|
|
Theoretical study of broadband near-field optical spectrum of twisted bilayer graphene |
Lu Wen1, Yijun Liu2, Guoyu Luo1, Xinyu Lv1, Kaiyuan Wang2, Wang Zhu2, Lei Wang2, Zhiqiang Li1() |
1. College of Physics, Sichuan University, Chengdu 610064, China 2. National Laboratory of Solid-State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China |
|
|
Abstract We theoretically study the broadband near-field optical spectrum of twisted bilayer graphene (TBG) at various twist angles near the magic angle using two different models. The spectrum at low Fermi energy is characterized by a series of peaks that are almost at the same energies as the peaks in the far-field optical conductivity of TBG. When the Fermi energy is near a van Hove singularity, an additional strong peak appears at finite energy in the near-field spectrum, which has no counterpart in the optical conductivity. Based on a detailed calculation of the plasmon dispersion, we show that these spectroscopic features are associated with interband and intraband plasmons, which can provide critical information about the local band structure and plasmonic excitations in TBG. The near-field peaks evolve systematically with the twist angle, so they can serve as fingerprints for identifying the spatial dependent twist angle in TBG samples. Our findings pave the way for future experimental studies of the novel optical properties of TBG in the nanoscale.
|
Keywords
twisted bilayer graphene
SNOM
broadband near-field optical spectrum
optical conductivity
magic angle
|
Corresponding Author(s):
Zhiqiang Li
|
Issue Date: 28 March 2022
|
|
1 |
Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature 556(7699), 80 (2018)
https://doi.org/10.1038/nature26154
|
2 |
Y. Jiang, X. Lai, K. Watanabe, T. Taniguchi, K. Haule, J. Mao, and E. Y. Andrei, Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene, Nature 573(7772), 91 (2019)
https://doi.org/10.1038/s41586-019-1460-4
|
3 |
A. Kerelsky, L. J. Mc Gilly, D. M. Kennes, L. Xian, M. Yankowitz, S. Chen, K. Watanabe, T. Taniguchi, J. Hone, C. Dean, A. Rubio, and A. N. Pasupathy, Maximized electron interactions at the magic angle in twisted bilayer graphene, Nature 572(7767), 95 (2019)
https://doi.org/10.1038/s41586-019-1431-9
|
4 |
Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional super-conductivity in magic-angle graphene superlattices, Nature 556(7699), 43 (2018)
https://doi.org/10.1038/nature26160
|
5 |
M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Tuning superconductivity in twisted bilayer graphene, Science 363(6431), 1059 (2019)
https://doi.org/10.1126/science.aav1910
|
6 |
X. Lu, P. Stepanov, W. Yang, M. Xie, M. A. Aamir, I. Das, C. Urgell, K. Watanabe, T. Taniguchi, G. Zhang, A. Bachtold, A. H. MacDonald, and D. K. Efetov, Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene, Nature 574(7780), 653 (2019)
https://doi.org/10.1038/s41586-019-1695-0
|
7 |
Y. Xie, B. Lian, B. Jäck, X. Liu, C. L. Chiu, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene, Nature 572(7767), 101 (2019)
https://doi.org/10.1038/s41586-019-1422-x
|
8 |
M. Serlin, C. L. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. F. Young, Intrinsic quantized anomalous Hall effect in a moire heterostructure, Science 367(6480), 900 (2020)
