【《拓扑材料分类研究文献综述》3400字】

拓扑材料分类研究文献综述目录TOC\o"1-3"\h\u31550拓扑材料分类研究文献综述 1217791.1拓扑绝缘体 121001.2拓扑半金属 31.1拓扑绝缘体拓扑绝缘体是一种新的量子物态，是对绝缘体进行的再分类。引入拓扑概念到凝聚态物质，最早可以追溯到1980年发现量子霍尔效应。研究人员在金属-氧化物-半导体界面中发现体内的电子是做回旋运动的，但是表面的电子是形成回路的ADDINEN.CITE<EndNote><Cite><Author>Klitzing</Author><Year>1980</Year><RecNum>62</RecNum><DisplayText><styleface="superscript">[6]</style></DisplayText><record><rec-number>62</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616726052">62</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Klitzing,K.v</author><author>Dorda,G.</author><author>Pepper,M.</author></authors></contributors><titles><title>NewMethodforHigh-AccuracyDeterminationoftheFine-StructureConstantBasedonQuantizedHallResistance</title><secondary-title>PhysicalReviewLetters</secondary-title></titles><periodical><full-title>PhysicalReviewLetters</full-title></periodical><pages>494-497</pages><volume>45</volume><number>6</number><dates><year>1980</year><pub-dates><date>08/11/</date></pub-dates></dates><publisher>AmericanPhysicalSociety</publisher><urls><related-urls><url>/doi/10.1103/PhysRevLett.45.494</url></related-urls></urls><electronic-resource-num>10.1103/PhysRevLett.45.494</electronic-resource-num></record></Cite></EndNote>[6]。并且电阻表现出阶梯状的形态，每个平台都对应一个整数。在每一个量子化的平台下，纵向的电阻都降为零，所以边界的电子做无耗散的运动。在很低的温度条件(1.5K)和很强的磁场条件(18T)下，这个霍尔电导是e2/h的整数倍，整数的取值随着磁场或栅压变化。量子霍尔效应极其精确，可以用来测量精细结构常数，并且在一定范围内与具体的材料体系，磁场和掺杂状态无关。在图1.2中，给出了相应的原理图。图1.2量子霍尔效应和量子化的电导平台。为了从理论上解释这个新的效应，Thouless等提出著名的TKNN定理，从拓扑的角度理解量子霍尔效应ADDINEN.CITE<EndNote><Cite><Author>Thouless</Author><Year>1982</Year><RecNum>63</RecNum><DisplayText><styleface="superscript">[7]</style></DisplayText><record><rec-number>63</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616726171">63</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Thouless,D.J.</author><author>Kohmoto,M.</author><author>Nightingale,M.P.</author><author>denNijs,M.</author></authors></contributors><titles><title>QuantizedHallConductanceinaTwo-DimensionalPeriodicPotential</title><secondary-title>PhysicalReviewLetters</secondary-title></titles><periodical><full-title>PhysicalReviewLetters</full-title></periodical><pages>405-408</pages><volume>49</volume><number>6</number><dates><year>1982</year><pub-dates><date>08/09/</date></pub-dates></dates><publisher>AmericanPhysicalSociety</publisher><urls><related-urls><url>/doi/10.1103/PhysRevLett.49.405</url></related-urls></urls><electronic-resource-num>10.1103/PhysRevLett.49.405</electronic-resource-num></record></Cite></EndNote>[7]。他们将二维系统的电导表达成一个k空间中的旋度场在二维布里渊区的面积分，并利用数学中的斯托克斯定理表达式写成环路积分的形式。由于环路积分是2π的整数倍，因此霍尔电导必须是e2/h整数倍。环路积分隐含拓扑不变量的思想，人们很快意识到这种拓扑不变量有更普适的物理意义ADDINEN.CITE<EndNote><Cite><Author>Bansil</Author><Year>2016</Year><RecNum>96</RecNum><DisplayText><styleface="superscript">[8]</style></DisplayText><record><rec-number>96</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1617627108">96</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Bansil,A.