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Recently, black phosphorus (BP), an emerging layered two-dimensional (2D) material, has aroused much research interest. Distinguished from most of other 2D materials, BP is always a direct bandgap semiconductor regardless of the thickness, with the bandgap ranging from 0.3 eV (bulk) to 1.7 eV (monolayer), which is just fill the gap in the bandgap between graphene and transition metal dichalcogenides (TMDCs) in this frequency range. Besides, the BP exhibits many intriguing properties, such as high carrier mobility, highly tunable and anisotropic physical properties, which render the BP another star 2D material following graphene and TMDCs. In this review, we mainly focus on the advances in the optical properties of 2D BP, with the content covering the intrinsic optical properties and external perturbation effects on optical properties. Regarding the intrinsic optical properties, we introduce the anisotropic and layer-dependent optical absorption from interband transitions, the layer-dependent exciton binding energy and exciton absorption, visible-to-infrared photoluminescence, and stability of absorption and photoluminescence. As for external perturbation effects on optical properties, we introduce in-plane uniaxial and biaxial strain effects, gate-induced quantum confined Franz-Keldysh effect and Burstein-Moss effect. And finally we give a brief summary and outlook, pointing out some several interesting and important issues of BP, which need further studying urgently such as hyperbolic plasmons, intersubband transitions, optical properties in heterostructures and twist angle moiré superlattice and so on. This review gives an overview of the optical properties of BP and is expected to arouse the interest in further studying the BP.
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Keywords:
- two-dimensional materials /
- black phosphorus /
- optical properties /
- infrared spectrum
[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
Google Scholar
[2] Xu M, Liang T, Shi M, Chen H 2013 Chem. Rev. 113 3766
Google Scholar
[3] Novoselov K S, Mishchenko A, Carvalho A, Castro Neto A H 2016 Science 353 aac9439
Google Scholar
[4] Huang B, Clark G, Navarro-Moratalla E, Klein D R, Cheng R, Seyler K L, Zhong D, Schmidgall E, McGuire M A, Cobden D H, Yao W, Xiao D, Jarillo-Herrero P, Xu X D 2017 Nature 546 270
Google Scholar
[5] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
Google Scholar
[6] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
Google Scholar
[7] Stander N, Huard B, Goldhaber-Gordon D 2009 Phys. Rev. Lett. 102 026807
Google Scholar
[8] Geim A K, Grigorieva I V 2013 Nature 499 419
Google Scholar
[9] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43
Google Scholar
[10] Dean C R, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M, Taniguchi T, Watanabe K, Shepard K L, Hone J, Kim P 2013 Nature 497 598
Google Scholar
[11] Rivera P, Schaibley J R, Jones A M, Ross J S, Wu S, Aivazian G, Klement P, Seyler K, Clark G, Ghimire N J, Yan J, Mandrus D G, Yao W, Xu X 2015 Nat. Commun. 6 6242
Google Scholar
