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Floquet engineering based on the strong light-matter interaction is expected to drive quantum materials into nonequilibrium states on an ultrafast timescale, thereby engineering their electronic structure and physical properties, and achieving novel physical effects which have no counterpart in equilibrium states. In recent years, Floquet engineering has attracted a lot of research interest, and there have been numerous rich theoretical predictions. In addition, important experimental research progress has also been made in several representative materials such as topological insulators, graphene, and black phosphorus. Herein, we briefly introduce the important theoretical and experimental progress in this field, and prospect the research future, experimental challenges, and development directions.
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Keywords:
- Floquet engineering /
- light-matter interaction /
- nonequilibrium states /
- topological materials /
- two-dimensional materials
[1] Warren B E 1990 X-Ray Diffraction(Courier Corporation
[2] Long D A 1977 Raman Spectroscopy (New York and London: McGraw-Hill
[3] Henderson B, Imbusch G F 2006 Optical Spectroscopy of Inorganic Solids (Cambridge: Oxford University Press
[4] Damascelli A, Hussain Z, Shen Z X 2003 Rev. Mod. Phys. 75 473Google Scholar
[5] Hüfner S 2013 Photoelectron Spectroscopy: Principles and Applications (Springer Science & Business Media
[6] Basov D N, Averitt R D, Hsieh D 2017 Nat. Mater. 16 1077Google Scholar
[7] Bao C H, Tang P Z, Sun D, Zhou S Y 2021 Nat. Rev. Phys. 4 33Google Scholar
[8] Oka T, Aoki H 2009 Phys. Rev. B 79 081406(RGoogle Scholar
[9] Kitagawa T, Oka T, Brataas A, Fu L, Demler E 2011 Phys. Rev. B 84 235108Google Scholar
[10] Lindner N H, Refael G, Galitski V 2011 Nat. Phys. 7 490Google Scholar
[11] Ashcroft N W, Mermin N D 1976 Solid State Physics (Philadelphia: Saunders College
[12] Sambe H 1973 Phys. Rev. A 7 2203Google Scholar
[13] Haldane F D M 1988 Phys. Rev. Lett. 61 2015Google Scholar
[14] Oka T, Kitamura S 2019 Annu. Rev. Condens. Matter Phys. 10 387Google Scholar
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[16] de la Torre A, Kennes D M, Claassen M, Gerber S, McIver J W, Sentef M A 2021 Rev. Mod. Phys. 93 041002Google Scholar
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[18] Cooper N R, Dalibard J, Spielman I B 2019 Rev. Mod. Phys. 91 015005Google Scholar
[19] Ozawa T, Price H M, Amo A, Goldman N, Hafezi M, Lu L, Rechtsman M C, Schuster D, Simon J, Zilberberg O, Carusotto I 2019 Rev. Mod. Phys. 91 015006Google Scholar
[20] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237Google Scholar
[21] Görg F, Messer M, Sandholzer K, Jotzu G, Desbuquois R, Esslinger T 2018 Nature 553 481Google Scholar
[22] Rechtsman M C, Zeuner J M, Plotnik Y, et al. 2013 Nature 496 196Google Scholar