</author><author>Lin,Hsin</author><author>Das,Tanmoy</author></authors></contributors><titles><title>Colloquium:Topologicalbandtheory</title><secondary-title>ReviewsofModernPhysics</secondary-title></titles><periodical><full-title>ReviewsofModernPhysics</full-title></periodical><pages>021004</pages><volume>88</volume><number>2</number><dates><year>2016</year><pub-dates><date>06/29/</date></pub-dates></dates><publisher>AmericanPhysicalSociety</publisher><urls><related-urls><url>/doi/10.1103/RevModPhys.88.021004</url></related-urls></urls><electronic-resource-num>10.1103/RevModPhys.88.021004</electronic-resource-num></record></Cite></EndNote>[8]。拓扑绝缘体最显著的特点是特殊的表面态或者边界态，其体相和普通的绝缘体一样，只是在表面或者边界处有线性的能量动量色散关系。边界态的出现受到时间反演对称性的保护，对外界条件的影响不敏感。石墨烯是第一个被预测是二维拓扑绝缘体的体系ADDINEN.CITE<EndNote><Cite><Author>Kane</Author><Year>2005</Year><RecNum>91</RecNum><DisplayText><styleface="superscript">[9]</style></DisplayText><record><rec-number>91</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1617240756">91</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Kane,C.L.</author><author>Mele,E.J.</author></authors></contributors><titles><title>QuantumSpinHallEffectinGraphene</title><secondary-title>PhysicalReviewLetters</secondary-title></titles><periodical><full-title>PhysicalReviewLetters</full-title></periodical><pages>226801</pages><volume>95</volume><number>22</number><dates><year>2005</year><pub-dates><date>11/23/</date></pub-dates></dates><publisher>AmericanPhysicalSociety</publisher><urls><related-urls><url>/doi/10.1103/PhysRevLett.95.226801</url></related-urls></urls><electronic-resource-num>10.1103/PhysRevLett.95.226801</electronic-resource-num></record></Cite></EndNote>[9]。通过建模预测，在石墨烯的一维的纳米带上会出现导电的边界态。因为能带的宽度太小了，实验上观测非常的困难。实验上观测到的拓扑绝缘体材料较少，第一次观测到的体系是HgTe/CdTe量子阱ADDINEN.CITE<EndNote><Cite><Author>Bernevig</Author><Year>2006</Year><RecNum>64</RecNum><DisplayText><styleface="superscript">[10]</style></DisplayText><record><rec-number>64</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616726594">64</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Bernevig,B.Andrei</author><author>Hughes,TaylorL.</author><author>Zhang,Shou-Cheng</author></authors></contributors><titles><title>QuantumSpinHallEffectandTopologicalPhaseTransitioninHgTeQuantumWells</title><secondary-title>Science</secondary-title></titles><periodical><full-title>Science</full-title></periodical><pages>1757</pages><volume>314</volume><number>5806</number><dates><year>2006</year></dates><urls><related-urls><url>/content/314/5806/1757.abstract</url></related-urls></urls><electronic-resource-num>10.1126/science.1133734</electronic-resource-num></record></Cite></EndNote>[10]。HgTe/CdTe量子阱的拓扑能隙起源于Г点的能带反转,通过调节量子阱的宽度或调节外偏压可以实现此能带反转。在图1.3中给出了HgTe/CdTe量子阱的示意图和量子化的导电平台。但是该样品制备复杂，需要精确调控。并且因为带隙太小，只能在极低的温度下工作。因此，寻找大带隙，材料易于制备稳定性好的拓扑绝缘体，是研究人员的目标。图1.3HgTe/CdTe量子阱和霍尔电导平台。