石墨烯的电子结构与磁性
摘要
碳元素的特点之一是存在着众多的同素异形体,涵盖从零维到三维所有形态,例如零维的有以C60为代表的富勒烯、准一维的碳纳米管、二维的石墨烯、和三维的金刚石和石墨。
它们具有极好的力/热学性能、奇特的电子学特性、以至于有着广泛的应用前景。在未来电子学应用方面,它们被认为是可以取代硅基半导体材料的主要候选对象之一。本论文将介绍石墨烯和一维石墨纳米条带材料的一些基本的物理性质。从而达到为实验工作者们提供理论支持工作的目的。
本论文主要采用了两种理论方法:vasp软件和紧束缚近似方法。vasp软件是基于密度泛函赝势的第一性原理计算方法,本文主要是利用vasp进行数值计算,并将所得到的结果与紧束缚近似方法的结果进行对比。
本论文研究了材料的多种结构,包括三维周期性石墨、二维单层石墨烯、二维双层石墨烯、二维一层半石墨烯,一维石墨纳米条带、以及简单形状碳纳米管的结构。本文所研究的物理性质主要是导电性(能带、态密度)和磁性(顺磁性、铁磁性、反铁磁性)。
通过研究我们发现,石墨的边界和形状对于石墨的导电性和磁性均能产生重大的影响。本论文研究得到的一些定性的结果将为石墨材料在纳米器件上的应用提供理论指导。
Carbon widely exists in nature especially in the form of simple substance. Carbon materials are found in variety forms such as graphite, diamond, fullerenes, and carbon nanotubes. The reason why carbon assumes many structural forms is that a carbon atom can form several distinct types of valence bonds, where the chemical bonds refer to the hybridization of orbitals by physicists. In sp 3 hybridization, fourσbonds defining a regular tetrahedron are sufficient to form a three-dimensional structure known as the diamond structure. It is interesting that sp 2hybridization which forms not only a planar structure in two-dimensiona1 graphite but also forms a planar local structure in the closed polyhedra (0-dimensional) of the fullerene family and in the cylinders (1-dimensional) called carbon nanotubes.
In 2004, the single-layer graphene with the ideal two-dimensional structure and unique electronic properties have been successfully prepared, which triggered the research boom of a new wave of carbon-based materials.From the theory of physical,graphene is a zero-band gap semi-metal/semiconductor materials, its carrier mobility is much higher than silicon. Graphene has obvious two-dimensional electronic characteristics.
In 2006-2008 years, graphene has been made of ballistic transport transistor, FET plane, which is attracted a large number of interests of scientists. It is succeeded in creating a planar field-effect transistor and in observing to the quantum interference effect, and in developing graphene-based circuits based on this study.
Recently, a significant Quantum Hall Effect and fractional Quantum Hall Effect observed in graphene have confirmed that it is very promising material of nano-electronic devices. Therefore, there is an important value of theoretical research in graphene, and it has quickly become the materials science and condensed matter physics research hotspot in recent years.
A carbon nanotube is a honeycomb lattice rolled into a cylinder. The diameter of a carbon nanotube is of nanometer size and the length of the nanotube can be more than lpm. It is a quasi-one-dimensional carbon nano-wire
The nanotube diameter is much smaller in size than the most advanced semiconductor devices obtained so far. Thus the availability of carbon nanotubes may have a large impact on semiconductor physics because of its very small size and the special electronic properties that are unique to carbon nanotubes.
In this paper,the structure of our study include: bulk graphite、a single graphene layer、two graphene layers、three graphene layers、two-dimensional one and a half of graphene layers、two-dimensional two graphene layers、a single layer of graphene nonoribbons, two layers of graphene nonoribbon and a simple shape of the structure of carbon nanotube.
In this paper,the physical properties which we studied is mainly conductivity (energy band, density of state) and magnetic (nomagnetic, ferromagnetic, anti-ferromagnetic)
Through research we found that the boundaries and shape of graphite make an impact on electrical conductivity and magnetic properties of graphite
The results which we obtained from this paper will provide theoretical guidance for the graphite material using in nano-device applications.
它们具有极好的力/热学性能、奇特的电子学特性、以至于有着广泛的应用前景。在未来电子学应用方面,它们被认为是可以取代硅基半导体材料的主要候选对象之一。本论文将介绍石墨烯和一维石墨纳米条带材料的一些基本的物理性质。从而达到为实验工作者们提供理论支持工作的目的。
本论文主要采用了两种理论方法:vasp软件和紧束缚近似方法。vasp软件是基于密度泛函赝势的第一性原理计算方法,本文主要是利用vasp进行数值计算,并将所得到的结果与紧束缚近似方法的结果进行对比。
本论文研究了材料的多种结构,包括三维周期性石墨、二维单层石墨烯、二维双层石墨烯、二维一层半石墨烯,一维石墨纳米条带、以及简单形状碳纳米管的结构。本文所研究的物理性质主要是导电性(能带、态密度)和磁性(顺磁性、铁磁性、反铁磁性)。
通过研究我们发现,石墨的边界和形状对于石墨的导电性和磁性均能产生重大的影响。本论文研究得到的一些定性的结果将为石墨材料在纳米器件上的应用提供理论指导。
Carbon widely exists in nature especially in the form of simple substance. Carbon materials are found in variety forms such as graphite, diamond, fullerenes, and carbon nanotubes. The reason why carbon assumes many structural forms is that a carbon atom can form several distinct types of valence bonds, where the chemical bonds refer to the hybridization of orbitals by physicists. In sp 3 hybridization, fourσbonds defining a regular tetrahedron are sufficient to form a three-dimensional structure known as the diamond structure. It is interesting that sp 2hybridization which forms not only a planar structure in two-dimensiona1 graphite but also forms a planar local structure in the closed polyhedra (0-dimensional) of the fullerene family and in the cylinders (1-dimensional) called carbon nanotubes.
