查看“︁石墨烯纳米带”︁的源代码

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'''石墨烯纳米带'''是指大概宽度小于50 [[纳米|nm]]的石墨烯条带。其理论模型最初于1996年提出<ref name = "Edgestate">{{cite journal|author=Fujita M., Wakabayashi K., Nakada K. and Kusakabe K.|doi=10.1143/JPSJ.65.1920|title=Peculiar Localized State at Zigzag Graphite Edge|year=1996|journal=Journal of the Physics Society Japan|volume=65|issue=7|pages=1920|bibcode = 1996JPSJ...65.1920F }}</ref><ref name = "Estatenakada">{{cite journal|author=Nakada K., Fujita M., Dresselhaus G. and Dresselhaus M.S. |doi=10.1103/PhysRevB.54.17954|title=Edge state in graphene ribbons: Nanometer size effect and edge shape dependence|year=1996|journal=Physical Review B|volume=54|issue=24|pages=17954|bibcode = 1996PhRvB..5417954N }}</ref><ref name = "MagPro">{{cite journal|author=Wakabayashi K., Fujita M., Ajiki H. and Sigrist M.|doi=10.1103/PhysRevB.59.8271|title=Electronic and magnetic properties of nanographite ribbons|year=1999|journal=Physical Review B|volume=59|issue=12|pages=8271|arxiv = cond-mat/9809260 |bibcode = 1999PhRvB..59.8271W }}</ref>。
[[File:cnt zz v3.gif|thumb|350px|right|鋸齒形石墨烯納米帶的二維結構。採用[[緊束縛近似]]模型做出的計算，顯示出鋸齒形具有金屬鍵性質。]]
[[File:cnt gnrarm v3.gif|thumb|350px|right|扶手椅形石墨烯納米帶的二維結構。採用[[緊束縛近似]]模型做出的計算，顯示出扶手椅形具有金屬鍵性質或半導體性質，依寬度而定。]]

==电子结构==
為了要賦予單層石墨烯某種電性，會按照特定樣式切割石墨烯，形成石墨烯纳米带（{{lang|en|Graphene nanoribbon}}）。切開的邊緣形狀可以分為鋸齒形和扶手椅形。採用[[緊束縛近似]]模型做出的計算，預測鋸齒形具有[[金屬鍵]]性質，又預測扶手椅形具有金屬鍵性質或[[半導體]]性質；到底是哪種性質，要依寬度而定<ref name="ReviewPCCPChung2016">{{cite journal |first1=H. C. |last1=Chung |first2=C. P. |last2=Chang |first3=C. Y. |last3=Lin |first4=M. F. |last4=Lin |year=2016 |title=Electronic and optical properties of graphene nanoribbons in external fields |journal=Physical Chemistry Chemical Physics |volume=18 |issue=11 |pages=7573-7616 |doi=10.1039/C5CP06533J }}</ref>。可是，近來根據[[密度泛函理論]]計算得到的結果，顯示出扶手椅形具有半導體性質，其[[能隙]]與納米帶帶寬成反比<ref name = "ArmchRibb">{{Cite journal|author = Barone, V., Hod, O., and Scuseria, G. E.|title = Electronic Structure and Stability of Semiconducting Graphene Nanoribbons|doi=10.1021/nl0617033|journal = Nano Lett.| volume = 6| page = 2748|year = 2006|pmid = 17163699|issue = 12}}</ref>。實驗結果確實地展示出，隨著納米帶帶寬減小，能隙會增大<ref name = "EgEngGNR">{{Cite journal|author = Han., M.Y., Özyilmaz, B., Zhang, Y., and Kim, P.|doi=10.1103/PhysRevLett.98.206805|journal = Phys. Rev. Lett.| volume = 98| page = 206805|year = 2007|title = Energy Band-Gap Engineering of Graphene Nanoribbons}}</ref>。但是，直至2009年, 尚沒有任何測量能隙的實驗試著辨識精確邊緣結構。
通過施加外磁場，石墨烯納米帶的光學響應也可以調整至[[太赫茲]]頻域 <ref>{{Cite journal| doi = 10.1063/1.2964093| journal=Appl Phys Lett| author = Junfeng Liu, A. R. Wright, Chao Zhang, and Zhongshui Ma| volume = 93| pages = 041106–041110|date = 29 July 2008| title= Strong terahertz conductance of graphene nanoribbons under a magnetic field}}</ref>。

