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拓扑绝缘体是根据动量空间的拓扑不变量来定义的一类区别于普通绝缘体的新兴拓扑非平庸材料, 其体态和表面态分别表现为绝缘和金属性质, 并且其表面态具有独特的自旋结构(自旋-动量锁定), 因此该类材料在光电器件和自旋电子器件领域有很多潜在的应用. 由于开展这些应用研究首先需要对这类材料中的电荷与自旋动力学有全面的了解, 所以拓扑绝缘体中的非平衡物理性质的研究引起了人们极大兴趣. 本文对这一研究领域所作的研究工作做了一个较全面的描述, 特别是跟时间分辨超快光谱相关的实验工作. 并希望文中的讨论能激发研究者尤其是理论工作者对这一领域进一步的探讨, 同时期待目标研究对象也能扩展到其他拓扑材料体系.Topological insulators (TIs), with unique bulk insulating and two-dimensional surface conducting states, show great promise of future optospintronics and spintronics applications, where a complete knowledge of the charge and spin dynamics is quite essential. Thus, the non-equilibrium properties inside TIs have attracted enormous attention. Here in this paper, we review the latest achievements in this field. The focus will be mainly on the experimental study, covering the ultrafast dynamical properties of charge, phonon, and spin. We hope that this review can stimulate further studies, especially theoretical research concerning the properties of topological insulators out of thermodynamic equilibrium.
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Keywords:
- topological insulator /
- ultrafast pump-probe /
- charge dynamics /
- spin dynamics
[1] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057Google Scholar
[2] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[3] Zhang H J, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438Google Scholar
[4] Hajlaoui M, Papalazarou E, Mauchain J, Lantz G, Moisan N, Boschetto D, Jiang Z, Miotkowski I, Chen Y P, Taleb-Ibrahimi A, Perfetti L, Marsi M 2012 Nano Lett. 12 3532Google Scholar
[5] Xia Y, Wray L, Qian D, Hsieh D, Pal A, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J, Hasan M Z 2008 arXiv 0812 2078
[6] Hsieh D, Xia Y, Qian D, Wray L, Dil J H, Osterwalder J, Patthey L, Checkelsky J G, Ong N P, Fedorov A V, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J, Hasan M Z 2009 Nature 460 1101Google Scholar
[7] Qi J, Chen X, Yu W, Cadden-Zimansky P, Smirnov D, Tolk N H, Miotkowski I, Cao H, Chen Y P, Wu Y, Qiao S, Jiang Z 2010 Appl. Phys. Lett. 97 182102Google Scholar
[8] Wang M C, Qiao S, Jiang Z, Luo S N, Qi J 2016 Phys. Rev. Lett. 116 036601Google Scholar
[9] 王明聪 2017 强关联及拓扑材料的超快光谱研究 (绵阳: 中国工程物理研究院)
Wang M C 2017 Ultrafast optical spectroscopy research of strong correlated and topological materials (Mianyang: China Academy of Engineering Physics)(in Chinese)
[10] Basov D N, Averitt R D, Van Der Marel D, Dressel M, Haule, K 2011 Rev. Mod. Phys. 83 471Google Scholar
[11] Kumar N, Brian A R, Butch N P, Syers P, Kirshenbaum K, Paglione J, Zhao H 2011 Phys. Rev. B 83 235306Google Scholar
[12] Luo L, Yang X, Liu X, Liu Z, Vaswani C, Cheng D, Mootz M, Zhao X, Yao Y, Wang C Z, Ho K M, Perakis I E, Dobrowolska M, Furdyna J K, Wang J 2019 Nat. Commun. 10 607Google Scholar
