查看“︁拓扑绝缘体”︁的源代码

{{expand|time=2015-05-02}}
[[File:Topological insulator band structure.svg|thumb|拓扑绝缘体理想的能带结构。其费米能级位于块材的带隙，该带隙被拓扑保护的表面量子态所填满。]] 

'''拓扑绝缘体'''是一种内部绝缘，界面允许电荷移动的材料。

在拓扑绝缘体的内部，电子[[能带结构]]和常规的[[絕緣體|绝缘体]]相似，其[[费米能|费米能级]]位于[[导带]]和[[价带]]之间。在拓扑绝缘体的边界或是表面存在一些特殊的量子态，这些量子态位于块体能带结构的带隙之中，从而允许导电<ref name="Kane Mele 2005 p. ">{{cite journal | last=Kane | first=C. L. | last2=Mele | first2=E. J. | title=Quantum Spin Hall Effect in Graphene | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=95 | issue=22 | pages = 226801  | date=2005-11-23 | doi=10.1103/physrevlett.95.226801 | page=}}</ref>。拓扑绝缘体的块体可以用类似[[拓扑学]]中的[[亏格]]的整数表征，是[[拓扑序]]的一个特例<ref>{{Cite journal
| last = Kane | first = C. L.  | coauthors = Mele, E. J.  | date = 30 September 2005 
| title = Z<sub>2</sub> Topological Order and the Quantum Spin Hall Effect
| journal = [[Physical Review Letters]] | volume = 95 | issue = 14 | pages = 146802
| doi = 10.1103/PhysRevLett.95.146802
| url = http://link.aps.org/doi/10.1103/PhysRevLett.95.146802
}}</ref>。利用体边对应，可以预言材料在开边界条件下拓扑边缘态的性质。

