外磁场中单壁碳纳米管π电子能隙的理论计算  

Theoretical calculation of π-electron energy gap for single-walled carbon nanotube in external magnetic field

作　　者：郭连权[1] 张平[1] 冷利[1] 马贺[1] 李大业[2] 

机构地区：[1]沈阳工业大学理学院,沈阳110023 [2]沈阳工业大学基础教育学院,沈阳110023

出　　处：《沈阳工业大学学报》2013年第4期390-394,共5页Journal of Shenyang University of Technology

基　　金：辽宁省教育厅基金资助项目(LR201030)

摘　　要：为了得到单壁碳纳米管在外磁场作用下的电子结构规律,从紧束缚模型出发,利用量子理论和固体理论计算了在外磁场作用下单壁碳纳米管(SWNTs)中π电子的能带表达式.在此基础上,利用SWNTs的周期性边界条件和晶体中的布洛赫定理,得到了扶手椅型SWNTs中π电子的能带表达式,进而推导了外磁场作用下能隙宽度的表达式,从而得知能隙是磁通量Φ的周期函数.由金属型SWNTs的判据m-n=3J(J=0,1,2,3,…)可知,扶手椅型SWNTs(m=n)均为金属型,但由于其在外磁场的作用下可能产生能隙,由此证明了扶手椅型SWNTs可以由金属型转变为半导体型的规律.In order to obtain the electronic structure law of single-walled carbon nanotubes （SWNTs） under the action of external magnetic field, the energy band expression of w-electron of SWNTs under the action of external magnetic field was calculated with both quantum and solid state theories on the basis of tight-binding model. And then, the energy band expression of w-electron for the armchair SWNTs was obtained with the periodic boundary condition of SWNTs and crystal Bloch theorem. Furthermore, the expression of energy gap width under the action of external magnetic field was derived. And it was known that the energy gap was a periodic function of magnetic flux Ф. According to the criterion of metallic SWNTs, │ m -n│ = 3J（J = 0, 1, 2, 3, ...）, the armchair SWNTs （m = n） are all metallic type. However, because the energy gap may be generated under the action of external magnetic field, the law that the armchair SWNTs can transform from the metallic type into the semiconductor type gets proved.

关 键 词：磁场 单壁碳纳米管 紧束缚模型 Π电子 能带 能隙 金属型 半导体型 

分 类 号：TB303[一般工业技术—材料科学与工程]