2009年理论预测的三维拓扑绝缘体Bi2Se3家族材料ADDINEN.CITE<EndNote><Cite><Author>Zhang</Author><Year>2009</Year><RecNum>65</RecNum><DisplayText><styleface="superscript">[11]</style></DisplayText><record><rec-number>65</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616726695">65</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Zhang,Haijun</author><author>Liu,Chao-Xing</author><author>Qi,Xiao-Liang</author><author>Dai,Xi</author><author>Fang,Zhong</author><author>Zhang,Shou-Cheng</author></authors></contributors><titles><title><styleface="normal"font="default"size="100%">TopologicalinsulatorsinBi</style><styleface="subscript"font="default"size="100%">2</style><styleface="normal"font="default"size="100%">Se</style><styleface="subscript"font="default"size="100%">3</style><styleface="normal"font="default"size="100%">,Bi</style><styleface="subscript"font="default"size="100%">2</style><styleface="normal"font="default"size="100%">Te</style><styleface="subscript"font="default"size="100%">3</style><styleface="normal"font="default"size="100%">andSb</style><styleface="subscript"font="default"size="100%">2</style><styleface="normal"font="default"size="100%">Te</style><styleface="subscript"font="default"size="100%">3</style><styleface="normal"font="default"size="100%">withasingleDiracconeonthesurface</style></title><secondary-title>NaturePhysics</secondary-title></titles><periodical><full-title>NaturePhysics</full-title></periodical><pages>438-442</pages><volume>5</volume><number>6</number><dates><year>2009</year><pub-dates><date>2009/06/01</date></pub-dates></dates><isbn>1745-2481</isbn><urls><related-urls><url>/10.1038/nphys1270</url></related-urls></urls><electronic-resource-num>10.1038/nphys1270</electronic-resource-num></record></Cite></EndNote>[11]，掀起了研究拓扑绝缘体的热潮。该材料简单易得，不需要复杂的制备调控。如图1.4所示，Bi2Se3是由五个原子层为一个单元组成的层状结构。此外该材料的带隙很大，能带宽度为0.3eV。在被第一性原理计算预测之后不久，很快就得到了实验上的验证ADDINEN.CITE<EndNote><Cite><Author>Chen</Author><Year>2009</Year><RecNum>68</RecNum><DisplayText><styleface="superscript">[12]</style></DisplayText><record><rec-number>68</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616727191">68</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Chen,Y.L.</author><author>Analytis,J.G.</author><author>Chu,J.H.</author><author>Liu,Z.K.</author><author>Mo,S.K.</author><author>Qi,X.L.</author><author>Zhang,H.J.</author><author>Lu,D.H.</author><author>Dai,X.</author><author>Fang,Z.</author><author>Zhang,S.C.</author><author>Fisher,I.R.</author><author>Hussain,Z.</author><author>Shen,Z.X.</author></authors></contributors><titles><title><styleface="normal"font="default"size="100%">ExperimentalRealizationofaThree-DimensionalTopologicalInsulator,Bi</style><styleface="subscript"font="default"size="100%">2</style><styleface="normal"font="default"size="100%">Te</style><styleface="subscript"font="default"size="100%">3</style></title><secondary-title>Science</secondary-title></titles><periodical><full-title>Science</full-title></periodical><pages>178</pages><volume>325</volume><number>5937</number><dates><year>2009</year></dates><urls><related-urls><url>/content/325/5937/178.abstract</url></related-urls></urls><electronic-resource-num>10.1126/science.1173034</electronic-resource-num></record></Cite></EndNote>[12]。