https://doi.org/10.1126/science.aay5533
|
9 |
A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney, K. Watanabe, T. Taniguchi, M. A. Kastner, and D. Goldhaber-Gordon, Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene, Science 365(6453), 605 (2019)
https://doi.org/10.1126/science.aaw3780
|
10 |
R. Bistritzer and A. H. MacDonald, Moire bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. USA 108(30), 12233 (2011)
https://doi.org/10.1073/pnas.1108174108
|
11 |
E. Suárez Morell, J. D. Correa, P. Vargas, M. Pacheco, and Z. Barticevic, Flat bands in slightly twisted bilayer graphene: Tight-binding calculations, Phys. Rev. B 82(12), 121407 (2010)
https://doi.org/10.1103/PhysRevB.82.121407
|
12 |
H. Yoo, R. Engelke, S. Carr, S. Fang, K. Zhang, P. Cazeaux, S. H. Sung, R. Hovden, A. W. Tsen, T. Taniguchi, K. Watanabe, G. C. Yi, M. Kim, M. Luskin, E. B. Tadmor, E. Kaxiras, and P. Kim, Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene, Nat. Mater. 18(5), 448 (2019)
https://doi.org/10.1038/s41563-019-0346-z
|
13 |
S. Y. Dai, Y. Xiang, and D. J. Srolovitz, Twisted bilayer graphene: Moire with a twist, Nano Lett. 16(9), 5923 (2016)
https://doi.org/10.1021/acs.nanolett.6b02870
|
14 |
N. N. T. Nam and M. Koshino, Lattice relaxation and energy band modulation in twisted bilayer graphene, Phys. Rev. B 96(7), 075311 (2017)
https://doi.org/10.1103/PhysRevB.96.075311
|
15 |
N. Y. Kim, H. Y. Jeong, J. H. Kim, G. Kim, H. S. Shin, and Z. Lee, Evidence of local commensurate state with lattice match of graphene on hexagonal boron nitride, ACS Nano 11(7), 7084 (2017)
https://doi.org/10.1021/acsnano.7b02716
|
16 |
M. M. van Wijk, A. Schuring, M. I. Katsnelson, and A. Fasolino, Relaxation of moiré patterns for slightly misaligned identical lattices: Graphene on graphite, 2D Mater. 2, 034010 (2015)
https://doi.org/10.1088/2053-1583/2/3/034010
|
17 |
F. Gargiulo and O. V. Yazyev, Structural and electronic transformation in low-angle twisted bilayer graphene, 2D Mater. 5, 015019 (2017)
https://doi.org/10.1088/2053-1583/aa9640
|
18 |
X. Chen, D. Hu, R. Mescall, G. You, D. N. Basov, Q. Dai, and M. Liu, Modern scattering-type scanning near-field optical microscopy for advanced material research, Adv. Mater. 31(24), 1804774 (2019)
https://doi.org/10.1002/adma.201804774
|
19 |
A. J. Huber, J. Wittborn, and R. Hillenbrand, Infrared spectroscopic near-field mapping of single nanotransistors, Nanotechnology 21(23), 235702 (2010)
https://doi.org/10.1088/0957-4484/21/23/235702
|
20 |
G. Dominguez, A. S. Mcleod, Z. Gainsforth, P. Kelly, H. A. Bechtel, F. Keilmann, A. Westphal, M. Thiemens, and D. N. Basov, Nanoscale infrared spectroscopy as a non-destructive probe of extraterrestrial samples, Nat. Commun. 5(1), 5445 (2014)
https://doi.org/10.1038/ncomms6445
|
21 |
Z. Fei, G. O. Andreev, W. Bao, L. M. Zhang, A. S. Mc Leod, C. Wang, M. K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, M. M. Fogler, M. J. Tauber, A. H. Castro-Neto, C. N. Lau, F. Keilmann, and D. N. Basov, Infrared nanoscopy of Dirac plasmons at the graphene–SiO2 interface, Nano Lett. 11(11), 4701 (2011)
https://doi.org/10.1021/nl202362d
|
22 |