[23] Maczewsky L J, Zeuner J M, Nolte S, Szameit A 2017 Nat. Commun. 8 13756Google Scholar
[24] Mukherjee S, Spracklen A, Valiente M, Andersson E, Öhberg P, Goldman N, Thomson R R 2017 Nat. Commun. 8 13918Google Scholar
[25] Ezawa M 2013 Phys. Rev. Lett. 110 026603Google Scholar
[26] Claassen M, Jia C, Moritz B, Devereaux T P 2016 Nat. Commun. 7 13074Google Scholar
[27] Wang R, Wang B G, Shen R, Sheng L, Xing D Y 2014 EPL 105 17004Google Scholar
[28] Chan C K, Lee P A, Burch K S, Han J H, Ran Y 2016 Phys. Rev. Lett. 116 026805Google Scholar
[29] Hübener H, Sentef M A, De Giovannini U, Kemper A F, Rubio A 2017 Nat. Commun. 8 13940Google Scholar
[30] Yan Z B, Wang Z 2016 Phys. Rev. Lett. 117 087402Google Scholar
[31] Ezawa M 2017 Phys. Rev. B 96 041205(RGoogle Scholar
[32] Deng T W, Zheng B B, Zhan F Y, Fan J, Wu X Z, Wang R 2020 Phys. Rev. B 102 201105Google Scholar
[33] Liu H, Sun J T, Cheng C, Liu F, Meng S 2018 Phys. Rev. Lett. 120 237403Google Scholar
[34] Chan C K, Oh Y T, Han J H, Lee P A 2016 Phys. Rev. B 94 121106(RGoogle Scholar
[35] Zhou L W, Gong J B 2018 Phys. Rev. B 98 205417Google Scholar
[36] Wu H, An J H 2022 Phys. Rev. B 105 L121113Google Scholar
[37] Topp G E, Jotzu G, McIver J W, Xian L, Rubio A, Sentef M A 2019 Phys. Rev. Res. 1 023031Google Scholar
[38] Rodriguez-Vega M, Vogl M, Fiete G A 2021 Ann. Phys. 435 168434Google Scholar
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[40] Vogl M, Rodriguez-Vega M, Fiete G A 2020 Phys. Rev. B 101 235411Google Scholar
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[42] Kim H, Dehghani H, Aoki H, Martin I, Hafezi M 2020 Phys. Rev. Res. 2 043004Google Scholar
[43] Shin D, Hubener H, De Giovannini U, Jin H, Rubio A, Park N 2018 Nat. Commun. 9 638Google Scholar
[44] Mentink J H, Balzer K, Eckstein M 2015 Nat. Commun. 6 6708Google Scholar
[45] Kitamura S, Oka T, Aoki H 2017 Phys. Rev. B 96 014406Google Scholar
[46] Claassen M, Jiang H C, Moritz B, Devereaux T P 2017 Nat. Commun. 8 1192Google Scholar
[47] Katz O, Refael G, Lindner N H 2020 Phys. Rev. B 102 155123Google Scholar
[48] Morimoto T, Kitamura S, Nagaosa N 2023 J. Phys. Soc. Jpn. 92 072001Google Scholar
[49] Sie E J, McIver J W, Lee Y H, Fu L, Kong J, Gedik N 2015 Nat. Mater. 14 290Google Scholar
[50] Kim J, Hong X, Jin C, Shi S F, Chang C Y, Chiu M H, Li L J, Wang F 2014 Science 346 1205Google Scholar
[51] Sie E J, Lui C H, Lee Y H, Fu L, Kong J, Gedik N 2017 Science 355 1066Google Scholar
[52] Shan J Y, Ye M, Chu H, Lee S, Park J G, Balents L, Hsieh D 2021 Nature 600 235Google Scholar
[53] McIver J W, Schulte B, Stein F U, Matsuyama T, Jotzu G, Meier G, Cavalleri A 2020 Nat. Phys. 16 38Google Scholar
[54] Park S, Lee W, Jang S, Choi Y B, Park J, Jung W, Watanabe K, Taniguchi T, Cho G Y, Lee G H 2022 Nature 603 421Google Scholar
[55] Smallwood C L, Kaindl R A, Lanzara A 2016 EPL 115 27001Google Scholar
[56] Sobota J A, He Y, Shen Z X 2021 Rev. Mod. Phys. 93 025006Google Scholar