[12] Seyler K L, Rivera P, Yu H, Wilson N P, Ray E L, Mandrus D G, Yan J, Yao W, Xu X 2019 Nature 567 66
Google Scholar
[13] Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80
Google Scholar
[14] Chen G, Jiang L, Wu S, Lyu B, Li H, Chittari B L, Watanabe K, Taniguchi T, Shi Z, Jung J, Zhang Y, Wang F 2019 Nat. Phys. 15 237
Google Scholar
[15] Regan E C, Wang D, Jin C, Bakti Utama M I, Gao B, Wei X, Zhao S, Zhao W, Zhang Z, Yumigeta K, Blei M, Carlstrom J D, Watanabe K, Taniguchi T, Tongay S, Crommie M, Zettl A, Wang F 2020 Nature 579 359
Google Scholar
[16] Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H, Feng D, Chen X H, Zhang Y 2014 Nat. Nanotechnol. 9 372
Google Scholar
[17] Ling X, Wang H, Huang S, Xia F, Dresselhaus M S 2015 Proc. Natl. Acad. Sci. USA 112 4523
Google Scholar
[18] Xia F N, Wang H, Jia Y C 2014 Nat. Commun. 5 4458
Google Scholar
[19] Liu H, Neal A T, Zhu Z, Luo Z, Xu X F, Tomanek D, Ye P D 2014 ACS Nano 8 4033
Google Scholar
[20] Qiao J, Kong X, Hu Z X, Yang F, Ji W 2014 Nat. Commun. 5 4475
Google Scholar
[21] Luo Z, Maassen J, Deng Y, Du Y, Garrelts R P, Lundstrom M S, Ye P D, Xu X 2015 Nat. Commun. 6 8572
Google Scholar
[22] Rodin A S, Carvalho A, Castro Neto A H 2014 Phys. Rev. Lett. 112 176801
Google Scholar
[23] Asahina H, Morita A 1984 J. Phys. C: Solid State 17 1839
Google Scholar
[24] Li L, Kim J, Jin C, Ye G J, Qiu D Y, da Jornada F H, Shi Z, Chen L, Zhang Z, Yang F, Watanabe K, Taniguchi T, Ren W, Louie S G, Chen X H, Zhang Y, Wang F 2017 Nat. Nanotechnol. 12 21
Google Scholar
[25] Mak K F, Sfeir M Y, Wu Y, Lui C H, Misewich J A, Heinz T F 2008 Phys. Rev. Lett. 101 196405
Google Scholar
[26] Wang F, Zhang Y B, Tian C S, Girit C, Zettl A, Crommie M, Shen Y R 2008 Science 320 206
Google Scholar
[27] Rudenko A N, Katsnelson M I 2014 Phys. Rev. B 89 201408
Google Scholar
[28] Zhang G W, Huang S, Chaves A, Song C, Ozcelik V O, Low T, Yan H 2017 Nat. Commun. 8 14071
Google Scholar
[29] Zhang G W, Huang S, Wang F, Xing Q, Song C, Wang C, Lei Y, Huang M, Yan H 2020 Nat. Commun. 11 1847
Google Scholar
[30] Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R, Geim A K 2008 Science 320 1308
Google Scholar
[31] Chernikov A, Berkelbach T C, Hill H M, Rigosi A, Li Y L, Aslan O B, Reichman D R, Hybertsen M S, Heinz T F 2014 Phys. Rev. Lett. 113 076802
Google Scholar
[32] He K, Kumar N, Zhao L, Wang Z, Mak K F, Zhao H, Shan J 2014 Phys. Rev. Lett. 113 026803
Google Scholar
[33] Tran V, Soklaski R, Liang Y, Yang L 2014 Phys. Rev. B 89 235319
Google Scholar
[34] Wang X, Jones A M, Seyler K L, Tran V, Jia Y, Zhao H, Wang H, Yang L, Xu X, Xia F 2015 Nat. Nanotechnol. 10 517
Google Scholar
[35] Qiu D Y, da Jornada F H, Louie S G 2017 Nano Lett. 17 4706
Google Scholar
[36] Zhang G W, Chaves A, Huang S Y, Wang F J, Xing Q X, Low T, Yan H G 2018 Sci. Adv. 4 eaap9977
Google Scholar
[37] Keldysh L V 1979 JETP Lett. 29 658
[38] Olsen T, Latini S, Rasmussen F, Thygesen K S 2016 Phys. Rev. Lett. 116 056401
Google Scholar
[39] Masumoto Y, Matsuura M, Tarucha S, Okamoto H 1985 Phys. Rev. B 32 4275
Google Scholar
[40] Masselink W T, Pearah P J, Klem J, Peng C K, Morkoc H, Sanders G D, Chang Y C 1985 Phys. Rev. B 32 8027
Google Scholar