S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S. E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, Graphene on hexagonal boron nitride as a tunable hyperbolic meta-material, Nat. Nanotechnol. 10(8), 682 (2015)
https://doi.org/10.1038/nnano.2015.131
|
23 |
J. M. Stiegler, Y. Abate, A. Cvitkovic, Y. E. Romanyuk, A. J. Huber, S. R. Leone, and R. Hillenbrand, Nanoscale infrared absorption spectroscopy of individual nanoparticles enabled by scattering-type near-field microscopy, ACS Nano 5(8), 6494 (2011)
https://doi.org/10.1021/nn2017638
|
24 |
Z. Nuño, B. Hessler, B. Heiberg, R. Damato, T. Dunlap, Y. S. Shon, and Y. Abate, Nanoscale near-field infrared spectroscopic imaging of silica-shell/gold-core and pure silica nanoparticles, J. Nanopart. Res. 14(3), 766 (2012)
https://doi.org/10.1007/s11051-012-0766-z
|
25 |
I. Amenabar, S. Poly, M. Goikoetxea, W. Nuansing, P. Lasch, and R. Hillenbrand, Hyperspectral infrared nanoimaging of organic samples based on Fourier transform infrared nanospectroscopy, Nat. Commun. 8(1), 14402 (2017)
https://doi.org/10.1038/ncomms14402
|
26 |
M. Liu, A. J. Sternbach, M. Wagner, T. V. Slusar, T. Kong, S. L. Bud’ko, S. Kittiwatanakul, M. M. Qazilbash, A. Mc Leod, Z. Fei, E. Abreu, J. Zhang, M. Goldflam, S. Dai, G. X. Ni, J. Lu, H. A. Bechtel, M. C. Martin, M. B. Raschke, R. D. Averitt, S. A. Wolf, H. T. Kim, P. C. Canfield, and D. N. Basov, Phase transition in bulk single crystals and thin films of VO2 by nanoscale infrared spectroscopy and imaging, Phys. Rev. B 91(24), 245155 (2015)
https://doi.org/10.1103/PhysRevB.91.245155
|
27 |
Z. Shi, X. Hong, H. A. Bechtel, B. Zeng, M. C. Martin, K. Watanabe, T. Taniguchi, Y. R. Shen, and F. Wang, Observation of a Luttinger-liquid plasmon in metallic single-walled carbon nanotubes, Nat. Photon. 9(8), 515 (2015)
https://doi.org/10.1038/nphoton.2015.123
|
28 |
Z. Shi, H. A. Bechtel, S. Berweger, Y. Sun, B. Zeng, C. Jin, H. Chang, M. C. Martin, M. B. Raschke, and F. Wang, Amplitude-and phase-resolved nanospectral imaging of phonon polaritons in hexagonal boron nitride, ACS Photon. 2(7), 790 (2015)
https://doi.org/10.1021/acsphotonics.5b00007
|
29 |
H. A. Bechtel, E. A. Muller, R. L. Olmon, M. C. Martin, and M. B. Raschke, Ultrabroadband infrared nanospectroscopic imaging, Proc. Natl. Acad. Sci. USA 111(20), 7191 (2014)
https://doi.org/10.1073/pnas.1400502111
|
30 |
D. N. Basov, M. M. Fogler, A. Lanzara, F. Wang, and Y. Zhang, Colloquium: Graphene spectroscopy, Rev. Mod. Phys. 86(3), 959 (2014)
https://doi.org/10.1103/RevModPhys.86.959
|
31 |
A. Uri, S. Grover, Y. Cao, J. A. Crosse, K. Bagani, D. Rodan-Legrain, Y. Myasoedov, K. Watanabe, T. Taniguchi, P. Moon, M. Koshino, P. Jarillo-Herrero, and E. Zeldov, Mapping the twist-angle disorder and Landau levels in magic-angle graphene, Nature 581(7806), 47 (2020)
https://doi.org/10.1038/s41586-020-2255-3
|
32 |
N. P. Kazmierczak, M. Van Winkle, C. Ophus, K. C. Bustillo, S. Carr, H. G. Brown, J. Ciston, T. Taniguchi, K. Watanabe, and D. K. Bediako, Strain fields in twisted bilayer graphene, Nat. Mater. 20(7), 956 (2021)
https://doi.org/10.1038/s41563-021-00973-w
|
33 |
L. Wen, Z. Li, and Y. He, Optical conductivity of twisted bilayer graphene near the magic angle, Chin. Phys. B 30(1), 017303 (2021)