[57] Zhang H, Pincelli T, Jozwiak C, Kondo T, Ernstorfer R, Sato T, Zhou S 2022 Nat. Rev. Methods Primers 2 1Google Scholar
[58] Wang Y H, Steinberg H, Jarillo-Herrero P, Gedik N 2013 Science 342 453Google Scholar
[59] Mahmood F, Chan C-K, Alpichshev Z, Gardner D, Lee Y, Lee P A, Gedik N 2016 Nat. Phys. 12 306Google Scholar
[60] Ito S, Schüler M, Meierhofer M, et al. 2023 Nature 616 696Google Scholar
[61] Zhou S H, Bao C H, Fan B S, et al. 2023 Nature 614 75Google Scholar
[62] Aeschlimann S, Sato S A, Krause R, Chávez-Cervantes M, De Giovannini U, Hübener H, Forti S, Coletti C, Hanff K, Rossnagel K, Rubio A, Gierz I 2021 Nano Lett. 21 5028Google Scholar
[63] Jung S W, Ryu S H, Shin W J, Sohn Y, Huh M, Koch R J, Jozwiak C, Rotenberg E, Bostwick A, Kim K S 2020 Nat. Mater. 19 277Google Scholar
[64] Zhou S H, Bao C H, Fan B S, Wang F, Zhong H Y, Zhang H Y, Tang P Z, Duan W H, Zhou S Y 2023 Phys. Rev. Lett. 131 116401Google Scholar
[65] Bao C H, Zhong H Y, Zhou S H, Feng R, Wang Y H, Zhou S Y 2022 Rev. Sci. Instrum. 93 013902Google Scholar
[66] Bao C H, Li Q, Xu S, et al. 2022 Nano Lett. 22 1138Google Scholar
[67] Sato S A, McIver J W, Nuske M, Tang P Z, Jotzu G, Schulte B, Hübener H, De Giovannini U, Mathey L, Sentef M A, Cavalleri A, Rubio A 2019 Phys. Rev. B 99 214302Google Scholar
[68] Sato S A, Tang P Z, Sentef M A, Giovannini U D, Hübener H, Rubio A 2019 New J. Phys. 21 093005Google Scholar
[69] Nuske M, Broers L, Schulte B, Jotzu G, Sato S A, Cavalleri A, Rubio A, McIver J W, Mathey L 2020 Phys. Rev. Res. 2 043408Google Scholar
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图 2 (a)弗洛凯调控诱导的拓扑相变[7]; (b)在周期光场驱动前后的转角石墨烯平带电子结构[47]; (c)交换作用强度变化随时间的演化曲线[44]; (d)弗洛凯调控调节材料磁性的示意图[48]
Fig. 2. (a) Floquet engineering induced topological phase transition[7]; (b) flat band of twisted graphene before and after light driving[47]; (c) the evolution of exchange strength with time[44]; (d) a schematic for manipulating magnetic properties of materials by Floquet engineering[48].
图 3 (a)单层WS2中观测到的能谷选择的光学斯塔克效应[49]; (b) MnPS3中观测到的弗洛凯调控对于光学非线性系数的调控[52]; (c)石墨烯中观测到光诱导的反常霍尔效应[53]; (d)石墨烯-铝约瑟夫森结中在微波激发下的复制隧穿谱[54]
Fig. 3. (a) Observation of valley selective optical stark effect in monolayer WS2[49]; (b) manipulation of optical nonlinear coefficients in MnPS3 by Floquet engineering[52]; (c) observation of light-induced anomalous Hall effect in graphene[53]; (d) replica tunneling spectrum under the excitation of microwaves in graphene-aluminum Josephson junction[54].
图 4 (a)拓扑绝缘体Bi2Se3的超快电子能谱, 实现弗洛凯能带调控[58,59]; (b)拓扑绝缘体Bi2Te3的亚周期分辨的超快电子能谱和弗洛凯边带的形成过程[60]; (c)半导体黑磷的超快电子能谱, 实现弗洛凯能带调控[61]
Fig. 4. (a) TrARPES spectra of Floquet engineering in topological insulator Bi2Se3[58,59]; (b) sub-cycle resolved TrARPES spectra of topological insulator Bi2Te3 to show the formation of Floquet sidebands[60]; (c) TrARPES spectra of Floquet engineering in a semiconductor black phosphorus[61].