[13] Sobota J A, Yang S, Analytis J G, Chen Y L, Fisher I R, Kirchmann P S, and Shen Z X 2012 Phys. Rev. Lett. 108 117403Google Scholar
[14] Hsieh D, Mahmood F, McIver J W, Gardner D R, Lee Y S, Gedik N 2011 Phys. Rev. Lett. 107 077401Google Scholar
[15] Zouaghi W, Thomson M D, Rabia K, Hahn R, Blank V, Roskos H G 2013 Eur. J. Phys. 34 S179Google Scholar
[16] Smith P R, Auston D H, Nuss M C 1988 IEEE J. Quantum Electron. 24 255Google Scholar
[17] Averitt R D, Taylor A J 2002 J. Phys.: Condens. Matter 14 R1357
[18] Eschenlohr A, Battiato M, Maldonado P, Pontius N, Kachel T, Holldack K, Mitzner R, Föhlisch A, Oppeneer P M, Stamm C 2013 Nat. Mater. 12 332Google Scholar
[19] Demsar J, Sarrao J L, Taylor A J 2006 J. Phys.: Condens. Matter 18 R281Google Scholar
[20] Kastler A 1957 JOSA 47 460Google Scholar
[21] Fabian J, Sarma S Das 2004 Rev. Mod. Phys. 76 323Google Scholar
[22] Richard P, Sato T, Nakayama K, Takahashi T, Ding H 2011 Reports Prog. Phys. 74 124512Google Scholar
[23] Eich S, Stange A, Carr A V, Urbancic J, Popmintchev T, Wiesenmayer M, Jansen K, Ruffing A, Jakobs S, Rohwer T, Hellmann S, Chen C, Matyba P, Kipp L, Rossnagel K, Bauer M, Murnane M M, Kapteyn H C, Mathias S, Aeschlimann M 2014 J. Electron Spectros. Relat. Phenomena 195 231Google Scholar
[24] Cacho C, Crepaldi A, Battiato M, Braun J, Cilento F, Zacchigna M, Richter M C, Heckmann O, Springate E, Liu Y, Dhesi S S, Berger H, Bugnon Ph, Held K, Grioni M, Ebert H, Hricovini K, Minár J, Parmigiani F 2015 Phys. Rev. Lett. 114 097401Google Scholar
[25] Glinka Y D, Babakiray S, Johnson T A, Holcomb M B, Lederman D 2014 Appl. Phys. Lett. 105 171905Google Scholar
[26] Lai Y P, Chen H J, Wu K H, Liu J M 2014 Appl. Phys. Lett. 105 232110Google Scholar
[27] Weis M, Balin K, Rapacz R, Nowak A, Lejman M, Szade J, Ruello P 2015 Phys. Rev. B 92 014301Google Scholar
[28] Sánchez-Barriga J, Battiato M, Krivenkov M, Golias E, Varykhalov A, Romualdi A, Yashina L V, Minár J, Kornilov O, Ebert H, Held K, Braun J 2017 Phys. Rev. B 95 125405Google Scholar
[29] 李正中 2002 固体理论 (第2版) (北京:高等教育出版社) 第 40 页
Li Z Z 2002 Solid Theory (2nd Ed.) (Beijing: Higher Education Press) p40 (in Chinese)
[30] Cheng L, La-O-Vorakiat C, Tang C S, Nair S K, Xia B, Wang L, Zhu J X, Chia Elbert E M 2014 Appl. Phys. Lett. 104 211906Google Scholar
[31] Pan Z H, Fedorov A V, Gardner D, Lee Y S, Chu S, Valla T 2012 Phys. Rev. Lett. 108 187001Google Scholar
[32] Valdés Aguilar R, Qi J, Brahlek M, Bansal N, Azad A, Bowlan J, Oh S, Taylor A J, Prasankumar R P, Yarotski D A 2015 Appl. Phys. Lett. 106 011901Google Scholar
[33] Wu L, Brahlek M, Aguilar R Valdés, Stier A V, Morris C M, Lubashevsky Y, Bilbro L S, Bansal N, Oh S, Armitage N P 2013 Nat. Phys. 9 410Google Scholar
[34] Valdés Aguilar R, Stier A V, Liu W, Bilbro L S, George D K, Bansal N, Wu L, Cerne J, Markelz A G, Oh S, Armitage N P 2012 Phys. Rev. Lett. 108 087403Google Scholar
