Graphene电子结构应变效应的第一性原理研究
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摘要
本文采用紧束缚方法和基于密度泛函理论的第一性原理方法研究了单原子层graphene在不同应变状态下的电子结构,主要分析了三种典型应变下的情况:对称应变,锯齿方向单轴应变,扶手方向单轴应变,并得到如下主要的结论:
1)在对graphene体系外加对称应变的情况下,态密度伪带隙宽度随应变的增大线性减小。而对于体系的能带带隙,当外加应变小于30.1%时,带隙宽度始终保持不变,体系为0带隙的半金属;当外加应变超过30.1%时,体系的能带发生了较大的形变,能级在费米能级处出现了交叠,态密度开始大于0,体系显现为金属性。
2)在沿锯齿方向的单向拉伸过程中,graphene体系的能带带隙出现了变化,不再保持为0。带隙宽度随应变的增大出现了振荡现象,即体系的带隙宽度随应变的增大从零开始经过三次先增大后减小的波动,当应变增大到29.2%时,带隙重新变为0,进一步增大应变时,体系表现为金属性。同时还发现,体系的结构随应变的增大由简单斜方相向简单长方相转变。当应变处于38.9%至68.1%范围内时,体系存在两种相结构;当应变大于68.1%时,体系只存在简单长方相,即由相互作用的线性C单链组成的结构。继续增大应变,单链之间的距离逐渐增大,而相互作用逐渐减小,最终体系发展为纵向孤立的C单链。
3)在沿扶手方向的单向拉伸过程中,graphene体系的能带带隙随拉伸同样出现了振荡现象,经过两次先增大后减小的波动,当应变增大到26.2%时,带隙消失,体系由半金属经由半导体转化为金属。在整个应变范围内,体系没有出现新的相结构,并在大应变之下最终发展为横向孤立的C单链。
4)研究了graphene体系的泊松比,结果显示,当应变小于1.5%时,沿锯齿方向与沿扶手方向的泊松比相等,为0.1732;进一步增大应变,两者的泊松比不相等,沿锯齿方向的泊松比略大于沿扶手方向的泊松比,这说明,graphene体系在小应变下表现为各向同性,而在较大应变下表现为各向异性。
Electronic structures of graphene with different planar strain distributions have been studied using the tight-binding calculations and the first principles methods based on the density functional theory. Three types of typical strain distributions have been considered, namely, symmetrical strain distributions, uniaxial strain distributions along zigzag (ZZ) axes, and uniaxial strain distributions along armchair (AC) axes. The main results are as follows:
1) It was found that symmetrical strain distributions in graphene result in linear decrease of the pseudogap as the strain increases. When the strain is below 30.1%, the graphene system keeps be a zero bandgap semimetal. However, as the strain further increases, the shape of the band structure changes greatly, the band crosses at the Fermi level and the DOS at the Fermi level is larger than zero, indicating that the system becomes metallic.
2) Uniaxial strain distributions in graphene result in opening of band gaps at the Fermi level and the variation of band gaps exhibits an oscillatory behavior. For the graphene system with a uniaxial strain distribution along ZZ axes, its band gap firstly increases and then decrease with strain increasing. The phenomenon occurs three times until the strain up to 29.2%, and the band gap vanishes, which indicates that the system becomes metallic. When the strain is in the range of 38.9% and 68.1%, there exist a structural phase transformation in graphene, from the rhombic phase to a rectangular phase. The new phase configuration is made up of coupled linear atomic chains of carbon. As strain further increases, the distance between two carbon chains becomes larger and the interactions become weaker gradually. Consequently, the graphene system turns to be isolated vertical carbon chains.
3) For the graphene system with a strain distribution along AC axes, the same oscillatory phenomenon occurs only two times and the band gap vanishes when the strain up to 26.2%. Evidently, the graphene system changes from a semimetal to a metal via a semiconductor. In the whole strain process, the system holds only the rhombic phase and finally changes to lateral atomic chains of carbon under large enough strain.
4) The poisson ratio of graphene system under uniaxial strain distributions was studied. The results show that as strain approaches to infinitesimal, the poisson ratio is 0.1732, which indicates the graphene system is isotropic. As strain increases up to 1.5%, the poisson ratio of uniaxial strain along ZZ axes is slightly larger than that of uniaxial strain along AC axes, which indicates graphene system is anisotropic under large deformation.