[41] Bastard G, Mendez E E, Chang L L, Esaki L 1982 Phys. Rev. B 26 1974
Google Scholar
[42] Zhang S, Yang J, Xu R J, Wang F, Li W F, Ghufran M, Zhang Y W, Yu Z F, Zhang G, Qin Q H, Lu Y R 2014 ACS Nano 8 9590
Google Scholar
[43] Chen C, Chen F, Chen X, Deng B, Eng B, Jung D, Guo Q, Yuan S, Watanabe K, Taniguchi T, Lee M L, Xia F 2019 Nano Lett. 19 1488
Google Scholar
[44] Huang Y, Qiao J, He K, Bliznakov S, Sutter E, Chen X, Luo D, Meng F, Su D, Decker J, Ji W, Ruoff R S, Sutter P 2016 Chem. Mater. 28 8330
Google Scholar
[45] Luo W, Zemlyanov D Y, Milligan C A, Du Y C, Yang L M, Wu Y Q, Ye P D 2016 Nanotechnology 27 829
[46] Favron A, Gaufres E, Fossard F, Phaneuf-L’Heureux A L, Tang N Y, Levesque P L, Loiseau A, Leonelli R, Francoeur S, Martel R 2015 Nat Mater 14 826
Google Scholar
[47] Wang F, Zhang G, Huang S, Song C, Wang C, Xing Q, Lei Y, Yan H 2019 Phys. Rev. B 99 075427
Google Scholar
[48] Huang M Y, Yan H G, Chen C Y, Song D H, Heinz T F, Hone J 2009 P. Natl. Acad. Sci. USA 106 7304
Google Scholar
[49] Frisenda R, Druppel M, Schmidt R, de Vasconcellos S M, de Lara D P, Bratschitsch R, Rohlfing M, Castellanos-Gomez A 2017 Npj 2D Mater. Appl. 1 10
Google Scholar
[50] Song C, Fan F, Xuan N, Huang S, Zhang G, Wang C, Sun Z, Wu H, Yan H 2018 ACS Appl. Mater. Interfaces 10 3994
Google Scholar
[51] Wei Q, Peng X H 2014 App.l Phys. Lett. 104 251915
Google Scholar
[52] Quereda J, San-Jose P, Parente V, Vaquero-Garzon L, Molina-Mendoza A J, Agrait N, Rubio-Bollinger G, Guinea F, Roldan R, Castellanos-Gomez A 2016 Nano Letters 16 2931
Google Scholar
[53] Zhang Z C, Li L K, Horng J, Wang N Z, Yang F Y, Yu Y J, Zhang Y, Chen G R, Watanabe K, Taniguchi T, Chen X H, Wang F, Zhang Y B 2017 Nano Letters 17 6097
Google Scholar
[54] Ezawa M 2014 New J. Phys. 16 115004
Google Scholar
[55] Duan H J, Yang M, Wang R Q 2016 Physica E 81 177
Google Scholar
[56] Jiang J W, Park H S 2014 Nature Communications 5 4727
Google Scholar
[57] Huang S, Zhang G, Fan F, Song C, Wang F, Xing Q, Wang C, Wu H, Yan H 2019 Nat. Commun. 10 2447
Google Scholar
[58] Yongke S2010 Strain Effect in Semiconductors Theory and Device Applications (New York: Springer) p51
[59] Lin C, Grassi R, Low T, Helmy A S 2016 Nano Lett. 16 1683
Google Scholar
[60] Whitney W S, Sherrott M C, Jariwala D, Lin W H, Bechtel H A, Rossman G R, Atwater H A 2017 Nano Lett. 17 78
Google Scholar
[61] Sherrott M C, Whitney W S, Jariwala D, Biswas S, Went C M, Wong J, Rossman G R, Atwater H A 2019 Nano Lett. 19 269
Google Scholar
[62] Chen C, Lu X B, Deng B C, Chen X L, Guo Q S, Li C, Ma C, Yuan S F, Sung E, Watanabe K, Taniguchi T, Yang L, Xia F N 2020 Sci. Adv. 6 eaay6134
Google Scholar
[63] Deng B, Tran V, Xie Y, Jiang H, Li C, Guo Q, Wang X, Tian H, Koester S J, Wang H, Cha J J, Xia Q, Yang L, Xia F 2017 Nat. Commun. 8 14474
Google Scholar
[64] Chen X, Lu X, Deng B, Sinai O, Shao Y, Li C, Yuan S, Tran V, Watanabe K, Taniguchi T, Naveh D, Yang L, Xia F 2017 Nat. Commun. 8 1672
Google Scholar
[65] Yuan H, Liu X, Afshinmanesh F, Li W, Xu G, Sun J, Lian B, Curto A G, Ye G, Hikita Y, Shen Z, Zhang S C, Chen X, Brongersma M, Hwang H Y, Cui Y 2015 Nat. Nanotechnol. 10 707
Google Scholar
