Hidden Interactions?

Hidden One-Electron Interactions in Carbon Nanotubes Revealed in Graphene Nanostrips

C.T. White, J. Li, D. Gunlycke, and J.W. Mintmire

Nanoletters 7, 825--830 (2007)

URL: http://pubs.acs.org/doi/abs/10.1021/nl0627745


The authors explore the band gap of graphene nanoribbons. I was disappointed to discover that the "hidden interactions‚" they refer to are second and third nearest neighbor couplings that must be added to the tight binding model to reproduce the results of a density functional calculation. They predict that all armchair edge nanoribbons will have a gap.

These interactions are hidden in nanotubes because the curvature of a nanotube reduces the coupling between more distant neighbors. However, they should have been observable in large-radius nanotubes, in which curvature effects are very weak. The authors do not appear to have addressed this point.

I realize that density functional theory is a powerful tool for investigating the electronic structure of many materials. However, I do not know that it has been used successfully in graphene. Moreover, the authors state that the particular DFT package they used is "especially tailored to take advantage of helical symmetry"--- a symmetry possessed by carbon nanotubes, but not graphene nanoribbons. Moreover, claims that the method "has been successfully used in wide-ranging studies of single walled carbon nanotubes" only refer to studies carried out by the authors.

I am uncomfortable with the idea of taking an empirical model -- the tight-binding model for electrons in graphene -- and adjusting its parameters to fit the results of a density functional calculation. It would be a different matter entirely if the “hidden interactions” were necessary to fit experimental data.

I was discussing a similar idea with my adivsor the other day. We had just listened to a talk in which a biophysicist described the molecular dynamics simulations he had developed to study fluctuating membranes. Because the model reproduced some features of the experimental data, he inferred that the model captured some important physical property of the real system. White et al. do the same thing here, making the claim that because the amended tight-binding model reproduces the results of the DFT calculation, there must be 2nd and 3rd nearest neighbor interactions in graphene.

What this type of reasoning lacks is a proof of a one-to-one correspondence between models and the physical properties of the system. I.e., one would have to establish that a particular model is the only one they could generate a particular physical property before making any conclusions about real graphene samples or fluctuating membranes. I do not believe this type of correspondence exists. At best, one might be able to argue that the model and the physical system fall into the same universality class in the sense of the renormalization group.

In the end, experimental studies will determine whether or not these hidden interactions are physically relevant. The same experiments will also assess the validity of the DFT calculation. It will be interesting to see whether all armchair nanoribbons are semiconductors.