In 2004, the single-layer graphene with the ideal two-dimensional structure and unique electronic properties have been successfully prepared, which triggered the research boom of a new wave of carbon-based materials.From the theory of physical,graphene is a zero-band gap semi-metal/semiconductor materials, its carrier mobility is much higher than silicon. Graphene has obvious two-dimensional electronic characteristics.
In 2006-2008 years, graphene has been made of ballistic transport transistor, FET plane, which is attracted a large number of interests of scientists. It is succeeded in creating a planar field-effect transistor and in observing to the quantum interference effect, and in developing graphene-based circuits based on this study.
Recently, a significant Quantum Hall Effect and fractional Quantum Hall Effect observed in graphene have confirmed that it is very promising material of nano-electronic devices. Therefore, there is an important value of theoretical research in graphene, and it has quickly become the materials science and condensed matter physics research hotspot in recent years.
A carbon nanotube is a honeycomb lattice rolled into a cylinder. The diameter of a carbon nanotube is of nanometer size and the length of the nanotube can be more than lpm. It is a quasi-one-dimensional carbon nano-wire
The nanotube diameter is much smaller in size than the most advanced semiconductor devices obtained so far. Thus the availability of carbon nanotubes may have a large impact on semiconductor physics because of its very small size and the special electronic properties that are unique to carbon nanotubes.
In this paper,the structure of our study include: bulk graphite、a single graphene layer、two graphene layers、three graphene layers、two-dimensional one and a half of graphene layers、two-dimensional two graphene layers、a single layer of graphene nonoribbons, two layers of graphene nonoribbon and a simple shape of the structure of carbon nanotube.
In this paper,the physical properties which we studied is mainly conductivity (energy band, density of state) and magnetic (nomagnetic, ferromagnetic, anti-ferromagnetic)
Through research we found that the boundaries and shape of graphite make an impact on electrical conductivity and magnetic properties of graphite
The results which we obtained from this paper will provide theoretical guidance for the graphite material using in nano-device applications.
引文
[1] (a)K. S. Novoselov et al., Science 306, 666 (2004),(b)Proc. Natl Acod. Sci. U. S. A. 102,10451 (2005).
[2] Claire Berger et al. Science, 312, 1191(2006)
[3]吴代鸣,固体物理基础。高等教育出版社,2007.9。
[4]唐春梅,南京理工大学。富勒烯衍生物纳米材料的密度泛函研究,2008.6。
[5] SAITO R ,DRESSELHAUS G, DRESSELHAUS MS . Physical properties of carbon nanotubes [M]. London:Imperial college press, 1998.
[6] CASTRO NETO A H, GUINEA F, PERES N M.R, et al.The electronic properties of graphene[J]. REVIEWS OF MODERN PHYSICS, 2009, 81: 109-162.
[7] ANDO TSUNEYA,NAKANISHI TAKESHI,IGAMI MASATSURA.Effective-Mass theory of Carbon nanotubes with vacancy [J].Journal of the Physical Society of Japan,1999,68: 3994-4008.
[8] GEIM A K, NOVOSELOV K S. The rise of grapheme [J]. Nature Materials, 2007, 6:183-191.
[9] From graphene to graphite: Electronic structure around the Kpoint。B. Partoens* and F. M. Peeters。PHYSICAL REVIEW B 74, 075404(2006)
[10]李正中,固体理论。高等教育出版社,2001.10。
[11]冯端,金国钧。研究生教学用书:凝聚态物理学(上卷)。北京:高等教育出版社,2003。
[12] F.Bassani and G.Pastori Parravicini,lvuovo Cimento 50B,95(1967);Societa Italiana di Fisica
[13] Edge state in graphene ribbons:Nanometer size effect and edge shape dependence,Kyoko Nakada and Mitsutaka Fujita,PHYSICAL REVIEW B 54,17954 (1996)
[14] Coherent transport in graphene nanoconstrictions , F.Munoz-Rojas , D.Jacob ,J.Fernandez-Rossier,and J.J.Palacios,PHYSICAL REVIEW B 74,195417 (2006)
[15] Analytical study of electronic structure in armchair graphene nanoribbons,Huaixiu Zheng,Z.F.Wang,Tao Luo,Q.W.Shi,and Jie Chen,PHYSICAL REVIEW B 75, 165414(2007)
[16] ELECTRICAL CONDUCTANCE OF ZIGZAG NANOGRAPHITE RIBBONS WITHLOCALLY APPLIED GATE VOLTAGE,International Journal of Modern Physics B,Vol.16,No.32(2002) 4897-4909,KATSUNORI WAKABAYASHI,TAKA-SHI AOKI。
[17] Electronic structure and magnetic properties of graphitic ribbons,L.Pisani,J.A.Chan,B.Montanari,and N.M.Harrison,arXiv:cond-mat/0611344 v1 13 Nov 2006.