[66] Guo Q, Pospischil A, Bhuiyan M, Jiang H, Tian H, Farmer D, Deng B, Li C, Han S J, Wang H, Xia Q, Ma T P, Mueller T, Xia F 2016 Nano Lett. 16 4648
Google Scholar
[67] Bullock J, Amani M, Cho J, Chen Y Z, Ahn G H, Adinolfi V, Shrestha V R, Gao Y, Crozier K B, Chueh Y L, Javey A 2018 Nature Photonics 12 601
Google Scholar
[68] Zhang Y, Wang S, Chen S, Zhang Q, Wang X, Zhu X, Zhang X, Xu X, Yang T, He M, Yang X, Li Z, Chen X, Wu M, Lu Y, Ma R, Lu W, Pan A 2020 Adv. Mater. 32 e1808319
Google Scholar
[69] Wang J, Rousseau A, Yang M, Low T, Francoeur S, Kena-Cohen S 2020 Nano Lett. 20 3651
Google Scholar
[70] Nemilentsau A, Low T, Hanson G 2016 Phys. Rev. Lett. 116 006804
[71] Basov D N, Fogler M M, de Abajo F J G 2016 Science 354 1992
Google Scholar
[72] Helm M 2000 Semiconduct Semimet 62 1
[73] Zhao S, Wang E, Uzer E A, Guo S, Watanabe K, Taniguchi T, Nilges T, Zhang Y, Liu B, Zou X, Wang F 2019 arXiv 1912.03644 [cond-mat]
-
图 1 黑磷的原子结构 (a)两层黑磷的原子结构的立体图; (b)侧视图
Figure 1. Atomic structure of BP: (a) Structure of bilayer BP; (b) the side view.
图 2 二维黑磷的带间跃迁吸收 (a)−(c) 1−3层黑磷的反射谱(ΔR/R)[24]; (d)−(f) 7层、13层和块材黑磷的红外消光谱(1–T/T0)[28]; (g) 带间跃迁吸收峰随层数依赖关系[28]; (h) 不同量子数子带间的跃迁示意图
Figure 2. Interband transition absorption of 2D BP: (a)−(c) Reflection spectra(ΔR/R)[24] of 1−3 layers BP; (d)−(f) infrared extinction spectra of 4 layers, 7 layers, 13 layers, and bulk BP[28]; (g) interband transition energy as the function of layer number[28]; (h) schema-tic illustration of the optical transitions between quantized subband.
图 3 少层黑磷带隙附近连续的带间跃迁吸收 (a)聚二甲基硅氧烷(PDMS)衬底上6层黑磷的光电导[29]; (b) 不同子带间的带间跃迁带隙处连续吸收部分的吸收强度(图(a)中箭头所示)随层数的变化[29]
Figure 3. The absorption of continuum part near bandgap in few-layer BP: (a) Optical conductivity of 6 layers BP on PDMS substrate[29]; (b) the continuum height of each subband transition near the corresponding band edge (as indicated by arrows in fig. 3(a)) is plotted as a function of layer number[29].
图 4 层数依赖的激子 (a) PDMS衬底上4层黑磷的消光谱[36]; (b) 1s, 2s能级以及电子结构带隙的层数依赖[36]; (c) 激子束缚能的层数依赖关系[36]; (d) 激子吸收峰的积分面积随层数的变化, 散点为实验数据点, 黑色曲线为1/N曲线, 红色曲线为
${\rm{1/(}}{\chi _{0}}+N{\chi _1})$ 拟合曲线[29]Figure 4. Layer dependent exciton: (a) The extinction spectrum of 4 layers BP on PDMS substrate[36]; (b) layer dependence of 1s, 2s transition energies and quasi-particle bandgap[36]; (c) scaling behavior of exciton binding energy with layer number[36]; (d) the frequency-integrated conductivity of the 1 s exciton as a function of layer number. Dots are experimental data, which fitted by the red curve using the relation
${\rm{1/(}}{\chi _{0}}+N{\chi _1})$ , and the black dashed curve shows the 1/N relation[29].
图 5 二维黑磷的光致发光 (a)−(c) 77 K下单层黑磷的光致发光及反射谱, 其中黑线为探测方向沿着AC的发光谱, 红线为探测方向沿着ZZ的发光谱, 蓝色虚线为反射谱[24]; (d)80 K下4.6 nm (约9层)到46 nm(约92层)的黑磷发光谱[43]; (e) 发光峰位随着层厚的变化关系[43]
Figure 5. Photoluminescence (PL) of 2D BP: (a)−(c) The PL and reflection spectra of 1 layer BP under 77 K, black curve is the PL detected alone AC, the red is PL detected alone ZZ and blue dashed curve is the reflection spectrum[24]; (d) PL of BP with thickness ranging from 4.6 nm (about 9 layers) to 46 nm (about 92 layers) under 80 K[43]; (e) layer dependence of PL peak position[43].