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[1] Warren B E 1990 X-Ray Diffraction(Courier Corporation
[2] Long D A 1977 Raman Spectroscopy (New York and London: McGraw-Hill
[3] Henderson B, Imbusch G F 2006 Optical Spectroscopy of Inorganic Solids (Cambridge: Oxford University Press
[4] Damascelli A, Hussain Z, Shen Z X 2003 Rev. Mod. Phys. 75 473Google Scholar
[5] Hüfner S 2013 Photoelectron Spectroscopy: Principles and Applications (Springer Science & Business Media
[6] Basov D N, Averitt R D, Hsieh D 2017 Nat. Mater. 16 1077Google Scholar
[7] Bao C H, Tang P Z, Sun D, Zhou S Y 2021 Nat. Rev. Phys. 4 33Google Scholar
[8] Oka T, Aoki H 2009 Phys. Rev. B 79 081406(RGoogle Scholar
[9] Kitagawa T, Oka T, Brataas A, Fu L, Demler E 2011 Phys. Rev. B 84 235108Google Scholar
[10] Lindner N H, Refael G, Galitski V 2011 Nat. Phys. 7 490Google Scholar
[11] Ashcroft N W, Mermin N D 1976 Solid State Physics (Philadelphia: Saunders College
[12] Sambe H 1973 Phys. Rev. A 7 2203Google Scholar
[13] Haldane F D M 1988 Phys. Rev. Lett. 61 2015Google Scholar
[14] Oka T, Kitamura S 2019 Annu. Rev. Condens. Matter Phys. 10 387Google Scholar
[15] Rudner M S, Lindner N H 2020 Nat. Rev. Phys. 2 229Google Scholar
[16] de la Torre A, Kennes D M, Claassen M, Gerber S, McIver J W, Sentef M A 2021 Rev. Mod. Phys. 93 041002Google Scholar
[17] Eckardt A 2017 Rev. Mod. Phys. 89 011004Google Scholar
[18] Cooper N R, Dalibard J, Spielman I B 2019 Rev. Mod. Phys. 91 015005Google Scholar
[19] Ozawa T, Price H M, Amo A, Goldman N, Hafezi M, Lu L, Rechtsman M C, Schuster D, Simon J, Zilberberg O, Carusotto I 2019 Rev. Mod. Phys. 91 015006Google Scholar
[20] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237Google Scholar
[21] Görg F, Messer M, Sandholzer K, Jotzu G, Desbuquois R, Esslinger T 2018 Nature 553 481Google Scholar
[22] Rechtsman M C, Zeuner J M, Plotnik Y, et al. 2013 Nature 496 196Google Scholar
[23] Maczewsky L J, Zeuner J M, Nolte S, Szameit A 2017 Nat. Commun. 8 13756Google Scholar
[24] Mukherjee S, Spracklen A, Valiente M, Andersson E, Öhberg P, Goldman N, Thomson R R 2017 Nat. Commun. 8 13918Google Scholar
[25] Ezawa M 2013 Phys. Rev. Lett. 110 026603Google Scholar
[26] Claassen M, Jia C, Moritz B, Devereaux T P 2016 Nat. Commun. 7 13074Google Scholar
[27] Wang R, Wang B G, Shen R, Sheng L, Xing D Y 2014 EPL 105 17004Google Scholar
[28] Chan C K, Lee P A, Burch K S, Han J H, Ran Y 2016 Phys. Rev. Lett. 116 026805Google Scholar
[29] Hübener H, Sentef M A, De Giovannini U, Kemper A F, Rubio A 2017 Nat. Commun. 8 13940Google Scholar
[30] Yan Z B, Wang Z 2016 Phys. Rev. Lett. 117 087402Google Scholar
[31] Ezawa M 2017 Phys. Rev. B 96 041205(RGoogle Scholar
[32] Deng T W, Zheng B B, Zhan F Y, Fan J, Wu X Z, Wang R 2020 Phys. Rev. B 102 201105Google Scholar
[33] Liu H, Sun J T, Cheng C, Liu F, Meng S 2018 Phys. Rev. Lett. 120 237403Google Scholar
[34] Chan C K, Oh Y T, Han J H, Lee P A 2016 Phys. Rev. B 94 121106(RGoogle Scholar
[35] Zhou L W, Gong J B 2018 Phys. Rev. B 98 205417Google Scholar
[36] Wu H, An J H 2022 Phys. Rev. B 105 L121113Google Scholar
[37] Topp G E, Jotzu G, McIver J W, Xian L, Rubio A, Sentef M A 2019 Phys. Rev. Res. 1 023031Google Scholar
[38] Rodriguez-Vega M, Vogl M, Fiete G A 2021 Ann. Phys. 435 168434Google Scholar
