Researchers calculated the electronic band energy of the carbon nanotube with some special form of crystalline potentials which yield to inaccurate equations. We thus modified the orthogonalized-plane-wave and tight binding methods. These methods are employed to introduce a matrix of carbon nanotube band energy.
Some researchers obtained the phonon dispersion relation of carbon nanotube by considering harmonic oscillation of carbon atoms. Recently, we could find an alternative method for determining carbon nanotube band energy by modifying orthogonalized-plane-wave method and combining it with tight binding method. Here, we did some calculations based on these methods and solved the dynamical matrix of carbon nanotube by referring the above methods and using force constant model. Some necessary adjustments are made in order to take into account the effect of the second nearest neighbor atoms which are not harmonic vibrations.
The holographic approach to study strongly coupled superconductors in the presence of dark matter is reviewed. We discuss the influence of dark matter on the superconducting transition temperature of both s-wave and p-wave holographic superconductors. The upper critical field, coherence length, penetration depth of holographic superconductors as well as the metal-insulator transitions have also been analysed. Issues related to the validity of anti-de Sitter/conformal field theory correspondence for the description of superconductors studied in the laboratory and possible experiments directed towards the detection of dark matter are discussed. In doing so we shall compare our assumptions and assertions with those generally accepted in the elementary particle experiments aimed at the detection of dark matter particles.
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