Annotation: Researchers from the Faculty of Physics (the group under the leadership of Professor V.Ch. Zhukovsky, Department of Theoretical Physics) in collaboration with Russian (the group under the leadership of Professor K.G. Klimenko, IHEP, Protvino) and foreign (Professor D. Ebert, Humboldt University, Berlin, Germany) colleagues investigated the theoretical model, that allows to describe electron excitations in carbon nanotubes under the influence of the magnetic field.
Проф. В.Ч.Жуковский
In recent years, after the announcement of successful synthesis of graphene, i.e. a single layer of graphite (2004), that is a planar carbon polymer with the honeycomb lattice, investigation of the properties of carbon polymers became a field of special interest for the scientists. Due to its unusual properties graphene and other carbon structures, such as carbon nanotubes (that can be considered as one or several layers of graphene rolled into a cylinder) are especially interesting. As shown even before the synthesis of actual polymer, low-energy electrons in graphene can be effectively described by the equation having the same form as relativistic Dirac equation that allows establishing a relationship between the electron properties of graphene and high energy physics and, consequently, applying the well-developed methods of the quantum field theory.
Models of the quantum field theory such as described above are being investigated by the researchers of the Department of theoretical Physics in a group under the leadership of Professor V.Ch. Zhukovsky in collaboration with their colleagues from Russian and foreign universities (group under the leadership of Professor K.G.Klimenko, IHEP, Protvino; Professor D. Ebert, Institute of Physics, Humboldt University, Berlin, Germany). One of the recent results of the group, obtained by Prof. V.Ch. Zhukovsky and PhD student P.B. Kolmakov in collaboration with their colleagues (Prof. K.G.Klimenko and Prof. D. Ebert), is the investigation of the phase structure of fermionic condensates on the honeycomb polymer lattice rolled into a cylinder, that models carbon nanotubes, and investigation of the magnetic properties of this structure under the influence of external magnetic field leading to Zeeman and Aharonov–Bohm effects.
Work includes the analytical calculation of the effective potentials for several models with four-fermion interaction that model phenomena in the planar graphene and carbon nanotubes under the influence of finite temperature, chemical potential, external magnetic field, and spatial compactification (in nanotubes).
Based on the obtained effective potential the phase structure of the models have been investigated and a symmetry between the influence of the finite temperature and spatial compactification was found for particular values of the external magnetic flux through the cross-section of the nanotube. It was shown that the phase structure of the model depends on the magnitude of the magnetic field. Also, the finite chemical potential have been considered and the phenomenon of dimensional reduction from (2+1)-dimensional to (1+1)-dimensional space-time in case of periodic boundary conditions as well as the lack of such a reduction in case of antiperiodic boundary conditions was shown. These results are of interest both in high energy physics and in low-dimensional condensed matter physics.
The results are published in: D. Ebert, K.G. Klimenko, P.B. Kolmakov, V.Ch. Zhukovsky, Annals of Physics, 371, 254 (2016).