[35] Choi Y G, Zhung C J, Park S H, Park J B, Kim J S, Kim S H, Park J H, Lee J S 2018 Phys. Rev. B 97 075307Google Scholar
[36] Wang Y H, Hsieh D, Sie E J, Steinberg H, Gardner D R, Lee Y S, Jarillo-Herrero P, Gedik N 2012 Phys. Rev. Lett. 109 127401Google Scholar
[37] Sobota J A, Yang S L, Leuenberger D, Kemper A F, Analytis J G, Fisher I R, Kirchmann P S, Devereaux T P, Shen Z X 2014 J. Electron Spectros. Relat. Phenomena 195 249Google Scholar
[38] Saha K, Garate I 2014 Phys. Rev. B 90 245418Google Scholar
[39] Shapourian H, Hughes T L, Ryu S 2015 Phys. Rev. B 92 165131Google Scholar
[40] Yazyev O V, Moore J E, Louie S G 2010 Phys. Rev. Lett. 105 266806Google Scholar
[41] Liu C X, Qi X L, Zhang H J, Dai X, Fang Z, Zhang S C 2010 Phys. Rev. B 82 045122Google Scholar
[42] Kamaraju N, Sunil K, Sood A K 2010 Europhys. Lett. 92 47007Google Scholar
[43] Li Y W, Stoica Vladimir A, Endicott L, Wang G Y, Uher C, Clarke R 2010 Appl. Phys. Lett. 97 171908Google Scholar
[44] Wang Y, Xu X, Venkatasubramanian R 2008 Appl. Phys. Lett. 93 113114Google Scholar
[45] Cheng T K, Vidal J, Zeiger H. J, Dresselhaus G, Dresselhaus M S, Ippen E P 1991 Appl. Phys. Lett 59 1923Google Scholar
[46] Richter W, Kohler H, Becker C R 1977 Phys. Status Solidi 84 619Google Scholar
[47] Merlin R 1997 Solid State Commun. 102 207Google Scholar
[48] Sobota J A, Yang S L, Leuenberger D, Kemper A F, Analytis J G, Fisher I R, Kirchmann P S, Devereaux T P, Shen Z X 2014 Phys. Rev. Lett. 113 157401Google Scholar
[49] Xu Y, Khafizov M, Satrapinsky L, Kúš P, Plecenik A, Sobolewski R 2003 Phys. Rev. Lett. 91 197004Google Scholar
[50] Taneda T, Pepe G P, Parlato L, Golubov A A, Sobolewski R 2007 Phys. Rev. B 75 174507Google Scholar
[51] Giraud S, Egger R 2011 Phys. Rev. B 83 245322Google Scholar
[52] Giraud S, Kundu A, Egger R 2012 Phys. Rev. B 85 035441Google Scholar
[53] Iyer V, Chen Y P, Xu X 2018 Phys. Rev. Lett. 121 026807Google Scholar
[54] Hertel R 2005 arXiv:cond-mat 0509 0509060
[55] Sobota J A, Yang S L, Kemper A F, Lee J J, Schmitt F T, Li W, Moore R G, Analytis J G, Fisher I R, Kirchmann P S, Devereaux T P, Shen Z X 2013 Phys. Rev. Lett. 111 136802Google Scholar
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图 6 Bi2Se3薄膜的OPTP信号[32] (a)无光抽运下的Bi2Se3电导; (b)有光抽运下透过Bi2Se3的太赫兹波形; (c), (d)不同样品厚度以及不同功率下太赫兹电场峰值随着抽运延时变化; (e)—(h)为在不同抽运延迟下, 通过用Drude-Lorentz拟合的对于不同厚度样品散射率和等离子频率
Fig. 6. OPTP signals of Bi2Se3 thin film[32]: (a) Conductance of Bi2Se3 without optical pump; (b) transmitted terahertz electric field after sample under optical pump; (c), (d) transient THz peak signal of samples with different thickness and pump power; (e)—(h) scattering rate and plasma frequency obtained from the fitting of conductance of Bi2Se3 by Drude-Lorentz model with different sample thickness and pump delay.