图 6 暴漏在空气中黑磷的光学性质[47] (a) 暴露在空气中3层黑磷消光谱的变化; (b) 3层和8层黑磷的光学带隙(E11)在空气中的变化图; 插图为空气中黑磷导带结构变化的示意图, Δ为黑磷氧化后引入的附加势垒; (c)暴露在空气中的3层吸收峰以及PL峰位的变化
Figure 6. Optical properties of air-exposed BP[47]: (a) Evolution of extinction spectrum of an air-exposed 3 layers BP; (b) evolution of E11 peak energies of the air-exposed 3 layers and 8 layers samples, and the inset fig is the schematic illustration of evolution of conduction band in air-exposed BP; Δ is a barrier introduced by oxide; (c) blue shifts of absorption and PL peaks in an air-exposed 3 layers BP.
图 7 应变效应 (a) 两点法对柔性衬底聚对苯二甲酸乙二醇酯(PET)施加单轴应变示意图[28]; (b)在不同张应变下6层黑磷的消光谱, 其中x代表应变沿着AC方向, y为ZZ方向[28]; (c)不同的带间跃迁吸收E11, E22峰位随应变的变化关系, 散点为实验数据点, 直线为线性拟合[28]; (d)通过加热或者冷却聚丙烯(PP)衬底实现施加双轴应变的示意图[57]; (e) 两层黑磷中垂直于面方向的跃迁参数
${t^1_ \bot}$ 的示意图[57]; (f) 2—10层黑磷中E11, E22, E33峰位的移动速率与层数间的关系, 散点为平均后的数据点, 曲线为紧束缚模型的拟合曲线[57]Figure 7. Strain effect: (a) Schematic illustration of two-point bending apparatus using a flexible polyethylene terephthalate (PET) substrate[28]; (b) extinction spectra of a 6 layers BP under varying tensile strains, with strain applied along AC (red) and ZZ (blue) directions[28]; (c) the E11 and E22 peak energies as a function of tensile strain, dots are experimental data and solid lines are linear fits[28]; (d) schematic illustration of the experiment set-up used for applying in-plane biaxial strain by heating or cooling the PP substrate[57]; (e) schematic illustration of the out-of-plane hopping parameter
${t^1_ \bot }$ in bilayer BP[57]; (f) averaged shift rates of E11, E22, E33 peaks as a function of layer number in 2–10 layers BP, the solid curves are fitted to the data using the tight-binding model[57].
图 8 电场效应 (a) 5 nm厚黑磷的光电导(
${\sigma _{xx}}$ )实部随载流子浓度Ns的变化情况[59]; (b)硝酸蒸汽掺杂前后9层黑磷的消光谱, 黑色代表掺杂前, 红色为掺杂后[28]; (c)用来调控PL的器件示意图, 该器件结构为氮化硼/黑磷/氮化硼并且用CVD生长的石墨烯作为顶栅[62]; (d) 20层厚黑磷在0—0.48 V/nm电场下的PL, 其中点为实验数据点, 曲线为拟合曲线[62]; (e)双栅压调控的红外吸收测试器件示意图, 其中黑磷在Si/SiO2衬底上(SiO2厚285 nm)并蒸镀45 nm厚的Al2O3及5 nm厚的钯作为顶栅[61]; (f)在黑磷不接电极(左图)和接电极(右图)时, 调控黑磷沿着AC吸收强度的能力随栅压的变化[61]Figure 8. Electric field effect: (a) Evolution of real part of optical conductivity (
${\sigma _{xx}}$ ) due to increasing carrier density Ns[59]; (b) extinction spectrum of a 9 layers BP before (black) and after (red) chemical doping through HNO3 vapor treatment[28]; (c) schematic illustration of the dual-gate hBN/BP/hBN device with CVD graphene as the top gate for tunable light emission[62]; (d) the measured (dot) and fitted (lines) tunable PL spectra of the 20 layers BP device under different displacement field from 0 to 0.48 V/nm[62]; (e) schematic illustration of infrared tunability device. BP was exfoliated on the 285 nm SiO2/Si substrate and then capped with 45 nm Al2O3 and 5 nm Pd as top gate[61]; (f) tunability of BP oscillator strength with a field applied to the floating device (left) and connect device (right), for light polarized along AC[61]. -