在2010年，理论预言将磁性元素掺杂到BiSe材料拓扑绝缘体薄膜里ADDINEN.CITE<EndNote><Cite><Author>Zhang</Author><Year>2010</Year><RecNum>66</RecNum><DisplayText><styleface="superscript">[13]</style></DisplayText><record><rec-number>66</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616726957">66</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Zhang,Yi</author><author>He,Ke</author><author>Chang,Cui-Zu</author><author>Song,Can-Li</author><author>Wang,Li-Li</author><author>Chen,Xi</author><author>Jia,Jin-Feng</author><author>Fang,Zhong</author><author>Dai,Xi</author><author>Shan,Wen-Yu</author><author>Shen,Shun-Qing</author><author>Niu,Qian</author><author>Qi,Xiao-Liang</author><author>Zhang,Shou-Cheng</author><author>Ma,Xu-Cun</author><author>Xue,Qi-Kun</author></authors></contributors><titles><title><styleface="normal"font="default"size="100%">Crossoverofthethree-dimensionaltopologicalinsulatorBi</style><styleface="subscript"font="default"size="100%">2</style><styleface="normal"font="default"size="100%">Se</style><styleface="subscript"font="default"size="100%">3</style><styleface="normal"font="default"size="100%">tothetwo-dimensionallimit</style></title><secondary-title>NaturePhysics</secondary-title></titles><periodical><full-title>NaturePhysics</full-title></periodical><pages>584-588</pages><volume>6</volume><number>8</number><dates><year>2010</year><pub-dates><date>2010/08/01</date></pub-dates></dates><isbn>1745-2481</isbn><urls><related-urls><url>/10.1038/nphys1689</url></related-urls></urls><electronic-resource-num>10.1038/nphys1689</electronic-resource-num></record></Cite></EndNote>[13]，可以实现量子反常霍尔效应，在2013年实验上首次观测到了这个现象ADDINEN.CITEADDINEN.CITE.DATA[14-16]。图1.4Bi2Se3的晶体结构和能带。拓扑绝缘体中受特殊对称性保护的电子态带来了令人激动的应用前景，提供了新平台来探索基础科学问题ADDINEN.CITEADDINEN.CITE.DATA[17-19]。拓扑绝缘体最显著的特征来源于其特殊的能带结构，其体态有带隙而表面态无带隙。在二维体系中，通过构造特殊的边界条件可以获得这样的边缘态。对于三维体系，也可以构造类似的无带隙的表面态，同时产生自旋-动量锁定等性质。以及实现用于热电，自旋电子学，信息处理的多功能拓扑设备和其他应用ADDINEN.CITEADDINEN.CITE.DATA[20-22]。1.2拓扑半金属除了拓扑绝缘体，拓扑半金属也是一种新的量子拓扑物态，引起了人们的极大研究兴趣。根据对拓扑绝缘体的研究可知，拓扑不变量是定义在闭合曲面上的，例如动量空间布里渊区。然而金属的布里渊区不是封闭的，金属中有部分占据的能带，所以不能在整个布里渊区中定义拓扑。但是金属的费米面是闭合的，因此可以类似的定义拓扑金属态。拓扑半金属的块体能带是无间隙的，导带和价带仅在布里渊区的一些离散点相接触。拓扑半金属包含狄拉克半金属和外尔半金属ADDINEN.CITE<EndNote><Cite><Author>Son</Author><Year>2013</Year><RecNum>103</RecNum><DisplayText><styleface="superscript">[23,24]</style></DisplayText><record><rec-number>103</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1617634462">103</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Son,D.T.</author><author>Spivak,B.Z.</author></authors></contributors><titles><title>ChiralanomalyandclassicalnegativemagnetoresistanceofWeylmetals</title><secondary-title>PhysicalReviewB</secondary-title></titles><periodical><full-title>PhysicalReviewB</full-title></periodical><pages>104412</pages><volume>88</volume><number>10</number><dates><year>2013</year><pub-dates><date>09/13/</date></pub-dates></dates><publisher>AmericanPhysicalSociety</publisher><urls><related-urls><url>/doi/10.1103/PhysRevB.88.104412</url></related-urls></urls><electronic-