图 8 Bi2Se3的Tr-ARPES信号[13] (a) p型掺杂的Bi2Se3受光激发后不同能带的弛豫过程; (b)用于参考的Bi2Se3的能带; (c)平衡态Bi2Se3的能带结构, 由于掺杂导致费米能级较低, 表面态和体态导带并没有被占据; (d)在刚刚被抽运光激发时, 电子被激发到较高能级处; (e)—(g)则描述了较高能量的电子的弛豫过程
Fig. 8. Experimental Tr-ARPES data[13]: (a) The relaxation process for different bands of p-doped Bi2Se3 excited by light; (b) schematic of the electronic band structures of Bi2Se3 for reference; (c) electronic band structures for Bi2Se3, and the surface states and bulk conduction band are unoccupied due to the Fermi energy sitting inside the bulk valence band; (d) electrons are excited to high energy band after the excitation; (e)–(g) relaxation process of high energy electrons.
图 13 (a) Bi2Se3样品在10 K和80 K时的克尔转角光谱, 红线代表抽运激光为左旋圆偏振光, 蓝色实线代表右旋圆偏振光[8]; (b) Bi2Se3样品在不同光子能量和不同温度下的克尔转角光谱[8]; (c) Bi2Se3实验数据拟合[8]; (d)二次谐波克尔光谱(斜入射抽运光)测得的实验数据[14]; (e)−(h)左右圆偏振光激发后反射率变化随时间变化的实验数据[53]
Fig. 13. (a) Time-resolved Kerr rotation of Bi2Se3 at 10 K and 80 K. Red line indicates that the pump laser is left circularly polarized while the blue one is right circularly polarized[8]. (b) Time-resolved Kerr rotation of Bi2Se3 excited at different photon energies for different temperatures[8]. (c) fittings of the TRKR experimental data for Bi2Se3[8]. (d) Kerr rotation experimental data via second harmonic generation(oblique pump)[14]. (e)−(h) transient reflectivity corresponding to the left and right circularly polarized pump light[53].
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[1] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057Google Scholar
[2] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[3] Zhang H J, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438Google Scholar
[4] Hajlaoui M, Papalazarou E, Mauchain J, Lantz G, Moisan N, Boschetto D, Jiang Z, Miotkowski I, Chen Y P, Taleb-Ibrahimi A, Perfetti L, Marsi M 2012 Nano Lett. 12 3532Google Scholar
[5] Xia Y, Wray L, Qian D, Hsieh D, Pal A, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J, Hasan M Z 2008 arXiv 0812 2078
[6] Hsieh D, Xia Y, Qian D, Wray L, Dil J H, Osterwalder J, Patthey L, Checkelsky J G, Ong N P, Fedorov A V, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J, Hasan M Z 2009 Nature 460 1101Google Scholar
[7] Qi J, Chen X, Yu W, Cadden-Zimansky P, Smirnov D, Tolk N H, Miotkowski I, Cao H, Chen Y P, Wu Y, Qiao S, Jiang Z 2010 Appl. Phys. Lett. 97 182102Google Scholar
[8] Wang M C, Qiao S, Jiang Z, Luo S N, Qi J 2016 Phys. Rev. Lett. 116 036601Google Scholar
[9] 王明聪 2017 强关联及拓扑材料的超快光谱研究 (绵阳: 中国工程物理研究院)
Wang M C 2017 Ultrafast optical spectroscopy research of strong correlated and topological materials (Mianyang: China Academy of Engineering Physics)(in Chinese)
[10] Basov D N, Averitt R D, Van Der Marel D, Dressel M, Haule, K 2011 Rev. Mod. Phys. 83 471Google Scholar