[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
Google Scholar
[2] Xu M, Liang T, Shi M, Chen H 2013 Chem. Rev. 113 3766
Google Scholar
[3] Novoselov K S, Mishchenko A, Carvalho A, Castro Neto A H 2016 Science 353 aac9439
Google Scholar
[4] Huang B, Clark G, Navarro-Moratalla E, Klein D R, Cheng R, Seyler K L, Zhong D, Schmidgall E, McGuire M A, Cobden D H, Yao W, Xiao D, Jarillo-Herrero P, Xu X D 2017 Nature 546 270
Google Scholar
[5] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
Google Scholar
[6] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
Google Scholar
[7] Stander N, Huard B, Goldhaber-Gordon D 2009 Phys. Rev. Lett. 102 026807
Google Scholar
[8] Geim A K, Grigorieva I V 2013 Nature 499 419
Google Scholar
[9] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43
Google Scholar
[10] Dean C R, Wang L, Maher P, Forsythe C, Ghahari F, Gao Y, Katoch J, Ishigami M, Moon P, Koshino M, Taniguchi T, Watanabe K, Shepard K L, Hone J, Kim P 2013 Nature 497 598
Google Scholar
[11] Rivera P, Schaibley J R, Jones A M, Ross J S, Wu S, Aivazian G, Klement P, Seyler K, Clark G, Ghimire N J, Yan J, Mandrus D G, Yao W, Xu X 2015 Nat. Commun. 6 6242
Google Scholar
[12] Seyler K L, Rivera P, Yu H, Wilson N P, Ray E L, Mandrus D G, Yan J, Yao W, Xu X 2019 Nature 567 66
Google Scholar
[13] Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80
Google Scholar
[14] Chen G, Jiang L, Wu S, Lyu B, Li H, Chittari B L, Watanabe K, Taniguchi T, Shi Z, Jung J, Zhang Y, Wang F 2019 Nat. Phys. 15 237
Google Scholar
[15] Regan E C, Wang D, Jin C, Bakti Utama M I, Gao B, Wei X, Zhao S, Zhao W, Zhang Z, Yumigeta K, Blei M, Carlstrom J D, Watanabe K, Taniguchi T, Tongay S, Crommie M, Zettl A, Wang F 2020 Nature 579 359
Google Scholar
[16] Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H, Feng D, Chen X H, Zhang Y 2014 Nat. Nanotechnol. 9 372
Google Scholar
[17] Ling X, Wang H, Huang S, Xia F, Dresselhaus M S 2015 Proc. Natl. Acad. Sci. USA 112 4523
Google Scholar
[18] Xia F N, Wang H, Jia Y C 2014 Nat. Commun. 5 4458
Google Scholar
[19] Liu H, Neal A T, Zhu Z, Luo Z, Xu X F, Tomanek D, Ye P D 2014 ACS Nano 8 4033
Google Scholar
[20] Qiao J, Kong X, Hu Z X, Yang F, Ji W 2014 Nat. Commun. 5 4475
Google Scholar
[21] Luo Z, Maassen J, Deng Y, Du Y, Garrelts R P, Lundstrom M S, Ye P D, Xu X 2015 Nat. Commun. 6 8572
Google Scholar
[22] Rodin A S, Carvalho A, Castro Neto A H 2014 Phys. Rev. Lett. 112 176801
Google Scholar
[23] Asahina H, Morita A 1984 J. Phys. C: Solid State 17 1839
Google Scholar
[24] Li L, Kim J, Jin C, Ye G J, Qiu D Y, da Jornada F H, Shi Z, Chen L, Zhang Z, Yang F, Watanabe K, Taniguchi T, Ren W, Louie S G, Chen X H, Zhang Y, Wang F 2017 Nat. Nanotechnol. 12 21
Google Scholar
[25] Mak K F, Sfeir M Y, Wu Y, Lui C H, Misewich J A, Heinz T F 2008 Phys. Rev. Lett. 101 196405
