Floquet engineering in quantum materials

Bao Chang-Hua; Fan Ben-Shu; Tang Pei-Zhe; Duan Wen-Hui; Zhou Shu-Yun

doi:10.7498/aps.72.20231423

Abstract

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.

Keywords:

Authors and contacts

1.
Department of Physics, Tsinghua University, Beijing 100084, China
2.
State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
3.
School of Materials Science and Engineering, Beihang University, Beijing 100191, China
4.
Max Planck Institute for the Structure and Dynamics of Matter, Hamburg 22761, Germany
5.
Institute for Advanced Study, Tsinghua University, Beijing 100084, China

Corresponding author: Zhou Shu-Yun, syzhou@mail.tsinghua.edu.cn

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References

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Cited By

图 1 (a) 实空间周期性导致电子能带在动量空间的复制示意图; (b)时间周期性导致电子在能量维度的复制示意图; (c)弗洛凯调控示意图^[7]

Figure 1. (a) Spatially periodic potential and Bloch bands in the k-space; (b) time-periodic potential and Floquet bands in energy; (c) schematics for Floquet engineering^[7].

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

map

[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. 75 473 Google 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 1077 Google Scholar
[7]	Bao C H, Tang P Z, Sun D, Zhou S Y 2021 Nat. Rev. Phys. 4 33 Google Scholar
[8]	Oka T, Aoki H 2009 Phys. Rev. B 79 081406(R Google Scholar
[9]	Kitagawa T, Oka T, Brataas A, Fu L, Demler E 2011 Phys. Rev. B 84 235108 Google Scholar
[10]	Lindner N H, Refael G, Galitski V 2011 Nat. Phys. 7 490 Google Scholar
[11]	Ashcroft N W, Mermin N D 1976 Solid State Physics (Philadelphia: Saunders College
[12]	Sambe H 1973 Phys. Rev. A 7 2203 Google Scholar
[13]	Haldane F D M 1988 Phys. Rev. Lett. 61 2015 Google Scholar
[14]	Oka T, Kitamura S 2019 Annu. Rev. Condens. Matter Phys. 10 387 Google Scholar
[15]	Rudner M S, Lindner N H 2020 Nat. Rev. Phys. 2 229 Google Scholar
[16]	de la Torre A, Kennes D M, Claassen M, Gerber S, McIver J W, Sentef M A 2021 Rev. Mod. Phys. 93 041002 Google Scholar
[17]	Eckardt A 2017 Rev. Mod. Phys. 89 011004 Google Scholar
[18]	Cooper N R, Dalibard J, Spielman I B 2019 Rev. Mod. Phys. 91 015005 Google 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 015006 Google Scholar
[20]	Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237 Google Scholar
[21]	Görg F, Messer M, Sandholzer K, Jotzu G, Desbuquois R, Esslinger T 2018 Nature 553 481 Google Scholar
[22]	Rechtsman M C, Zeuner J M, Plotnik Y, et al. 2013 Nature 496 196 Google Scholar
[23]	Maczewsky L J, Zeuner J M, Nolte S, Szameit A 2017 Nat. Commun. 8 13756 Google Scholar
[24]	Mukherjee S, Spracklen A, Valiente M, Andersson E, Öhberg P, Goldman N, Thomson R R 2017 Nat. Commun. 8 13918 Google Scholar
[25]	Ezawa M 2013 Phys. Rev. Lett. 110 026603 Google Scholar
[26]	Claassen M, Jia C, Moritz B, Devereaux T P 2016 Nat. Commun. 7 13074 Google Scholar
[27]	Wang R, Wang B G, Shen R, Sheng L, Xing D Y 2014 EPL 105 17004 Google Scholar
[28]	Chan C K, Lee P A, Burch K S, Han J H, Ran Y 2016 Phys. Rev. Lett. 116 026805 Google Scholar
