Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2022 Jun 7;12(12):1953.
doi: 10.3390/nano12121953.

Quantum Revivals in Curved Graphene Nanoflakes

Sergio de-la-Huerta-Sainz  1 , Angel Ballesteros  1 , Nicolás A Cordero  1   2   3
Affiliations

Quantum Revivals in Curved Graphene Nanoflakes

Sergio de-la-Huerta-Sainz et al. Nanomaterials (Basel). .

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.

Keywords: DFT; curvature; graphene; phase transition; quantum revivals.

PubMed Disclaimer

Conflict of interest statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Figures

Figure 1
Figure 1
Graphene flake used in the calculations (image generated using GausView 6 [69]).
Figure 2
Figure 2
Optimized geometries for a (quasi-)spherical graphene flake of radius 40 Å (image generated using GausView 6 [69]).
Figure 3
Figure 3
Energy of a (quasi-)spherical graphene flake as a function of its curvature. Flat configuration is taken as energy origin. Lines are merely guides for the eye.
Figure 4
Figure 4
Log–log plot of the energy of a spherical graphene flake as a function of its curvature. Flat configuration is taken as energy origin. Lines are merely guides for the eye.
Figure 5
Figure 5
Value of n in Equation (2) as a function of the radius of the spherical carbon nanoflake calculated with the hybrid MM/DFT approximation.
Figure 6
Figure 6
A simple example of the time evolution of the squared modulus of the autocorrelation function in blue with its upper envelope in orange. Classical time is marked in red and revival time in green.
Figure 7
Figure 7
Classical times for a curved graphene nanoflake. Points correspond to numerical values while dotted lines represent analytical ones.
Figure 8
Figure 8
Revival times for a curved graphene nanoflake. Points correspond to numerical values while dotted lines represent analytical ones.
See this image and copyright information in PMC

References

    1. Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A. Electric Field Effect in Atomically Thin Carbon Films. Science. 2004;306:666–669. doi: 10.1126/science.1102896. - DOI - PubMed
    1. Web of Science™. [(accessed on 22 April 2022)]. Available online: https://www.webofscience.com.
    1. Lalwani G., Henslee A.M., Farshid B., Lin L., Kasper F.K., Qin Y.X., Mikos A.G., Sitharaman B. Two-Dimensional Nanostructure-Reinforced Biodegradable Polymeric Nanocomposites for Bone Tissue Engineering. Biomacromolecules. 2013;14:900–909. doi: 10.1021/bm301995s. - DOI - PMC - PubMed
    1. Dimov D., Amit I., Gorrie O., Barnes M.D., Townsend N.J., Neves A.I.S., Withers F., Russo S., Craciun M.F. Ultrahigh Performance Nanoengineered Graphene–Concrete Composites for Multifunctional Applications. Adv. Funct. Mater. 2018;28:1705183. doi: 10.1002/adfm.201705183. - DOI
    1. Berman D., Erdemir A., Sumant A.V. Reduced wear and friction enabled by graphene layers on sliding steel surfaces in dry nitrogen. Carbon. 2013;59:167–175. doi: 10.1016/j.carbon.2013.03.006. - DOI

LinkOut - more resources