Mechanical Properties of Carbon Nanotubes in a Chiral Model of Graphene


Yuri P. Rybakov,Medina Umar,Muhammad Iskandar,



Chiral Model,Chiral Current ,Grapheme ,Young’s Modulus ,CarbonNanotubes,


Taking into account the 2 sp -hybridization effect for valence electrons in carbon atoms, we introduce a unitary matrix U as an order parameter and suggest a scalar chiral model of graphene for the description of carbon nanotubes. We consider both single-walled and two-walled carbon nanotubes, analyze corresponding solutions to the model equations and estimate the Young’s modulus. We discuss also the possible extension of the model in question to describe fullerenes as three-dimensional hedgehog structures (skyrmions). We find the corresponding Lagrangian density for the spherirically-symmetric chiral angle. The other extension of the model concerns spin and magnetic excitations of graphene-based configurations. To this end, the 8- spinor field should be introduced as a new order parameter (Rybakov, 2015).


I.Bolotin K.I., Sikes K.J., Jiang Z., Klima M., Fudenberg G., Hone J., Kim P., Stormer H.L.(2008). Ultrahigh electron mobility in suspended graphene. Solid State Communications, 146(9-10): 351-355.Available online:

II.Derrick G.H. (1964). Comments on nonlinear wave equations as a model for elementary particles. Journal of Mathematical Physics, 5(9): 1252-1254.Available online:

III.Geim A.K. (2009). Graphene: status and prospects. Science, 324: 1530-1534.Available online:

IV.Hobart R.H. (1963). On the instability of a class of unitary field models. Proceedings of the Physical Society, 82(2): 201-203.Available online:

V.Lee C., Wei X., Kysar J.W., Hone J.(2008). Measurement of elastic properties and intrinsic strength of monolayer graphene. Science, 321(5887): 385-388.Available online:

VI.Lu X., Chen Z. (2005). Curved pi-conjugation aromaticity, and the related chemistry of small fullerenes (<C60)and single-walled carbon nanotubes. Chemical Review, 105(10): 3643-3696.Available online:

VII.Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A.(2004). Electric field effect in atomically thin carbon films. Science, 306(5696): 666-669.Available online:

VIII.Rybakov Yu.P. (2012). On chiral model of graphene. Solid State Phenomena, 190: 59-62.Available online:

IX.Rybakov Yu.P. (2015). Spin excitations in chiral model of graphene. Solid State Phenomena, 233-234: 16-19.Available online:

X.Semenoff G.W. (1984). Condensed-matter simulation of a three-dimensional anomaly. Physical Review Letters, 53: 2449-2452.Available online:

XI.Skyrme T.H.R. (1962). A unified field theory of mesons and baryons. Nuclear Physics, 31(4): 556-569.Available online:

XII.Terrones M. (2003). Science and technology of the twenty-first century: synthesis, properties, and applications of carbon nanotubes. Annual Review of Materials Research, 33: 419-501.Available online:

XIII.Yu M.F., Files B.S., Arepalli S., Ruoff R.S. (2000). Tensile loading of ropes of single wallcarbon nanotubes and their mechanical properties. Physical Review Letters, 84(24): 5552-5555.Available online:

View | Download