resource-num>10.1103/PhysRevB.88.104412</electronic-resource-num></record></Cite><Cite><Author>Liu</Author><Year>2013</Year><RecNum>104</RecNum><record><rec-number>104</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1617634569">104</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Liu,Chao-Xing</author><author>Ye,Peng</author><author>Qi,Xiao-Liang</author></authors></contributors><titles><title>ChiralgaugefieldandaxialanomalyinaWeylsemimetal</title><secondary-title>PhysicalReviewB</secondary-title></titles><periodical><full-title>PhysicalReviewB</full-title></periodical><pages>235306</pages><volume>87</volume><number>23</number><dates><year>2013</year><pub-dates><date>06/10/</date></pub-dates></dates><publisher>AmericanPhysicalSociety</publisher><urls><related-urls><url>/doi/10.1103/PhysRevB.87.235306</url></related-urls></urls><electronic-resource-num>10.1103/PhysRevB.87.235306</electronic-resource-num></record></Cite></EndNote>[23,24]。这是通过体系的对称性来区分的，对称性不同，能带的简并度不同，交点的形态也不一样。狄拉克半金属中的每条能是二重简并的，所以交点是四重简并的点，可以看作是由两个拓扑电荷相反的外尔点组成的。和拓扑绝缘体表面或者边界上的狄拉克点一样，狄拉克半金属中的能带交叉点是零维的。Na3Bi材料是第一性原理预测的稳定的狄拉克半金属材料，其狄拉克点受晶体对称性保护。该材料表面有非平庸的费米弧，当对称性被打破时，会诱导出不同的拓扑相变ADDINEN.CITE<EndNote><Cite><Author>Wang</Author><Year>2012</Year><RecNum>72</RecNum><DisplayText><styleface="superscript">[25]</style></DisplayText><record><rec-number>72</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616729327">72</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Wang,Zhijun</author><author>Sun,Yan</author><author>Chen,Xing-Qiu</author><author>Franchini,Cesare</author><author>Xu,Gang</author><author>Weng,Hongming</author><author>Dai,Xi</author><author>Fang,Zhong</author></authors></contributors><titles><title><styleface="normal"font="default"size="100%">DiracsemimetalandtopologicalphasetransitionsinA</style><styleface="subscript"font="default"size="100%">3</style><styleface="normal"font="default"size="100%">Bi(A=Na,K,Rb)</style></title><secondary-title>PhysicalReviewB</secondary-title></titles><periodical><full-title>PhysicalReviewB</full-title></periodical><volume>85</volume><number>19</number><dates><year>2012</year></dates><isbn>1098-0121 1550-235X</isbn><urls></urls><electronic-resource-num>10.1103/PhysRevB.85.195320</electronic-resource-num></record></Cite></EndNote>[25]。这些材料是有相互关联的，在一定的外界条件下，可以进行相变转化。外尔半金属的能带也显示出围绕交叉点的线性色散关系，可以看作是石墨烯的三维版本。TaAs是一个理想的外尔半金属材料，该材料有表面费米弧，和手性磁传输性质ADDINEN.CITE<EndNote><Cite><Author>Yang</Author><Year>2015</Year><RecNum>73</RecNum><DisplayText><styleface="superscript">[26]</style></DisplayText><record><rec-number>73</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616729443">73</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Yang,L.X.</author><author>Liu,Z.K.</author><author>Sun,Y.</author><author>Peng,H.</author><author>Yang,H.F.</author><author>Zhang,T.</author><author>Zhou,B.</author><author>Zhang,Y.</author><author>Guo,Y.F.</author><author>Rahn,M.</author><author>Prabhakaran,D.</author><author>Hussain,Z.</author><author>Mo,S.K.</author><author>Felser,C.