Google Scholar
[26] Wang F, Zhang Y B, Tian C S, Girit C, Zettl A, Crommie M, Shen Y R 2008 Science 320 206
Google Scholar
[27] Rudenko A N, Katsnelson M I 2014 Phys. Rev. B 89 201408
Google Scholar
[28] Zhang G W, Huang S, Chaves A, Song C, Ozcelik V O, Low T, Yan H 2017 Nat. Commun. 8 14071
Google Scholar
[29] Zhang G W, Huang S, Wang F, Xing Q, Song C, Wang C, Lei Y, Huang M, Yan H 2020 Nat. Commun. 11 1847
Google Scholar
[30] Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M R, Geim A K 2008 Science 320 1308
Google Scholar
[31] Chernikov A, Berkelbach T C, Hill H M, Rigosi A, Li Y L, Aslan O B, Reichman D R, Hybertsen M S, Heinz T F 2014 Phys. Rev. Lett. 113 076802
Google Scholar
[32] He K, Kumar N, Zhao L, Wang Z, Mak K F, Zhao H, Shan J 2014 Phys. Rev. Lett. 113 026803
Google Scholar
[33] Tran V, Soklaski R, Liang Y, Yang L 2014 Phys. Rev. B 89 235319
Google Scholar
[34] Wang X, Jones A M, Seyler K L, Tran V, Jia Y, Zhao H, Wang H, Yang L, Xu X, Xia F 2015 Nat. Nanotechnol. 10 517
Google Scholar
[35] Qiu D Y, da Jornada F H, Louie S G 2017 Nano Lett. 17 4706
Google Scholar
[36] Zhang G W, Chaves A, Huang S Y, Wang F J, Xing Q X, Low T, Yan H G 2018 Sci. Adv. 4 eaap9977
Google Scholar
[37] Keldysh L V 1979 JETP Lett. 29 658
[38] Olsen T, Latini S, Rasmussen F, Thygesen K S 2016 Phys. Rev. Lett. 116 056401
Google Scholar
[39] Masumoto Y, Matsuura M, Tarucha S, Okamoto H 1985 Phys. Rev. B 32 4275
Google Scholar
[40] Masselink W T, Pearah P J, Klem J, Peng C K, Morkoc H, Sanders G D, Chang Y C 1985 Phys. Rev. B 32 8027
Google Scholar
[41] Bastard G, Mendez E E, Chang L L, Esaki L 1982 Phys. Rev. B 26 1974
Google Scholar
[42] Zhang S, Yang J, Xu R J, Wang F, Li W F, Ghufran M, Zhang Y W, Yu Z F, Zhang G, Qin Q H, Lu Y R 2014 ACS Nano 8 9590
Google Scholar
[43] Chen C, Chen F, Chen X, Deng B, Eng B, Jung D, Guo Q, Yuan S, Watanabe K, Taniguchi T, Lee M L, Xia F 2019 Nano Lett. 19 1488
Google Scholar
[44] Huang Y, Qiao J, He K, Bliznakov S, Sutter E, Chen X, Luo D, Meng F, Su D, Decker J, Ji W, Ruoff R S, Sutter P 2016 Chem. Mater. 28 8330
Google Scholar
[45] Luo W, Zemlyanov D Y, Milligan C A, Du Y C, Yang L M, Wu Y Q, Ye P D 2016 Nanotechnology 27 829
[46] Favron A, Gaufres E, Fossard F, Phaneuf-L’Heureux A L, Tang N Y, Levesque P L, Loiseau A, Leonelli R, Francoeur S, Martel R 2015 Nat Mater 14 826
Google Scholar
[47] Wang F, Zhang G, Huang S, Song C, Wang C, Xing Q, Lei Y, Yan H 2019 Phys. Rev. B 99 075427
Google Scholar
[48] Huang M Y, Yan H G, Chen C Y, Song D H, Heinz T F, Hone J 2009 P. Natl. Acad. Sci. USA 106 7304
Google Scholar
[49] Frisenda R, Druppel M, Schmidt R, de Vasconcellos S M, de Lara D P, Bratschitsch R, Rohlfing M, Castellanos-Gomez A 2017 Npj 2D Mater. Appl. 1 10
Google Scholar
[50] Song C, Fan F, Xuan N, Huang S, Zhang G, Wang C, Sun Z, Wu H, Yan H 2018 ACS Appl. Mater. Interfaces 10 3994