https://doi.org/10.1088/1674-1056/abb65d
|
34 |
Z. B. Dai, Y. He, and Z. Li, Effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene, Phys. Rev. B 104(4), 045403 (2021)
https://doi.org/10.1103/PhysRevB.104.045403
|
35 |
P. Moon and M. Koshino, Optical absorption in twisted bilayer graphene, Phys. Rev. B 87(20), 205404 (2013)
https://doi.org/10.1103/PhysRevB.87.205404
|
36 |
J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, Continuum model of the twisted graphene bilayer, Phys. Rev. B 86(15), 155449 (2012)
https://doi.org/10.1103/PhysRevB.86.155449
|
37 |
M. Koshino, N. F. Q. Yuan, T. Koretsune, M. Ochi, K. Kuroki, and L. Fu, Maximally localized wannier orbitals and the extended hubbard model for twisted bilayer graphene, Phys. Rev. X 8(3), 031087 (2018)
https://doi.org/10.1103/PhysRevX.8.031087
|
38 |
Z. Bi, N F Q. Yuan, and L. Fu, Designing flat bands by strain, Phys. Rev. B 100(3), 035448 (2019)
https://doi.org/10.1103/PhysRevB.100.035448
|
39 |
T. Stauber, P. San-Jose, and L. Brey, Optical conductivity, Drude weight and plasmons in twisted graphene bilayers, New J. Phys. 15(11), 113050 (2013)
https://doi.org/10.1088/1367-2630/15/11/113050
|
40 |
R. Hillenbrand and F. Keilmann, Complex optical constants on a subwavelength scale, Phys. Rev. Lett. 85(14), 3029 (2000)
https://doi.org/10.1103/PhysRevLett.85.3029
|
41 |
R. Hillenbrand, B. Knoll, and F. Keilmann, Pure optical contrast in scattering-type scanning near-field microscopy, J. Microsc. 202, 77 (2001)
https://doi.org/10.1046/j.1365-2818.2001.00794.x
|
42 |
A. Cvitkovic, N. Ocelic, and R. Hillenbrand, Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy, Opt. Express 15(14), 8550 (2007)
https://doi.org/10.1364/OE.15.008550
|
43 |
B. Hauer, A. Engelhardt, and T. Taubner, Quasianalytical model for scattering infrared near-field microscopy on layered systems, Opt. Express 20(12), 13173 (2012)
https://doi.org/10.1364/OE.20.013173
|
44 |
B. Y. Jiang, L. M. Zhang, A. H. Castro Neto, D. N. Basov, and M. M. Fogler, Generalized spectral method for near-field optical microscopy, J. Appl. Phys. 119(5), 054305 (2016)
https://doi.org/10.1063/1.4941343
|
45 |
S. T. Chui, X. Chen, M. Liu, Z. Lin, and J. Zi, Scattering of electromagnetic waves from a cone with conformal mapping: Application to scanning near-field optical microscope, Phys. Rev. B 97(8), 081406 (2018)
https://doi.org/10.1103/PhysRevB.97.081406
|
46 |
I. V. Lindell and K. I. Nikoskinen, Electrostatic image theory for the dielectric prolate spheroid, J. Electromagn. Waves Appl. 15(8), 1075 (2001)
https://doi.org/10.1163/156939301X00436
|
47 |
S. Amarie and F. Keilmann, Broadband-infrared assessment of phonon resonance in scattering-type near-field microscopy, Phys. Rev. B 83(4), 045404 (2011)
https://doi.org/10.1103/PhysRevB.83.045404
|
48 |
V. P. Gusynin and S. G. Sharapov, Transport of Dirac quasiparticles in graphene: Hall and optical conductivities, Phys. Rev. B 73(24), 245411 (2006)
https://doi.org/10.1103/PhysRevB.73.245411
|
49 |
T. Stauber and H. Kohler, Quasi-flat plasmonic bands in twisted bilayer graphene, Nano Lett. 16(11), 6844 (2016)
https://doi.org/10.1021/acs.nanolett.6b02587
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|