</author><author>Yan,B.</author><author>Chen,Y.L.</author></authors></contributors><titles><title>Weylsemimetalphaseinthenon-centrosymmetriccompoundTaAs</title><secondary-title>NaturePhysics</secondary-title></titles><periodical><full-title>NaturePhysics</full-title></periodical><pages>728-732</pages><volume>11</volume><number>9</number><dates><year>2015</year></dates><isbn>1745-2473 1745-2481</isbn><urls></urls><electronic-resource-num>10.1038/nphys3425</electronic-resource-num></record></Cite></EndNote>[26]。另外，还有第二类外尔半金属化合物，这类体系破坏了洛伦兹不变性。第二类外尔半金属材料，已经在WTe2，MoTe2体系中被发现ADDINEN.CITE<EndNote><Cite><Author>Deng</Author><Year>2016</Year><RecNum>74</RecNum><DisplayText><styleface="superscript">[27]</style></DisplayText><record><rec-number>74</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616744426">74</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Deng,Ke</author><author>Wan,Guoliang</author><author>Deng,Peng</author><author>Zhang,Kenan</author><author>Ding,Shijie</author><author>Wang,Eryin</author><author>Yan,Mingzhe</author><author>Huang,Huaqing</author><author>Zhang,Hongyun</author><author>Xu,Zhilin</author><author>Denlinger,Jonathan</author><author>Fedorov,Alexei</author><author>Yang,Haitao</author><author>Duan,Wenhui</author><author>Yao,Hong</author><author>Wu,Yang</author><author>Fan,Shoushan</author><author>Zhang,Haijun</author><author>Chen,Xi</author><author>Zhou,Shuyun</author></authors></contributors><titles><title><styleface="normal"font="default"size="100%">ExperimentalobservationoftopologicalFermiarcsintype-IIWeylsemimetalMoTe</style><styleface="subscript"font="default"size="100%">2</style></title><secondary-title>NaturePhysics</secondary-title></titles><periodical><full-title>NaturePhysics</full-title></periodical><pages>1105-1110</pages><volume>12</volume><number>12</number><dates><year>2016</year><pub-dates><date>2016/12/01</date></pub-dates></dates><isbn>1745-2481</isbn><urls><related-urls><url>/10.1038/nphys3871</url></related-urls></urls><electronic-resource-num>10.1038/nphys3871</electronic-resource-num></record></Cite></EndNote>[27]。此外，一项最近的研究工作表明，一组狄拉克点在布里渊区中也可以形成一条环线，称为拓扑节点线半金属，其中导带和价带沿着节点线相交ADDINEN.CITEADDINEN.CITE.DATA[4,28,29]。在图1.5里，我们给出了不同种类的拓扑半金属能带示意图ADDINEN.CITE<EndNote><Cite><Author>Weng</Author><Year>2016</Year><RecNum>84</RecNum><DisplayText><styleface="superscript">[3]</style></DisplayText><record><rec-number>84</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616914378">84</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Weng,Hongming</author><author>Dai,Xi</author><author>Fang,Zhong</author></authors></contributors><titles><title>Topologicalsemimetalspredictedfromfirst-principlescalculations</title><secondary-title>JournalofPhysics:CondensedMatter</secondary-title></titles><periodical><full-title>JournalofPhysics:CondensedMatter</full-title></periodical><pages>303001</pages><volume>28</volume><number>30</number><dates><year>2016</year><pub-dates><date>2016/06/08</date></pub-dates></dates><publisher>IOPPublishing</publisher><isbn>0953-8984 1361-648X</isbn><urls><related-urls><url>/10.1088/0953-8984/28/30/303001</url></related-urls></urls><electronic-resource-num>10.1088/0953-8984/28/30/303001</electronic-resource-num></record></Cite></EndNote>[3]。