[11] Kumar N, Brian A R, Butch N P, Syers P, Kirshenbaum K, Paglione J, Zhao H 2011 Phys. Rev. B 83 235306Google Scholar
[12] Luo L, Yang X, Liu X, Liu Z, Vaswani C, Cheng D, Mootz M, Zhao X, Yao Y, Wang C Z, Ho K M, Perakis I E, Dobrowolska M, Furdyna J K, Wang J 2019 Nat. Commun. 10 607Google Scholar
[13] Sobota J A, Yang S, Analytis J G, Chen Y L, Fisher I R, Kirchmann P S, and Shen Z X 2012 Phys. Rev. Lett. 108 117403Google Scholar
[14] Hsieh D, Mahmood F, McIver J W, Gardner D R, Lee Y S, Gedik N 2011 Phys. Rev. Lett. 107 077401Google Scholar
[15] Zouaghi W, Thomson M D, Rabia K, Hahn R, Blank V, Roskos H G 2013 Eur. J. Phys. 34 S179Google Scholar
[16] Smith P R, Auston D H, Nuss M C 1988 IEEE J. Quantum Electron. 24 255Google Scholar
[17] Averitt R D, Taylor A J 2002 J. Phys.: Condens. Matter 14 R1357
[18] Eschenlohr A, Battiato M, Maldonado P, Pontius N, Kachel T, Holldack K, Mitzner R, Föhlisch A, Oppeneer P M, Stamm C 2013 Nat. Mater. 12 332Google Scholar
[19] Demsar J, Sarrao J L, Taylor A J 2006 J. Phys.: Condens. Matter 18 R281Google Scholar
[20] Kastler A 1957 JOSA 47 460Google Scholar
[21] Fabian J, Sarma S Das 2004 Rev. Mod. Phys. 76 323Google Scholar
[22] Richard P, Sato T, Nakayama K, Takahashi T, Ding H 2011 Reports Prog. Phys. 74 124512Google Scholar
[23] Eich S, Stange A, Carr A V, Urbancic J, Popmintchev T, Wiesenmayer M, Jansen K, Ruffing A, Jakobs S, Rohwer T, Hellmann S, Chen C, Matyba P, Kipp L, Rossnagel K, Bauer M, Murnane M M, Kapteyn H C, Mathias S, Aeschlimann M 2014 J. Electron Spectros. Relat. Phenomena 195 231Google Scholar
[24] Cacho C, Crepaldi A, Battiato M, Braun J, Cilento F, Zacchigna M, Richter M C, Heckmann O, Springate E, Liu Y, Dhesi S S, Berger H, Bugnon Ph, Held K, Grioni M, Ebert H, Hricovini K, Minár J, Parmigiani F 2015 Phys. Rev. Lett. 114 097401Google Scholar
[25] Glinka Y D, Babakiray S, Johnson T A, Holcomb M B, Lederman D 2014 Appl. Phys. Lett. 105 171905Google Scholar
[26] Lai Y P, Chen H J, Wu K H, Liu J M 2014 Appl. Phys. Lett. 105 232110Google Scholar
[27] Weis M, Balin K, Rapacz R, Nowak A, Lejman M, Szade J, Ruello P 2015 Phys. Rev. B 92 014301Google Scholar
[28] Sánchez-Barriga J, Battiato M, Krivenkov M, Golias E, Varykhalov A, Romualdi A, Yashina L V, Minár J, Kornilov O, Ebert H, Held K, Braun J 2017 Phys. Rev. B 95 125405Google Scholar
[29] 李正中 2002 固体理论 (第2版) (北京:高等教育出版社) 第 40 页
Li Z Z 2002 Solid Theory (2nd Ed.) (Beijing: Higher Education Press) p40 (in Chinese)
[30] Cheng L, La-O-Vorakiat C, Tang C S, Nair S K, Xia B, Wang L, Zhu J X, Chia Elbert E M 2014 Appl. Phys. Lett. 104 211906Google Scholar
[31] Pan Z H, Fedorov A V, Gardner D, Lee Y S, Chu S, Valla T 2012 Phys. Rev. Lett. 108 187001Google Scholar