石墨烯納米帶的結構具有高電導率、高[[熱導率]]、低雜訊，這些優良品質促使石墨烯納米帶成為[[積體電路|積體電路互連]]材料的另一種選擇，有可能替代[[銅|銅金屬]]。有些研究者試著用石墨烯納米帶來製成[[量子點]]，他們在納米帶的某些特定位置改變寬度，形成[[量子禁閉]]（{{lang|en|quantum confinement}}）<ref>{{Cite journal|author =Wang, Z. F., Shi, Q. W., Li, Q., Wang, X., Hou, J. G., Zheng, H., et al.|title = Z-shaped graphene nanoribbon quantum dot device| doi=10.1063/1.2761266|journal = Applied Physics Letters| volume = 91| page = 053109|year = 2007}}</ref>。

石墨烯納米帶的低维結構具有非常重要的光电性能：粒子數反轉和寬帶光增益。這些優良品質促使石墨烯納米帶放在微腔或纳米腔体中形成[[激光器]] <ref>{{Cite journal|author =Shan, G.C., et al.|title = Nanolaser with a Single-Graphene-Nanoribbon in a Microcavity | doi=10.1166/jno.2011.1148 |journal = Journal of Nanoelectronics and Optoelectronics | volume = 6| page = 138-143 |year = 2011}}</ref> 和放大器。 
根据2012年10月的一份研究表明有些研究者試著将石墨烯納米帶应用于光通信系统，发展[[石墨烯]][[納米激光器]]  <ref> {{Cite journal|author =Shan, G.C.,Shek, C.H., |title = Modeling an Electrically Driven Graphene-Nanoribbon Laser for Optical Interconnects | doi=10.1109/PGC.2012.6458072 | publisher = IEEE  Conference | year = 2012 }}</ref>。

==光學性質==

最早的石墨烯奈米帶光學性質的數值結果是林與徐於2000年預測<ref name="ReviewPCCPChung2016" /><ref>{{cite journal |last1=Lin |first1=Ming-Fa |last2=Shyu |first2=Feng-Lin |title=Optical Properties of Nanographite Ribbons |journal=Journal of the Physical Society of Japan |date=2000-11-15 |volume=69 |issue=11 |pages=3529–3532 |doi=10.1143/JPSJ.69.3529}}</ref>。扶手椅和鋸齒形邊緣的石墨烯奈米帶中光學躍遷具有的不同選擇規則。這些結果在2007年得到了Hsu和Reichl的研究支持，其對鋸齒形石墨烯奈米帶與單壁扶手椅碳奈米管進行比較研究<ref>{{cite journal |last1=Hsu |first1=Han |last2=Reichl |first2=L. E. |title=Selection rule for the optical absorption of graphene nanoribbons |journal=Physical Review B |date=2007-07-19 |volume=76 |issue=4 |pages=045418 |doi=10.1103/PhysRevB.76.045418}}</ref>。結果表明，鋸齒形石墨烯奈米帶的選擇規則與碳奈米管的選擇規則不同，鋸齒帶的本徵態可分為對稱或反對稱。此外，也預測邊緣態應該在鋸齒形石墨烯奈米帶的光學吸收中發揮重要作用。邊緣態和體態之間的光學躍遷應造成低能量區域的吸收光譜 (<3 eV)。於2011年，對光學躍遷的特性出現理論與數值上的分析推導，並明確了選擇規則<ref name="#1">{{cite journal | first1=H. C. | last1=Chung | first2=M. H. | last2=Lee | first3=C. P.| last3=Chang | first4=M. F. | last4=Lin | title=Exploration of edge-dependent optical selection rules for graphene nanoribbons| journal=Optics Express | volume=19 | issue=23| pages=23350–63 | year=2011 | doi=10.1364/OE.19.023350| pmid=22109212 | bibcode=2011OExpr..1923350C| arxiv=1104.2688 }}</ref><ref name="#2">{{ cite journal | journal=Phys. Rev. B | first1=K.-I. | last1=Sasaki| first2=K. | last2=Kato| first3=Y. | last3=Tokura| first4=K. | last4=Oguri |  first5=T. | last5=Sogawa| title=Theory of optical transitions in graphene nanoribbons| volume=84| issue=8 | year=2011| page=085458|doi=10.1103/PhysRevB.84.085458| arxiv=1107.0795| bibcode=2011PhRvB..84h5458S | s2cid=119091338 }}</ref><ref name="ReviewPCCPChung2016" />，當入射光的極化方向平行於鋸齒形石墨烯奈米帶時，其光學選擇規則是<math> \Delta J = J_2 - J_1</math>要是奇數，其中<math>J_1</math>和<math>J_2</math>為能帶編號。而對於極化方向垂直於鋸齒形石墨烯納米帶時，<math> \Delta J = J_2 - J_1</math>是偶數。