[18] Half-Metallic Graphene Nanoribbons,Young-Woo Son,Marvin L.Cohen,and Steven G.Louie,arXiv:cond-mat/0611600 v1 [cond-mat.mes-hall]23 Nov 2006.
[19] Quasiparticle Energies and Band Gaps in Graphene Nanoribbons,Li Yang,Cheol-Hwan Park,Young-Woo Son ,Marvin L.Cohen,and Steven G.Louie,PRL 99,186801 (2007)
[20] First-principles calculations for the electronic band structures of small diameter single-wall carbon nanotubes,V. Zólyomi and J. Kürti,PHYSICAL REVIEW B 70, 085403 (2004)
[21] Band-gap formation in (n,0) single-walled carbon nanotubes (n=9,12,15,18…) : A first-principles study,Takashi Miyake and Susumu Saito,PHYSICAL REVIEW B 72, 0734042005
[2] Claire Berger et al. Science, 312, 1191(2006)
[3]吴代鸣,固体物理基础。高等教育出版社,2007.9。
[4]唐春梅,南京理工大学。富勒烯衍生物纳米材料的密度泛函研究,2008.6。
[5] SAITO R ,DRESSELHAUS G, DRESSELHAUS MS . Physical properties of carbon nanotubes [M]. London:Imperial college press, 1998.
[6] CASTRO NETO A H, GUINEA F, PERES N M.R, et al.The electronic properties of graphene[J]. REVIEWS OF MODERN PHYSICS, 2009, 81: 109-162.
[7] ANDO TSUNEYA,NAKANISHI TAKESHI,IGAMI MASATSURA.Effective-Mass theory of Carbon nanotubes with vacancy [J].Journal of the Physical Society of Japan,1999,68: 3994-4008.
[8] GEIM A K, NOVOSELOV K S. The rise of grapheme [J]. Nature Materials, 2007, 6:183-191.
[9] From graphene to graphite: Electronic structure around the Kpoint。B. Partoens* and F. M. Peeters。PHYSICAL REVIEW B 74, 075404(2006)
[10]李正中,固体理论。高等教育出版社,2001.10。
[11]冯端,金国钧。研究生教学用书:凝聚态物理学(上卷)。北京:高等教育出版社,2003。
[12] F.Bassani and G.Pastori Parravicini,lvuovo Cimento 50B,95(1967);Societa Italiana di Fisica
[13] Edge state in graphene ribbons:Nanometer size effect and edge shape dependence,Kyoko Nakada and Mitsutaka Fujita,PHYSICAL REVIEW B 54,17954 (1996)
[14] Coherent transport in graphene nanoconstrictions , F.Munoz-Rojas , D.Jacob ,J.Fernandez-Rossier,and J.J.Palacios,PHYSICAL REVIEW B 74,195417 (2006)
[15] Analytical study of electronic structure in armchair graphene nanoribbons,Huaixiu Zheng,Z.F.Wang,Tao Luo,Q.W.Shi,and Jie Chen,PHYSICAL REVIEW B 75, 165414(2007)
[16] ELECTRICAL CONDUCTANCE OF ZIGZAG NANOGRAPHITE RIBBONS WITHLOCALLY APPLIED GATE VOLTAGE,International Journal of Modern Physics B,Vol.16,No.32(2002) 4897-4909,KATSUNORI WAKABAYASHI,TAKA-SHI AOKI。
[17] Electronic structure and magnetic properties of graphitic ribbons,L.Pisani,J.A.Chan,B.Montanari,and N.M.Harrison,arXiv:cond-mat/0611344 v1 13 Nov 2006.
[18] Half-Metallic Graphene Nanoribbons,Young-Woo Son,Marvin L.Cohen,and Steven G.Louie,arXiv:cond-mat/0611600 v1 [cond-mat.mes-hall]23 Nov 2006.
[19] Quasiparticle Energies and Band Gaps in Graphene Nanoribbons,Li Yang,Cheol-Hwan Park,Young-Woo Son ,Marvin L.Cohen,and Steven G.Louie,PRL 99,186801 (2007)
[20] First-principles calculations for the electronic band structures of small diameter single-wall carbon nanotubes,V. Zólyomi and J. Kürti,PHYSICAL REVIEW B 70, 085403 (2004)
[21] Band-gap formation in (n,0) single-walled carbon nanotubes (n=9,12,15,18…) : A first-principles study,Takashi Miyake and Susumu Saito,PHYSICAL REVIEW B 72, 0734042005