Google Scholar
[51] Wei Q, Peng X H 2014 App.l Phys. Lett. 104 251915
Google Scholar
[52] Quereda J, San-Jose P, Parente V, Vaquero-Garzon L, Molina-Mendoza A J, Agrait N, Rubio-Bollinger G, Guinea F, Roldan R, Castellanos-Gomez A 2016 Nano Letters 16 2931
Google Scholar
[53] Zhang Z C, Li L K, Horng J, Wang N Z, Yang F Y, Yu Y J, Zhang Y, Chen G R, Watanabe K, Taniguchi T, Chen X H, Wang F, Zhang Y B 2017 Nano Letters 17 6097
Google Scholar
[54] Ezawa M 2014 New J. Phys. 16 115004
Google Scholar
[55] Duan H J, Yang M, Wang R Q 2016 Physica E 81 177
Google Scholar
[56] Jiang J W, Park H S 2014 Nature Communications 5 4727
Google Scholar
[57] Huang S, Zhang G, Fan F, Song C, Wang F, Xing Q, Wang C, Wu H, Yan H 2019 Nat. Commun. 10 2447
Google Scholar
[58] Yongke S2010 Strain Effect in Semiconductors Theory and Device Applications (New York: Springer) p51
[59] Lin C, Grassi R, Low T, Helmy A S 2016 Nano Lett. 16 1683
Google Scholar
[60] Whitney W S, Sherrott M C, Jariwala D, Lin W H, Bechtel H A, Rossman G R, Atwater H A 2017 Nano Lett. 17 78
Google Scholar
[61] Sherrott M C, Whitney W S, Jariwala D, Biswas S, Went C M, Wong J, Rossman G R, Atwater H A 2019 Nano Lett. 19 269
Google Scholar
[62] Chen C, Lu X B, Deng B C, Chen X L, Guo Q S, Li C, Ma C, Yuan S F, Sung E, Watanabe K, Taniguchi T, Yang L, Xia F N 2020 Sci. Adv. 6 eaay6134
Google Scholar
[63] Deng B, Tran V, Xie Y, Jiang H, Li C, Guo Q, Wang X, Tian H, Koester S J, Wang H, Cha J J, Xia Q, Yang L, Xia F 2017 Nat. Commun. 8 14474
Google Scholar
[64] Chen X, Lu X, Deng B, Sinai O, Shao Y, Li C, Yuan S, Tran V, Watanabe K, Taniguchi T, Naveh D, Yang L, Xia F 2017 Nat. Commun. 8 1672
Google Scholar
[65] Yuan H, Liu X, Afshinmanesh F, Li W, Xu G, Sun J, Lian B, Curto A G, Ye G, Hikita Y, Shen Z, Zhang S C, Chen X, Brongersma M, Hwang H Y, Cui Y 2015 Nat. Nanotechnol. 10 707
Google Scholar
[66] Guo Q, Pospischil A, Bhuiyan M, Jiang H, Tian H, Farmer D, Deng B, Li C, Han S J, Wang H, Xia Q, Ma T P, Mueller T, Xia F 2016 Nano Lett. 16 4648
Google Scholar
[67] Bullock J, Amani M, Cho J, Chen Y Z, Ahn G H, Adinolfi V, Shrestha V R, Gao Y, Crozier K B, Chueh Y L, Javey A 2018 Nature Photonics 12 601
Google Scholar
[68] Zhang Y, Wang S, Chen S, Zhang Q, Wang X, Zhu X, Zhang X, Xu X, Yang T, He M, Yang X, Li Z, Chen X, Wu M, Lu Y, Ma R, Lu W, Pan A 2020 Adv. Mater. 32 e1808319
Google Scholar
[69] Wang J, Rousseau A, Yang M, Low T, Francoeur S, Kena-Cohen S 2020 Nano Lett. 20 3651
Google Scholar
[70] Nemilentsau A, Low T, Hanson G 2016 Phys. Rev. Lett. 116 006804
[71] Basov D N, Fogler M M, de Abajo F J G 2016 Science 354 1992
Google Scholar
[72] Helm M 2000 Semiconduct Semimet 62 1
[73] Zhao S, Wang E, Uzer E A, Guo S, Watanabe K, Taniguchi T, Nilges T, Zhang Y, Liu B, Zou X, Wang F 2019 arXiv 1912.03644 [cond-mat]
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