[29]	Hübener H, Sentef M A, De Giovannini U, Kemper A F, Rubio A 2017 Nat. Commun. 8 13940 Google Scholar
[30]	Yan Z B, Wang Z 2016 Phys. Rev. Lett. 117 087402 Google Scholar
[31]	Ezawa M 2017 Phys. Rev. B 96 041205(R Google Scholar
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[35]	Zhou L W, Gong J B 2018 Phys. Rev. B 98 205417 Google Scholar
[36]	Wu H, An J H 2022 Phys. Rev. B 105 L121113 Google Scholar
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[38]	Rodriguez-Vega M, Vogl M, Fiete G A 2021 Ann. Phys. 435 168434 Google Scholar
[39]	Li Y, Fertig H A, Seradjeh B 2020 Phys. Rev. Res. 2 043275 Google Scholar
[40]	Vogl M, Rodriguez-Vega M, Fiete G A 2020 Phys. Rev. B 101 235411 Google Scholar
[41]	Vogl M, Rodriguez-Vega M, Fiete G A 2020 Phys. Rev. B 101 241408(R Google Scholar
[42]	Kim H, Dehghani H, Aoki H, Martin I, Hafezi M 2020 Phys. Rev. Res. 2 043004 Google Scholar
[43]	Shin D, Hubener H, De Giovannini U, Jin H, Rubio A, Park N 2018 Nat. Commun. 9 638 Google Scholar
[44]	Mentink J H, Balzer K, Eckstein M 2015 Nat. Commun. 6 6708 Google Scholar
[45]	Kitamura S, Oka T, Aoki H 2017 Phys. Rev. B 96 014406 Google Scholar
[46]	Claassen M, Jiang H C, Moritz B, Devereaux T P 2017 Nat. Commun. 8 1192 Google Scholar
[47]	Katz O, Refael G, Lindner N H 2020 Phys. Rev. B 102 155123 Google Scholar
[48]	Morimoto T, Kitamura S, Nagaosa N 2023 J. Phys. Soc. Jpn. 92 072001 Google Scholar
[49]	Sie E J, McIver J W, Lee Y H, Fu L, Kong J, Gedik N 2015 Nat. Mater. 14 290 Google 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 1205 Google Scholar
[51]	Sie E J, Lui C H, Lee Y H, Fu L, Kong J, Gedik N 2017 Science 355 1066 Google Scholar
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[53]	McIver J W, Schulte B, Stein F U, Matsuyama T, Jotzu G, Meier G, Cavalleri A 2020 Nat. Phys. 16 38 Google 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 603 421 Google Scholar
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[56]	Sobota J A, He Y, Shen Z X 2021 Rev. Mod. Phys. 93 025006 Google Scholar
[57]	Zhang H, Pincelli T, Jozwiak C, Kondo T, Ernstorfer R, Sato T, Zhou S 2022 Nat. Rev. Methods Primers 2 1 Google Scholar
[58]	Wang Y H, Steinberg H, Jarillo-Herrero P, Gedik N 2013 Science 342 453 Google Scholar
[59]	Mahmood F, Chan C-K, Alpichshev Z, Gardner D, Lee Y, Lee P A, Gedik N 2016 Nat. Phys. 12 306 Google Scholar
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[61]	Zhou S H, Bao C H, Fan B S, et al. 2023 Nature 614 75 Google 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 5028 Google 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. 19 277 Google 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 116401 Google Scholar
[65]	Bao C H, Zhong H Y, Zhou S H, Feng R, Wang Y H, Zhou S Y 2022 Rev. Sci. Instrum. 93 013902 Google Scholar
[66]	Bao C H, Li Q, Xu S, et al. 2022 Nano Lett. 22 1138 Google 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 214302 Google Scholar
[68]	Sato S A, Tang P Z, Sentef M A, Giovannini U D, Hübener H, Rubio A 2019 New J. Phys. 21 093005 Google 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 043408 Google Scholar

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