017

Graphene is an atomic-scale hexagonal lattice made of carbon atoms. Source: WikiCommonsGraphene is an atomic-scale hexagonal lattice made of carbon atoms. Source: WikiCommons

University of São Paulo’s Physics Institute (IF-USP) researchers have finally resolved a longstanding controversy regarding defects in graphene that has haunted the international research community for years. The debate is related to the calculation of the overall electronic structure of these defects. The configuration compromises many variables and was described in different ways, depending on the researcher and the model used.

The solution to this problem is identical for all models and compatible with experimental findings. It was found by Ana Maíra Valenica García and her Ph.D. supervisor, Marília Junqueria Caldas, who is a full Professor at IF-USP.

"There were divergences in the community regarding whether the vacancy formed by removing a single carbon atom from a graphene sheet's crystal lattice causes a weak or strong magnetic moment, and regarding the strength of the magnetic interaction between vacancies," Caldas said. The vacancy prompts the surrounding atoms to rearrange themselves into new combinations to accommodate the absence of an atom, forming electron clusters known as "floating orbitals" at the vacant site.

There are three important variables that are associated with the phenomenon: electron density (how the electrons are distributed), electron levels (the energy levels occupied by the electrons) and magnetic moment (the torque produced in the electrons by an external magnetic field).

When she reflected on the divergence, Caldas finds it odd that the proponents are all great researchers who are affiliated with renowned international institutions. Studies conducted by these researchers revealed that the divergent values that are derived from the use of different simulation methods.

"There are two ways to calculate the overall electron structure of the vacancy region, both derived from quantum mechanics: the Hartree-Fock (HF) method and density functional theory (DFT). In DFT the calculation is performed by making each electron interact with average electron density, which includes the electron in question. In HF the operator used excludes the electron and considers only its interaction with the others. HF produces more precise results for electron structure but the calculation is far more laborious," Caldas said.

"The two methods are often combined by means of hybrid functional, which have been mentioned in the scientific literature since the end of the twentieth century. I worked with them myself some time ago in a study on polymers, but they had never been used in the case of graphene. What Ana María [Valencia García] and I did was discover the hybrid functional that best describes the material. Applied to several models using computer simulation, our hybrid functional produced the same result for them all and this result matched the experimental data."

Other than solving this years-long controversy, an interesting aspect of this research is the motivation behind it.

"We came to it via the interest aroused by a material known as anthropogenic dark earth or ADE," Caldas explained. "ADE is a kind of very dark, fertile soil found in several parts of the world including the Amazon. It retains moisture even at high temperatures and remains fertile even under heavy rain. It's called anthropogenic because its composition derives from middens and cultivation by indigenous populations in the pre-Columbian period at least two millennia ago. This intriguing material was known to have resulted from multi-stacked layers of graphene nanoflakes. It was our interest in ADE that led us to study the phenomenon of the vacancy in graphene sheets."

It should be known that there are potential applications of the vacancy in graphene sheets since information can be encoded in the defect and not the entire structure. There is a lot more research that will be needed before applications can be developed.

This research was published in the journal Physical Review B.

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