Theoretical modeling for Gigahertz Absorption in Metallic Carbon Nanotubes by Considering Spin-Orbit Interaction and Magnetic Field

In this paper a quantitative analysis on the selection rules and the interband transitions of CNTs in the presence of spin-orbit interaction (SOI) and magnetic field is presented. It has been demonstrated that the SOI and magnetic field have effective role in gigahertz absorption of metallic SWCNTs. Such systems have so far been considered as gapless materials, but a small gap can be observed around the K-point of their band structures due to SOI. The mentioned interaction creates a constant phase accumulation which can be described by a spin-dependent flux through the CNT cross section and hence modifies the quantization of electron's wave-vector in circumferential direction. In addition to SOI, the Bohm-Aharonov flux induced by magnetic field and the Zeeman splitting effect can change the electron wave-vector and energy levels of CNTs. We have studied band diagrams of different CNTs in tight binding approach, by considering the SOI and magnetic field modification in circumferential k-vectors. The calculated gaps in metallic CNTs are in good agreement with recent experimental results. From the zone-folding point of view, in all armchair SCWNTs with any radii, the energy gap is absent, but in such CNTs, the selection rules show that the transition between the lowest conduction and top valence subbands is forbidden. However, in the so-called quasi metallic SWCNTs with n − m = 3p , where p is an integer, this transition is permissible. Our results show that the SOI created gap corresponded to gigahertz frequency can be tuned by magnetic field and observable in absorption spectra.

کلیدواژه ها:

Single Walled Carbon Nanotube ، Microwave Absorption ، Spin-Orbit Interaction ، Magnetic Field