图1.5狄拉克半金属，外尔半金属和节线半金属的能带示意图。在拓扑金属和拓扑半金属中，新的准粒子出现在受保护的带交叉点附近，其中一些粒子的特性超出了高能物理学中的基本费米子，并具有引人入胜的物理特性。该领域的大多数工作都集中在涉及重元素的材料上，因为目前的共识是强自旋轨道耦合会导致拓扑性质的发生ADDINEN.CITEADDINEN.CITE.DATA[30,31]。但人们也意识到，轻元素材料中也提供了类似的驱动作用。对于由轻元素（例如硼或碳）组成的材料，自旋轨道耦合作用很弱，是可以忽略的。因此，可以将电子自旋可以看作是虚拟的自由度，将出现的费米子视为“无自旋”的，这与具有强的自旋轨道耦合材料的“自旋”费米子有根本区别。关于碳材料研究已经有了一些相关的工作，揭示了几种三维碳同素异形体作为拓扑金属和拓扑半金属。这些材料中包含外尔费米子ADDINEN.CITE<EndNote><Cite><Author>Chen</Author><Year>2015</Year><RecNum>15</RecNum><DisplayText><styleface="superscript">[32]</style></DisplayText><record><rec-number>15</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616310988">15</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Chen,Yuanping</author><author>Xie,Yuee</author><author>Yang,ShengyuanA.</author><author>Pan,Hui</author><author>Zhang,Fan</author><author>Cohen,MarvinL.</author><author>Zhang,Shengbai</author></authors></contributors><titles><title>NanostructuredCarbonAllotropeswithWeyl-likeLoopsandPoints</title><secondary-title>NanoLetters</secondary-title></titles><periodical><full-title>NanoLetters</full-title></periodical><pages>6974-6978</pages><volume>15</volume><number>10</number><dates><year>2015</year><pub-dates><date>2015/10/14</date></pub-dates></dates><publisher>AmericanChemicalSociety</publisher><isbn>1530-6984</isbn><urls><related-urls><url>/10.1021/acs.nanolett.5b02978</url></related-urls></urls><electronic-resource-num>10.1021/acs.nanolett.5b02978</electronic-resource-num></record></Cite></EndNote>[32]，节线费米子ADDINEN.CITEADDINEN.CITE.DATA[33,34]，三重简并费米子ADDINEN.CITEADDINEN.CITE.DATA[35,36]等。最近，通过第一性原理确定一种独特的拓扑半金属，该半金属中呈现出多个相互连接的结线形成的节点网，并且在其表面上围绕费米能级附近具有两个耦合的鼓面状扁平带。节点网半金属态是在三维石墨烯网络结构中实现的，该结构可以通过将苯环插入bct-C4晶格的C-C键中得到或通过对(5,5)碳纳米管进行晶体修饰来构造ADDINEN.CITE<EndNote><Cite><Author>Wang</Author><Year>2018</Year><RecNum>20</RecNum><DisplayText><styleface="superscript">[37]</style></DisplayText><record><rec-number>20</rec-number><foreign-keys><keyapp="EN"db-id="pz9zv5xx2pxzdoe0vvzpvawe0vpsza2fpzsd"timestamp="1616317604">20</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Wang,J.T.</author><author>Nie,S.</author><author>Weng,H.</author><author>Kawazoe,Y.</author><author>Chen,C.</author></authors></contributors><auth-address>BeijingNationalLaboratoryforCondensedMatterPhysics,InstituteofPhysics,ChineseAcademyofSciences,Beijing100190,China. SchoolofPhysics,UniversityofChineseAcademyofSciences,Beijing100049,China. CollaborativeInnovationCenterofQuantumMatter,Beijing100190,China. NewIndustryCreationHatcheryCenter,TohokuUniversity,Sendai980-8579,Japan. DepartmentofPhysicsandHighPressureScienceandEngineeringCenter,UniversityofNevada,LasVegas,Nevada89154,USA.