[32] Valdés Aguilar R, Qi J, Brahlek M, Bansal N, Azad A, Bowlan J, Oh S, Taylor A J, Prasankumar R P, Yarotski D A 2015 Appl. Phys. Lett. 106 011901Google Scholar
[33] Wu L, Brahlek M, Aguilar R Valdés, Stier A V, Morris C M, Lubashevsky Y, Bilbro L S, Bansal N, Oh S, Armitage N P 2013 Nat. Phys. 9 410Google Scholar
[34] Valdés Aguilar R, Stier A V, Liu W, Bilbro L S, George D K, Bansal N, Wu L, Cerne J, Markelz A G, Oh S, Armitage N P 2012 Phys. Rev. Lett. 108 087403Google Scholar
[35] Choi Y G, Zhung C J, Park S H, Park J B, Kim J S, Kim S H, Park J H, Lee J S 2018 Phys. Rev. B 97 075307Google Scholar
[36] Wang Y H, Hsieh D, Sie E J, Steinberg H, Gardner D R, Lee Y S, Jarillo-Herrero P, Gedik N 2012 Phys. Rev. Lett. 109 127401Google Scholar
[37] Sobota J A, Yang S L, Leuenberger D, Kemper A F, Analytis J G, Fisher I R, Kirchmann P S, Devereaux T P, Shen Z X 2014 J. Electron Spectros. Relat. Phenomena 195 249Google Scholar
[38] Saha K, Garate I 2014 Phys. Rev. B 90 245418Google Scholar
[39] Shapourian H, Hughes T L, Ryu S 2015 Phys. Rev. B 92 165131Google Scholar
[40] Yazyev O V, Moore J E, Louie S G 2010 Phys. Rev. Lett. 105 266806Google Scholar
[41] Liu C X, Qi X L, Zhang H J, Dai X, Fang Z, Zhang S C 2010 Phys. Rev. B 82 045122Google Scholar
[42] Kamaraju N, Sunil K, Sood A K 2010 Europhys. Lett. 92 47007Google Scholar
[43] Li Y W, Stoica Vladimir A, Endicott L, Wang G Y, Uher C, Clarke R 2010 Appl. Phys. Lett. 97 171908Google Scholar
[44] Wang Y, Xu X, Venkatasubramanian R 2008 Appl. Phys. Lett. 93 113114Google Scholar
[45] Cheng T K, Vidal J, Zeiger H. J, Dresselhaus G, Dresselhaus M S, Ippen E P 1991 Appl. Phys. Lett 59 1923Google Scholar
[46] Richter W, Kohler H, Becker C R 1977 Phys. Status Solidi 84 619Google Scholar
[47] Merlin R 1997 Solid State Commun. 102 207Google Scholar
[48] Sobota J A, Yang S L, Leuenberger D, Kemper A F, Analytis J G, Fisher I R, Kirchmann P S, Devereaux T P, Shen Z X 2014 Phys. Rev. Lett. 113 157401Google Scholar
[49] Xu Y, Khafizov M, Satrapinsky L, Kúš P, Plecenik A, Sobolewski R 2003 Phys. Rev. Lett. 91 197004Google Scholar
[50] Taneda T, Pepe G P, Parlato L, Golubov A A, Sobolewski R 2007 Phys. Rev. B 75 174507Google Scholar
[51] Giraud S, Egger R 2011 Phys. Rev. B 83 245322Google Scholar
[52] Giraud S, Kundu A, Egger R 2012 Phys. Rev. B 85 035441Google Scholar
[53] Iyer V, Chen Y P, Xu X 2018 Phys. Rev. Lett. 121 026807Google Scholar
[54] Hertel R 2005 arXiv:cond-mat 0509 0509060
[55] Sobota J A, Yang S L, Kemper A F, Lee J J, Schmitt F T, Li W, Moore R G, Analytis J G, Fisher I R, Kirchmann P S, Devereaux T P, Shen Z X 2013 Phys. Rev. Lett. 111 136802Google Scholar
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