[39] Li Y, Fertig H A, Seradjeh B 2020 Phys. Rev. Res. 2 043275Google Scholar
[40] Vogl M, Rodriguez-Vega M, Fiete G A 2020 Phys. Rev. B 101 235411Google Scholar
[41] Vogl M, Rodriguez-Vega M, Fiete G A 2020 Phys. Rev. B 101 241408(RGoogle Scholar
[42] Kim H, Dehghani H, Aoki H, Martin I, Hafezi M 2020 Phys. Rev. Res. 2 043004Google Scholar
[43] Shin D, Hubener H, De Giovannini U, Jin H, Rubio A, Park N 2018 Nat. Commun. 9 638Google Scholar
[44] Mentink J H, Balzer K, Eckstein M 2015 Nat. Commun. 6 6708Google Scholar
[45] Kitamura S, Oka T, Aoki H 2017 Phys. Rev. B 96 014406Google Scholar
[46] Claassen M, Jiang H C, Moritz B, Devereaux T P 2017 Nat. Commun. 8 1192Google Scholar
[47] Katz O, Refael G, Lindner N H 2020 Phys. Rev. B 102 155123Google Scholar
[48] Morimoto T, Kitamura S, Nagaosa N 2023 J. Phys. Soc. Jpn. 92 072001Google Scholar
[49] Sie E J, McIver J W, Lee Y H, Fu L, Kong J, Gedik N 2015 Nat. Mater. 14 290Google Scholar
[50] Kim J, Hong X, Jin C, Shi S F, Chang C Y, Chiu M H, Li L J, Wang F 2014 Science 346 1205Google Scholar
[51] Sie E J, Lui C H, Lee Y H, Fu L, Kong J, Gedik N 2017 Science 355 1066Google Scholar
[52] Shan J Y, Ye M, Chu H, Lee S, Park J G, Balents L, Hsieh D 2021 Nature 600 235Google Scholar
[53] McIver J W, Schulte B, Stein F U, Matsuyama T, Jotzu G, Meier G, Cavalleri A 2020 Nat. Phys. 16 38Google Scholar
[54] Park S, Lee W, Jang S, Choi Y B, Park J, Jung W, Watanabe K, Taniguchi T, Cho G Y, Lee G H 2022 Nature 603 421Google Scholar
[55] Smallwood C L, Kaindl R A, Lanzara A 2016 EPL 115 27001Google Scholar
[56] Sobota J A, He Y, Shen Z X 2021 Rev. Mod. Phys. 93 025006Google Scholar
[57] Zhang H, Pincelli T, Jozwiak C, Kondo T, Ernstorfer R, Sato T, Zhou S 2022 Nat. Rev. Methods Primers 2 1Google Scholar
[58] Wang Y H, Steinberg H, Jarillo-Herrero P, Gedik N 2013 Science 342 453Google Scholar
[59] Mahmood F, Chan C-K, Alpichshev Z, Gardner D, Lee Y, Lee P A, Gedik N 2016 Nat. Phys. 12 306Google Scholar
[60] Ito S, Schüler M, Meierhofer M, et al. 2023 Nature 616 696Google Scholar
[61] Zhou S H, Bao C H, Fan B S, et al. 2023 Nature 614 75Google Scholar
[62] Aeschlimann S, Sato S A, Krause R, Chávez-Cervantes M, De Giovannini U, Hübener H, Forti S, Coletti C, Hanff K, Rossnagel K, Rubio A, Gierz I 2021 Nano Lett. 21 5028Google Scholar
[63] Jung S W, Ryu S H, Shin W J, Sohn Y, Huh M, Koch R J, Jozwiak C, Rotenberg E, Bostwick A, Kim K S 2020 Nat. Mater. 19 277Google Scholar
[64] Zhou S H, Bao C H, Fan B S, Wang F, Zhong H Y, Zhang H Y, Tang P Z, Duan W H, Zhou S Y 2023 Phys. Rev. Lett. 131 116401Google Scholar
[65] Bao C H, Zhong H Y, Zhou S H, Feng R, Wang Y H, Zhou S Y 2022 Rev. Sci. Instrum. 93 013902Google Scholar
[66] Bao C H, Li Q, Xu S, et al. 2022 Nano Lett. 22 1138Google Scholar
[67] Sato S A, McIver J W, Nuske M, Tang P Z, Jotzu G, Schulte B, Hübener H, De Giovannini U, Mathey L, Sentef M A, Cavalleri A, Rubio A 2019 Phys. Rev. B 99 214302Google Scholar
[68] Sato S A, Tang P Z, Sentef M A, Giovannini U D, Hübener H, Rubio A 2019 New J. Phys. 21 093005Google Scholar
[69] Nuske M, Broers L, Schulte B, Jotzu G, Sato S A, Cavalleri A, Rubio A, McIver J W, Mathey L 2020 Phys. Rev. Res. 2 043408Google Scholar
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