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中文摘要：
石墨烯纳米带（GNRs）是一种重要的纳米材料，碳纳米管可看作是GNRs卷曲而成的无缝圆筒．利用基于密度泛函理论的第一性原理方法，系统研究了GNRs卷曲变形到不同几何构型时，其电子特性，包括能带结构（特别是带隙）、态密度、透射谱的变化规律．结果表明：无论是锯齿型GNRs（ZGNRs）或扶手椅型GNRs（AGNRs），在其卷曲成管之前，其电子特性对卷曲形变均不敏感，这意味着GNRs的电子结构及输运特性有较强地抵抗卷曲变形的能力．当GNRs卷曲成管后，ZGNRs和AGNRs表现出完全不同的性质，ZGNRs几乎保持金属性不变或变为准金属；但AGNRs的电子特性有较大的变化，出现不同带隙半导体、准金属之间的转变，这也许密切关系到碳纳米管管口周长方向上的周期性边界条件及量子禁锢的改变．这些研究对于了解GNRs电子特性的卷曲效应、以及GNRs与碳纳米管电子特性的关系（结构与特性的关系）有重要意义．
英文摘要：
Graphene nanoribbons （GNRs） are important nanomaterials. A carbon nanotube can be viewed as a GNR rolled into a seamless cylinder. By using the first-principles method based on the density-functional theory, the rolling deformation-dependent electronic characteristics of GNRs, including the band structure （particularly the bandgap）, density of states （DOS）, and transmission spectrum, are studied systematically. It is found that before all types of GNRs are rolled into carbon nanotubes, they are not sensitive to the rolling deformations, which means that for electronic structures and transport properties, GNRs have a very strong ability to resist the rolling deformations. After GNRs are rolled into nanotubes, zigzag-edge GNRs （ZGNRs） and armchair-edge GNRs （AGNRs） present distinct differences in property, ZGNRs almost maintain unchanged metallic behaviors or become quasi-metallic. But for AGNRs, their electronic characteristics experience large variations, and transformations occur between the quasi-metal and semiconductor with various bandgaps, which might be closely related to the periodical boundary conduction along the direction of tubular circumference of a carbon nanotube and variation of quantum confinement. These studies presented here are of significance for understanding the rolling effects on electronic characteristic and relationship of electronic characteristics between GNRs and carbon nanotubes （structure- property relationship）.
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