1)在对graphene体系外加对称应变的情况下,态密度伪带隙宽度随应变的增大线性减小。而对于体系的能带带隙,当外加应变小于30.1%时,带隙宽度始终保持不变,体系为0带隙的半金属;当外加应变超过30.1%时,体系的能带发生了较大的形变,能级在费米能级处出现了交叠,态密度开始大于0,体系显现为金属性。
2)在沿锯齿方向的单向拉伸过程中,graphene体系的能带带隙出现了变化,不再保持为0。带隙宽度随应变的增大出现了振荡现象,即体系的带隙宽度随应变的增大从零开始经过三次先增大后减小的波动,当应变增大到29.2%时,带隙重新变为0,进一步增大应变时,体系表现为金属性。同时还发现,体系的结构随应变的增大由简单斜方相向简单长方相转变。当应变处于38.9%至68.1%范围内时,体系存在两种相结构;当应变大于68.1%时,体系只存在简单长方相,即由相互作用的线性C单链组成的结构。继续增大应变,单链之间的距离逐渐增大,而相互作用逐渐减小,最终体系发展为纵向孤立的C单链。
3)在沿扶手方向的单向拉伸过程中,graphene体系的能带带隙随拉伸同样出现了振荡现象,经过两次先增大后减小的波动,当应变增大到26.2%时,带隙消失,体系由半金属经由半导体转化为金属。在整个应变范围内,体系没有出现新的相结构,并在大应变之下最终发展为横向孤立的C单链。
4)研究了graphene体系的泊松比,结果显示,当应变小于1.5%时,沿锯齿方向与沿扶手方向的泊松比相等,为0.1732;进一步增大应变,两者的泊松比不相等,沿锯齿方向的泊松比略大于沿扶手方向的泊松比,这说明,graphene体系在小应变下表现为各向同性,而在较大应变下表现为各向异性。
Electronic structures of graphene with different planar strain distributions have been studied using the tight-binding calculations and the first principles methods based on the density functional theory. Three types of typical strain distributions have been considered, namely, symmetrical strain distributions, uniaxial strain distributions along zigzag (ZZ) axes, and uniaxial strain distributions along armchair (AC) axes. The main results are as follows:
1) It was found that symmetrical strain distributions in graphene result in linear decrease of the pseudogap as the strain increases. When the strain is below 30.1%, the graphene system keeps be a zero bandgap semimetal. However, as the strain further increases, the shape of the band structure changes greatly, the band crosses at the Fermi level and the DOS at the Fermi level is larger than zero, indicating that the system becomes metallic.
2) Uniaxial strain distributions in graphene result in opening of band gaps at the Fermi level and the variation of band gaps exhibits an oscillatory behavior. For the graphene system with a uniaxial strain distribution along ZZ axes, its band gap firstly increases and then decrease with strain increasing. The phenomenon occurs three times until the strain up to 29.2%, and the band gap vanishes, which indicates that the system becomes metallic. When the strain is in the range of 38.9% and 68.1%, there exist a structural phase transformation in graphene, from the rhombic phase to a rectangular phase. The new phase configuration is made up of coupled linear atomic chains of carbon. As strain further increases, the distance between two carbon chains becomes larger and the interactions become weaker gradually. Consequently, the graphene system turns to be isolated vertical carbon chains.
3) For the graphene system with a strain distribution along AC axes, the same oscillatory phenomenon occurs only two times and the band gap vanishes when the strain up to 26.2%. Evidently, the graphene system changes from a semimetal to a metal via a semiconductor. In the whole strain process, the system holds only the rhombic phase and finally changes to lateral atomic chains of carbon under large enough strain.
4) The poisson ratio of graphene system under uniaxial strain distributions was studied. The results show that as strain approaches to infinitesimal, the poisson ratio is 0.1732, which indicates the graphene system is isotropic. As strain increases up to 1.5%, the poisson ratio of uniaxial strain along ZZ axes is slightly larger than that of uniaxial strain along AC axes, which indicates graphene system is anisotropic under large deformation.
引文
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[8] Ajayan P M, Ebbesen T W, Ichihashi T, et al. Opening carbon nanotubes with oxygen and implications for filling [J]. Nature, 1993, 362: 522-525.
[9] Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films [J]. Science, 2004, 306: 666-669.
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[24] Yao Y G, Ye F, Qi X L, et al. Spin-orbit gap graphene: First-principles calculations [J]. Phys Rev B, 2007, 75: 041401-1-4.
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[27] Kane C L, Mele E J. Quantum spin hall effect in graphene [J]. Phys Rev Lett, 2005, 95: 226801-1-4.
[28] Anderson P W. Absence of diffusion in certain random lattices [J]. Phys Rev, 1958, 109: 1492-1505.
[29] Mikhail I Katsnelson. Graphene: carbon in two dimensions [J]. Materials Today, 2007, 10: 20-27.
[30] Kudin K N, Scuseria G E, Yakobson B I. C2F, BN, and C nanoshell elasticity from ab initio computations [J]. Phys Rev B, 2001, 64: 235406-1-10.
[31] Lier G V, Alsenoy C V, Doren V V, et al. Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene [J]. Chem Phys Lett, 2000, 326: 181-185.
[32] Reddy C D, Rajendran S, Liew K M. Equivalent continuum modeling of graphene sheets [J]. Int J Nanosci, 2005, 4: 631-636.
[33] Arroyo M, Belytschko T. Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule [J]. Phys Rev B, 2004, 69: 115415-1-11.
[34] Reddy C D, Rajendran S, Liew K M. Equilibrium configuration and continuum elastic properties of finite sized graphene [J]. Nanotechnology, 2006, 17: 864-870.
[35] Klitzing K v, Dorda G, Pepper M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance [J]. Phys Rev Lett, 1980, 45: 494-497.
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