對於扶手椅石墨烯奈米帶，當入射光的極化方向平行於扶手椅石墨烯奈米帶時，其光學選擇規則為<math> \Delta J = J_2 - J_1 = 0</math><ref name="#1"/><ref name="#2"/><ref name="ReviewPCCPChung2016" />。類似於碳奈米管中的電子躍遷，扶手椅石墨烯奈米帶禁止子帶間躍遷。儘管單壁扶手椅碳納奈管和鋸齒形石墨烯奈米帶的選擇規則不同，但吸收峰間的隱藏相關性已被預測<ref>{{cite journal | first1=V. A.| last1=Saroka | first2=M. V. | last2=Shuba | first3=M. E.| last3=Portnoi| title=Optical selection rules of zigzag graphene nanoribbons| journal=Phys. Rev. B| volume=95| issue=15| year=2017| page=155438| doi=10.1103/PhysRevB.95.155438| arxiv=1705.00757| bibcode=2017PhRvB..95o5438S}}</ref>。管晶胞中的原子數<math>N_t</math>與鋸齒形帶晶胞中的原子數<math>N_r</math>有如下的條件: <math>N_t = 2 N_r + 4</math> (這就是所謂的匹配條件週期性和硬壁邊界條件)。在最近鄰緊束縛模型的中獲得的這些結果已被考慮到交換和相關效應的第一性原理密度泛函理論計算所支持<ref>{{cite journal | first1=R.B. | last1=Payod| first2=D. | last2=Grassano| first3=G.N.C. | last3=Santos | first4=D.I. | last4=Levshov| first5=O. | last5=Pulci| first6=V. A.| last6=Saroka | title=2N+4-rule and an atlas of bulk optical resonances of zigzag graphene nanoribbons| journal=Nat. Commun.| volume=11| issue=1| year=2020| page=82| doi=10.1038/s41467-019-13728-8| pmid=31900390| pmc=6941967| bibcode=2020NatCo..11...82P| doi-access=free}}</ref>。

包含了準粒子校正和多體效應的第一原理計算研究了石墨烯基材料的電子和光學特性<ref>{{cite journal |journal=Rev. Mod. Phys. |year=2002 |volume=74 |page=601 |doi=10.1103/RevModPhys.74.601 |bibcode=2002RvMP...74..601O |title=Electronic excitations: Density-functional versus many-body Green's-function approaches |last1=Onida |first1=Giovanni |last2=Rubio |first2=Angel |issue=2|hdl=10261/98472 |hdl-access=free }}</ref>。通過GW計算，可以準確研究石墨烯基材料的特性，包括石墨烯奈米帶<ref>{{cite journal |last1=Prezzi |first1=Deborah |last2=Varsano |first2=Daniele |last3=Ruini |first3=Alice |last4=Marini |first4=Andrea |last5=Molinari |first5=Elisa |title=Optical properties of graphene nanoribbons: The role of many-body effects |journal=Physical Review B |date=2008-01-07 |volume=77 |issue=4 |pages=041404 |doi=10.1103/PhysRevB.77.041404}}</ref><ref>{{cite journal |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |title=Magnetic Edge-State Excitons in Zigzag Graphene Nanoribbons |journal=Physical Review Letters |date=2008-10-28 |volume=101 |issue=18 |pages=186401 |doi=10.1103/PhysRevLett.101.186401}}</ref><ref>{{cite journal |last1=Yang |first1=Li |last2=Cohen |first2=Marvin L. |last3=Louie |first3=Steven G. |title=Excitonic Effects in the Optical Spectra of Graphene Nanoribbons |journal=Nano Letters |date=2007-10-01 |volume=7 |issue=10 |pages=3112–3115 |doi=10.1021/nl0716404}}</ref>、邊緣和表面功能化的扶手椅石墨烯奈米帶<ref>{{cite journal |journal=J. Phys. Chem. C |year=2010 |volume=114 |page=17257 |doi=10.1021/jp102341b |title=Excitons of Edge and Surface Functionalized Graphene Nanoribbons |last1=Zhu |first1=Xi |last2=Su |first2=Haibin |issue=41}}</ref>以及扶手椅石墨烯奈米帶中的縮放特性<ref>{{cite journal |title=Scaling of Excitons in Graphene Nanoribbons with Armchair Shaped Edges |journal=Journal of Physical Chemistry A |year=2011 |volume=115 |issue=43 |pages=11998–12003 |doi=10.1021/jp202787h |pmid=21939213 |last1=Zhu |first1=Xi |last2=Su |first2=Haibin|bibcode=2011JPCA..11511998Z }}</ref>。


== 參見 ==
* [[石墨烯]]
* [[石墨]]
* [[奈米碳管]]
* [[藤田光孝]]
* [[若林克法]]
* [[矽烯]]

==参考文献==
{{reflist}}

== 外部連結 ==
*[http://xstructure.inr.ac.ru/x-bin/theme3.py?level=1&index1=181648  Graphene nanoribbons on arxiv.org]

[[Category:纳米材料]]
[[Category:半導體材料]]