==预言和发现==
受拓扑保护的边缘态（一维）在[[碲化汞]]/[[碲化镉]][[量子阱]]中被预言于2006年<ref>{{Cite journal | doi = 10.1126/science.1133734 | pmid = 17170299 | volume = 314 | issue = 5806 | pages = 1757–1761 | last = Bernevig | first = B. Andrei | coauthors = Taylor L. Hughes, Shou-Cheng Zhang | title = Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells | journal = Science | accessdate = 2010-03-25 | date = 2006-12-15 | url = http://www.sciencemag.org/cgi/content/abstract/314/5806/1757 | archive-date = 2008-06-17 | archive-url = https://web.archive.org/web/20080617152948/http://www.sciencemag.org/cgi/content/abstract/314/5806/1757 | dead-url = no }}</ref>，随后于2007年由实验观测证实<ref>{{Cite journal | doi = 10.1126/science.1148047 | pmid = 17885096 | volume = 318 | issue = 5851 | pages = 766–770 | last = Konig | first = Markus | coauthors = Steffen Wiedmann, Christoph Brune, Andreas Roth, Hartmut Buhmann, Laurens W. Molenkamp, Xiao-Liang Qi, Shou-Cheng Zhang | title = Quantum Spin Hall Insulator State in HgTe Quantum Wells | journal = Science | accessdate = 2010-03-25 | date = 2007-11-02 | url = http://www.sciencemag.org/cgi/content/abstract/318/5851/766 | archive-date = 2010-05-11 | archive-url = https://web.archive.org/web/20100511220233/http://www.sciencemag.org/cgi/content/abstract/318/5851/766 | dead-url = no }}</ref>。很快，拓扑绝缘体又被预言存在于含铋的二元化合物三维固体中<ref>{{Cite journal
| doi = 10.1103/PhysRevB.76.045302 | volume = 76 | issue = 4 | pages = 045302 | last = Fu | first = Liang | coauthors = C. L. Kane
| title = Topological insulators with inversion symmetry
| journal = Physical Review B | accessdate = 2010-03-26 | date = 2007-07-02
| url = http://link.aps.org/doi/10.1103/PhysRevB.76.045302
}}</ref><ref>{{Cite journal
| doi = 10.1088/1367-2630/9/9/356 | issn = 1367-2630 | volume = 9 | issue = 9 | pages = 356–356 | last = Shuichi Murakami
|title = Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
| journal = New Journal of Physics | accessdate = 2010-03-26 | date = 2007
| url = http://iopscience.iop.org/1367-2630/9/9/356/
}}</ref>。第一个实验实现的三维拓扑绝缘体是在锑化铋中被观察到<ref>{{Cite journal | doi = 10.1038/nature06843 | last = Hsieh | first = D. | coauthors = D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava & M. Z. Hasan | title = A Topological Dirac insulator in a 3D quantum spin Hall phase | journal = Nature | volume = 452 | issue = 9 | pages = 970–974 | accessdate = 2010 | date = 2008 | url = http://www.nature.com/nature/journal/v452/n7190/full/nature06843.html | pmid = 18432240 | archive-date = 2009-12-23 | archive-url = https://web.archive.org/web/20091223022215/http://www.nature.com/nature/journal/v452/n7190/full/nature06843.html | dead-url = no }}</ref>，随后不同实验组又通过[[角分辨光电子谱]]的方法，在锑，碲化铋，硒化铋，碲化锑中观察到了受拓扑保护的表面量子态<ref>{{Cite journal | last = Hasan | first = M. Z | coauthors = C. L Kane | title = Topological Insulators | journal = 1002.3895 | accessdate = 2010-04-27 | date = 2010-02-20 | url = http://arxiv.org/abs/1002.3895 | archive-date = 2021-03-08 | archive-url = https://web.archive.org/web/20210308200803/https://arxiv.org/abs/1002.3895 | dead-url = no }}</ref>。现在人们相信，在其他一些材料体系中，也存在拓扑绝缘态<ref>{{Cite journal
| doi = 10.1038/nmat2771 | pmid = 20512153 | issn = 1476-1122| volume = 9 | issue = 7 | pages = 546–549
| last = Lin | first = Hsin | coauthors = L. Andrew Wray, Yuqi Xia, Suyang Xu, Shuang Jia, Robert J. Cava, Arun Bansil, M. Zahid Hasan
|title = Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena
| journal = Nat Mater | accessdate = 2010-08-05 | date = 2010-07
| url = http://dx.doi.org.proxy.library.cornell.edu/10.1038/nmat2771
}}</ref>。在这些材料中，由于自然存在的缺陷，费米能级实际上是位于导带或是位于价带，必须通过[[掺杂]]或者通过改变其电势将费米能级调节到能隙之中，以观察拓扑保护的边缘态<ref>{{Cite journal
| doi = 10.1103/PhysRevLett.103.146401 | pmid = 19905585
| journal = Physical Review Letters | volume = 103| issue = 14| pages = 146401 | date = 2009
| last = Hsieh| first = D.| coauthors = Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, M. Z. Hasan
| title = Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi2Te3 and Sb2Te3
| url = http://link.aps.org/doi/10.1103/PhysRevLett.103.146401 | accessdate = 2010-03-25
}}</ref><ref>{{Cite journal
| doi = 10.1209/0295-5075/81/57006| volume = 81| issue = 5| pages = 57006
| last = Noh| first = H.-J.| coauthors = H. Koh, S.-J. Oh, J.-H. Park, H.-D. Kim, J. D. Rameau, T. Valla, T. E. Kidd, P. D. Johnson, Y. Hu and Q. Li 
|title = Spin-orbit interaction effect in the electronic structure of Bi2Te3 observed by angle-resolved photoemission spectroscopy
| journal = EPL Europhysics Letters| accessdate = 2010-04-25| date = 2008
| url = http://iopscience.iop.org/0295-5075/81/5/57006/
}}</ref>。