</auth-address><titles><title>TopologicalNodal-NetSemimetalinaGrapheneNetworkStructure</title><secondary-title>PhysicalReviewLetters</secondary-title></titles><periodical><full-title>PhysicalReviewLetters</full-title></periodical><pages>026402</pages><volume>120</volume><number>2</number><dates><year>2018</year><pub-dates><date>Jan12</date></pub-dates></dates><isbn>1079-7114(Electronic) 0031-9007(Linking)</isbn><accession-num>29376700</accession-num><urls><related-urls><url>/pubmed/29376700</url></related-urls></urls><electronic-resource-num>10.1103/PhysRevLett.120.026402</electronic-resource-num></record></Cite></EndNote>[37]。由于硼元素和碳有类似的一些特征，人们自然可以期望在三维硼同素异形体中寻找新型无自旋轨道费米子。目前，对该研究方向的探索才刚刚开始ADDINEN.CITEADDINEN.CITE.DATA[38,39]。参考文献[1] QiX-L,ZhangS-C.Topologicalinsulatorsandsuperconductors.ReviewsofModernPhysics,2011,83(4):1057-1110.[2] MooreJE.Thebirthoftopologicalinsulators.Nature,2010,464(7286):194-198.[3] WengH,DaiX,FangZ.Topologicalsemimetalspredictedfromfirst-principlescalculations.JournalofPhysics:CondensedMatter,2016,28(30):303001.[4] WengH,LiangY,XuQ,etal.Topologicalnode-linesemimetalinthree-dimensionalgraphenenetworks.PhysicalReviewB,2015,92(4).[5] YanB,FelserC.TopologicalMaterials:WeylSemimetals.AnnualReviewofCondensedMatterPhysics,2017,8(1):337-354.[6] KlitzingKV,DordaG,PepperM.NewMethodforHigh-AccuracyDeterminationoftheFine-StructureConstantBasedonQuantizedHallResistance.PhysicalReviewLetters,1980,45(6):494-497.[7] ThoulessDJ,KohmotoM,NightingaleMP,etal.QuantizedHallConductanceinaTwo-DimensionalPeriodicPotential.PhysicalReviewLetters,1982,49(6):405-408.[8] BansilA,LinH,DasT.Colloquium:Topologicalbandtheory.ReviewsofModernPhysics,2016,88(2):021004.[9] KaneCL,MeleEJ.QuantumSpinHallEffectinGraphene.PhysicalReviewLetters,2005,95(22):226801.[10] BernevigBA,HughesTL,ZhangS-C.QuantumSpinHallEffectandTopologicalPhaseTransitioninHgTeQuantumWells.Science,2006,314(5806):1757.[11] ZhangH,LiuC-X,QiX-L,etal.TopologicalinsulatorsinBi2Se3,Bi2Te3andSb2Te3withasingleDiracconeonthesurface.NaturePhysics,2009,5(6):438-442.[12] ChenYL,AnalytisJG,ChuJH,etal.ExperimentalRealizationofaThree-DimensionalTopologicalInsulator,Bi2Te3.Science,2009,325(5937):178.[13] ZhangY,HeK,ChangC-Z,etal.Crossoverofthethree-dimensionaltopologicalinsulatorBi2Se3tothetwo-dimensionallimit.NaturePhysics,2010,6(8):584-588.[14] ChangC-Z,ZhangJ,LiuM,etal.ThinFilmsofMagneticallyDopedTopologicalInsulatorwithCarrier-IndependentLong-RangeFerromagneticOrder.AdvancedMaterials,2013,25(7):1065-1070.[15] ZhangJ,ChangC-Z,TangP,etal.Topology-DrivenMagneticQuantumPhaseTransitioninTopologicalInsulators.Science,2013,339(6127):1582.[16] ChangC-Z,TangP,WangY-L,etal.Chemical-Potential-DependentGapOpeningattheDiracSurfaceStatesofBi2Se3InducedbyAggregatedSubstitutionalCrAtoms.PhysicalReviewLetters,2014,112(5):056801.[17] VaeziA,LiangY,NgaiDH,etal.TopologicalEdgeStatesataTiltBoundaryinGatedMultilayerGraphene.PhysicalReviewX,2013,3(2):021018.[18] WanX,SavrasovSY.Turningabandinsulatorintoanexoticsuperconductor.NatureCommunications,2014,5(1):4144.[19] WangE,DingH,FedorovAV,etal.FullygappedtopologicalsurfacestatesinBi2Se3filmsinducedbyad-wavehigh-temperatur