Quantum Revivals in Curved Graphene Nanoflakes

Abstract

Graphene nanostructures have attracted a lot of attention in recent years due to their unconventional properties. We have employed Density Functional Theory to study the mechanical and electronic properties of curved graphene nanoflakes. We explore hexagonal flakes relaxed with different boundary conditions: (i) all atoms on a perfect spherical sector, (ii) only border atoms forced to be on the spherical sector, and (iii) only vertex atoms forced to be on the spherical sector. For each case, we have analysed the behaviour of curvature energy and of quantum regeneration times (classical and revival) as the spherical sector radius changes. Revival time presents in one case a divergence usually associated with a phase transition, probably caused by the pseudomagnetic field created by the curvature. This could be the first case of a phase transition in graphene nanostructures without the presence of external electric or magnetic fields.

Gaussian Curvature Effects on Graphene Quantum Dots

“…The divergence found for the hyperboloid case looks similar to the divergence found in our previous work [ 70 ] for the fixed-surface spherical case with atom displacement from the configuration corresponding to the quantum-mechanical energy minimum, but it has nothing to do with it. There, the divergence was an effect of using a non-self-consistent calculation but a perturbative one.…”

“…While the fixed-surface cylindrical plots are essentially straight lines, as the least-squares linear fits plotted in Figure 5 prove—showing the linear dependence on characteristic of the continuum model applied to a nanotube [ 92 ]—the spherical and hyperboloidal ones are not. In our previous work [ 70 ], it was shown how this discrepancy with the continuum model could be connected in the spherical case to the small position changes derived from the use of quantum mechanics in the optimization instead of a classical force field. However, these new results prove that the continuum model is indeed valid for the cylindrical cases—that are curved surfaces—even when quantum mechanics is used to determine geometries, suggesting there are other important contributions besides the theory used for geometry optimization.…”

“…In a recent work [ 70 ], we presented results for mechanical and electronic properties of spherically-deformed graphene quantum dots. Spheres have positive Gaussian curvature.…”

“…From the many possibilities available for the theoretical study of graphene, each of them with its own advantages, reliability, and range of application, we chose the procedure described in our previous work [ 70 ] and used density functional theory (DFT) [ 71 , 72 , 73 ] as the main tool for simulating the properties of graphene quantum dots through use of the the Gaussian 16 [ 74 ] package. For the exchange-correlation functional, local density approximation (LDA) [ 75 , 76 ] was used, in virtue of its better performance for graphitic systems and higher calculation speed compared with general gradient approximations (GGAs) or hybrid functionals such as B3LYP [ 77 , 78 , 79 , 80 , 81 ], and because it has been successfully used to analyze interactions in carbon nanostructures [ 82 , 83 , 84 , 85 , 86 , 87 ].…”

“…We recently presented results on spherically deformed graphene quantum dots [ 70 ]. Those nanostructures have positive Gaussian curvature.…”