本文選題：M?bius介觀環(huán) + 石墨烯介觀環(huán)　； 參考：《華南理工大學》2015年碩士論文

【摘要】：在緊束縛近似下,研究了簡單納米管、M?bius介觀環(huán)和石墨烯介觀環(huán)中的電子態(tài)和持續(xù)電流問題。(1)解析推導(dǎo)了簡單納米管和M?bius介觀環(huán)的電子態(tài)和持續(xù)電流。M?bius介觀環(huán)中電子的能量本征值本征態(tài)依賴于橫向通道數(shù)的奇偶性。研究發(fā)現(xiàn),簡單納米管和M?bius介觀環(huán)產(chǎn)生的持續(xù)電流隨磁通的變化具有類似的變化關(guān)系,對于持續(xù)電流的研究得到了一些新的現(xiàn)象和結(jié)果。當橫向通道數(shù)與環(huán)周長滿足某特定關(guān)系時,持續(xù)電流隨磁通的變化呈線性或趨于正弦關(guān)系變化。(2)解析求解了扶手椅型邊界石墨烯介觀環(huán)和鋸齒型邊界石墨烯介觀環(huán)的能量本征值問題,計算和討論了不同大小尺寸的介觀環(huán)中持續(xù)電流隨Aharonov-Bohm(A-B)磁通的變化。研究表明,對于扶手椅型石墨烯介觀環(huán)持續(xù)電流顯著地依賴于介觀環(huán)的幾何結(jié)構(gòu);零能量附近的能級可以承載較大的持續(xù)電流,而遠離零能量的其它能級對持續(xù)電流的貢獻很小。分析研究了鋸齒型邊界石墨烯介觀環(huán)的兩種電子態(tài)即駐波態(tài)和邊緣態(tài);不同大小尺寸的介觀環(huán)中的持續(xù)電流隨Aharonov-Bohm(A-B)磁通的變化以及系統(tǒng)的邊緣態(tài)所產(chǎn)生的電流情況。研究表明,鋸齒型邊界石墨烯介觀環(huán)系統(tǒng)產(chǎn)生的持續(xù)電流隨磁通呈正弦關(guān)系變化。
[Abstract]:In the tight bound approximation, The electron states and persistent currents in the mesoscopic rings of simple nanotubes Mnbius and graphene were studied. The energy eigenvalues of electrons in simple nanotubes and M?bius mesoscopic rings were derived. The eigenstates depend on the parity of the number of transverse channels. It is found that the continuous current produced by simple nanotubes and M?bius mesoscopic rings has a similar relationship with magnetic flux. Some new phenomena and results have been obtained for the study of persistent current. When the number of transverse channels satisfies a particular relationship with the circumference of the ring, The energy eigenvalues of the armchair boundary graphene mesoscopic ring and the sawtooth boundary graphene mesoscopic ring are solved analytically. The variation of the sustained current with the Aharonov-Bohmm A-B) flux in mesoscopic rings of different sizes has been calculated and discussed. The results show that the sustained current of the armchair graphene mesoscopic ring is significantly dependent on the geometric structure of the mesoscopic ring, and the energy level near zero energy can carry a large sustained current. Other energy levels far away from zero energy contribute little to the sustained current. The two electronic states of the zigzag boundary graphene mesoscopic ring, the standing wave state and the edge state, the variation of the sustained current with the Aharonov-BohmmA-B) flux in the mesoscopic ring with different sizes and the current generated by the edge state of the system are studied. The results show that the continuous current generated by the zigzag boundary graphene mesoscopic ring system is sinusoidal with the flux.
【學位授予單位】：華南理工大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TQ127.11

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