类似的边缘效应同样出现于[[量子霍尔效应]]之中。以[[量子霍尔效应|整数量子霍尔效应]]为例，在强垂直[[磁场]]下，低温的二维系统体态性质可以被拓扑量子数标记。在数学中，此拓扑量子数被称作陈数（Chern numbers）。二维量子霍尔系统边缘出现手性边缘态，陈数对应手性边缘态的数目和量子化电导<math>\frac{e^2}{h}</math><ref name="pmid10055049">{{cite journal| author=Hatsugai Y| title=Chern number and edge states in the integer quantum Hall effect. | journal=Phys Rev Lett | year= 1993 | volume= 71 | issue= 22 | pages= 3697-3700 | pmid=10055049 | doi=10.1103/PhysRevLett.71.3697 | pmc= | url=https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=10055049  }} </ref>。在拓扑材料的理论研究中，体边对应一直扮演着重要的角色。体边对应指的是，当真实的材料包含的原子数目非常大（数量级为<math>10^{20}</math>或更多），我们可以把此材料近似于热力学极限，并用[[布洛赫定理]]与[[能带理论]]来描述材料体态性质，并根据体态性质来预言材料在开边界条件下受拓扑保护的边缘态的性质<ref name="Bernevig Hughes 2013 p. ">{{cite book | last=Bernevig | first=B. Andrei | last2=Hughes | first2=Taylor L. | title=Topological insulators and topological superconductors | publication-place=Princeton | date=2013 | isbn=978-1-4008-4673-3 | oclc=934514528 | page=}}</ref>。


<!-- 尚有待进一步扩充 拓扑绝缘体基于离散对称性的十种分类 -->

==参考文献==
<references/>

==更多阅读==
*{{Cite journal
| last = Moore | first = Joel | authorlink = | coauthors=  | year = 2010 | month =
|title = The Birth of Topological Insulators
| journal = [[Nature (journal)|Nature]] | volume =  464 | issue =   7286| pages = 194
| doi = 10.1038/nature08916
| url =  | accessdate = | quote =| pmid =20220837  }}
*{{Cite journal
| last = Kane | first = C. L.  | authorlink = | coauthors = Mele, E. J.  | year = 2006 | month =
|title = A New Spin on the Insulating State
| journal = [[Science (journal)|Science]] | volume = 314 | issue = 5806 | pages = 1692
| doi = 10.1126/science.1136573
| url =  | accessdate = | quote =| pmid =17170283  }}
*{{Cite journal
| last = Kane | first = C.L. | authorlink = | coauthors=  | year = 2008 | month =
|title = Topological Insulator: An Insulator with a Twist
| journal = [[Nature (journal)|Nature]] | volume =  4 | issue = 5  | pages = 348
| doi = 10.1038/nphys955
| url =  | accessdate = | quote =| pmid =  }}
*{{Cite journal | last = Witze | first = Alexandra | authorlink =  | coauthors =  | year = 2010 | month =  | title = Topological Insulators: Physics On the Edge | journal = [[Science News]] | volume =  | issue =  | pages =  | doi =  | url = http://www.sciencenews.org/view/feature/id/58909/title/Physics_on_the_edge | accessdate =  | quote =  | archive-date = 2012-09-27 | archive-url = https://web.archive.org/web/20120927010354/http://www.sciencenews.org/view/feature/id/58909/title/Physics_on_the_edge | dead-url = no }}
*{{Cite journal | last = Brumfield | first = Geoff | volume = 466 | issue = 7304 | pages = 310–311 | pmid = 20631773 | title = Topological insulators: Star material : Nature News | journal = Nature | date = 2010 | doi = 10.1038/466310a | url = http://www.nature.com/news/2010/100714/full/466310a.html | accessdate = 2010-08-06 | archive-date = 2017-10-12 | archive-url = https://web.archive.org/web/20171012063410/http://www.nature.com/news/2010/100714/full/466310a.html | dead-url = no }}
*{{Cite journal | last = Murakami | first = Shuichi | authorlink =  | coauthors =  | year = 2010 | month =  | title = Focus on Topological Insulators | journal = [[New Journal of Physics]] | volume =  | issue =  | pages =  | doi =  | url = http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Topological%20Insulators | accessdate =  | quote =  | archive-date = 2011-03-09 | archive-url = https://web.archive.org/web/20110309224557/http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Topological%20Insulators | dead-url = no }}


{{DEFAULTSORT:T}}
[[Category:凝聚体物理学]]
[[Category:半導體]]