Enery Band Calculation Of The-Electron Of Single-Walled Carbon Nanotubes In The Magnetic Field

Carbon nanotubes(CNTs) as one-dimensional nanomaterials were found in the 1990s, which have singular physical performance. As far as their electrical properties, they have the potential to be broadly used in nano-electronic devices. Nano-electronic devices are usually working in an external magnetic field, under which condition it is very important to understand and master the electronic structure of the device's material. Since Band Theory of Solids is one of the most successful theories in the condensed matter physics and in principle most basic physical properties of solids can be illustrated and explained by the band theory, it is significant to carry out the research energy band calculation of theπ-electron of single-walled carbon nanotubes in the magnetic field .Staring from the tight-binding model,π-electron secular equation of single-walled carbon nanotubes(SWNTs) in the external magnetic field was deduced by quantum theory and solid state theory. Further more, theπ-electron band expression of the SWNTs was obtained. Based on this, by use of periodic boundary conditions of SWNTs and the crystal Bloch theorem, theπ-electron energy band expression of armchair SWNTs was derived.In the reciprocal lattice space, for the three kinds of armchair SWNTs with the structure parameters (m, n) to be (6,6), (8,8) and (10,10) respectively, theπ-electron energy band curves in zero and different magnetic fields were calculated using C language programming. The results show that: in zero magnetic field, the three kinds of tubes are all metallic, which is consistent with the criterion of metallic SWNTs, i.e., |m-n|=3J(J=0,1,2,3,…). For the SWNTs (6,6) and (8,8), the energy gap widths of the energy band are 0.408eV, 1.216eV and 0.544eV, 0.746eV when the magnetic flux density B are 0.01T and 0.03T respectively. For the SWNTs (10, 10), the energy gap widths of the energy band are 0.560eV and 0.407eV when the magnetic flux density B are 0. 02Tand 0. 05T respectively. The results show that the SWNTs can be transformed from the metallic type into the semiconductor one on the effect of the external magnetic field. According to the definition of the energy gap, the expression ofπ-electron energy gap width of armchair SWNTs was caculated , known from which the magnitude of energy gap is a periodic function of the magnetic flux through the SWNTs.The reserch results above provide a useful theoretical reference for further study of the structure of the SWNTs.