Near-field optical characterization of atomic structures and polaritons in twisted two-dimensional materials

Xu Kun-Qi; Hu Cheng; Shen Pei-Yue; Ma Sai-Qun; Zhou Xian-Liang; Liang Qi; Shi Zhi-Wen

doi:10.7498/aps.72.20222145

Abstract

Polariton is a quasiparticle generated from strong interaction between a photon and an electric or magnetic dipole-carrying excitation. These polaritons can confine light into a small space that is beyond the diffraction limit of light, thus have greatly advanced the development of nano photonics, nonlinear optics, quantum optics and other related research. Van der Waals two-dimensional (2D) crystals provide an ideal platform for studying nano-polaritons due to reduced material dimensionality. In particular, stacking and twisting offer additional degree of freedom for manipulating polaritons that are not available in a single-layer material. In this paper, we review the near-field optical characterizations of various structures and polaritonic properties of stacked/twisted 2D crystals reported in recent years, including domain structures of stacked few-layer graphene, moiré superlattice structures of twisted 2D crystals, twisted topological polaritons, and twisted chiral plasmons. We also propose several exciting directions for future study of polaritons in stacked/twisted 2D crystals.

Keywords:

Authors and contacts

Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China

Corresponding author: Xu Kun-Qi, xukunqi@sjtu.edu.cn ; Shi Zhi-Wen, zwshi@sjtu.edu.cn

Funds: Project supported by the Open Research Fund of Songshan Lake Materials Laboratory, China (Grant No. 2021SLABFK07), the National Key Research and Development Program, China (Grant No. 2021YFA1202902), the National Natural Science Foundation of China (Grant No. 12074244), and the China Postdoctoral Science Foundation (Grant No. 2022M712087).

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Figure 1. Schematic diagram of a scattering-type scanning near-field optical microscope (s-SNOM).

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图 2 近场光信号与远场背景光信号的波形及其频谱示意图

Figure 2. Schematic diagram of the waveforms and Fourier components of near-field optical signal and far-field background noise.

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图 3 干法转移制备转角石墨烯的流程原理图 (a),(e)二维材料拾取示意图, 红色框表示半球形基板的放大视图; (b)—(d)和(f)—(h)连续堆叠步骤的示意图和相应光学显微照片^[17]

Figure 3. Schematic diagram of the dry transfer to fabricate twisted bilayer graphene^[17]: (a),(e) Schematic diagram of layer pick-up, the red box represents a zoom-in view of the hemispherical handle substrate; (b)–(d) and (f)–(h) the schematic diagrams and optical micrographs of successive stacking steps^[17].

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图 4 基于微型半球状聚合物凝胶的二维材料薄片折叠技术原理图^[21]　(a) PDMS微型半球状聚合物凝胶结构示意图; (b)—(e)二维材料薄片折叠连续操作示意图和相应光学显微照片

Figure 4. Schematic diagram of two-dimensional material sheet folding technology based on microdome polymer gel^[21]: (a) Schematic diagram of the structure of PDMS microdome polymer gel; (b)–(e) the schematic illustrations of folding two-dimensional material sheet and corresponding optical micrographs of successive steps.

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图 5 转角二维原子晶体的原位调控技术 (a)—(c)使用PDMS微型半球状聚合物凝胶操纵叠层二维材料实现转角操作, (a), (b)为方法示意图, (c)展示了样品转角前后的光学成像, 标尺为40 μm^[23]; (d), (e)使用AFM探针操纵双层二维原子晶体转角的原位调控技术, (d)为方法示意图, (e)为样品转角前后的AFM成像^[24]

Figure 5. In situ manipulation of twisted two-dimensional atomic crystals. (a)–(c) Applying PDMS microdome polymer gel to manipulate the stacked two-dimensional materials to twist. (a), (b) Schematic diagrams of the method. (c) The optical images of the sample before and after twisting. Scale bar is 40 μm^[23]. (d), (e) In situ manipulation of twisted bilayer two-dimensional atomic crystals using AFM probes. (d) A schematic diagram of the method. (e) The AFM images before and after twisting^[24].

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图 6 堆叠双层石墨烯中的孤子畴壁　(a)双层石墨烯样品在 SiO₂/Si 衬底上的 AFM 形貌图, 右下角的小三角形区域对应于单层石墨烯; (b)与图(a)对应的近场光学成像^[35]; (c)剪切(上图)和拉伸(下图)畴壁孤子的示意图, 虚线勾勒出 AB 堆叠平滑过渡到 BA 堆叠的畴壁区域, 箭头表示位错方向; (d)双层石墨烯的近场光学成像, 展示了弯曲的 L 形畴壁; (e)不同栅极电压下双层石墨烯中剪切孤子和拉伸孤子的近场光学成像, 标尺为 300 nm; (f)对应图(e)中白色虚线处的扫描线, 展示了在拉伸孤子处栅极依赖的等离激元干涉行为, 用虚线表示的两个峰对应于两条亮线, 它们的分离随着载流子密度的增大而增加^[36]

Figure 6. Soliton domain walls in stacked bilayer graphene: (a) AFM topography of the bilayer graphene sample on SiO₂/Si substrate, the small triangular area in the lower right corner corresponds to the monolayer graphene; (b) near-field optical image corresponding to Fig. (a)^[35]; (c) schematic diagrams of shear (top) and tensile (bottom) domain wall solitons, the dashed line outlines the domain wall region where the AB stacking domain smoothly transitions to the BA stacking domain, arrows indicate dislocation directions; (d) near-field optical imaging of bilayer graphene, showing L-shaped domain walls; (e) near-field optical images of shear and tensile solitons in bilayer graphene at different gate voltages, scale bar is 300 nm; (f) corresponds to the scan line at the white dashed line in Fig. (e), showing gate-dependent plasmon interference behavior at the tensile soliton, the two peaks represented by dashed lines correspond to two bright lines, and their separation increases with increasing carrier density^[36].

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图 7 三层石墨烯的多种畴区　(a)衬底上三层石墨烯的 AFM 形貌像和高度剖面图; (b), (c)三层石墨烯样品激光照射处理前、后的拉曼成像; (d)激光照射后三层石墨烯的近场光学成像, 具有不同堆叠顺序的畴区在近场光学像中显示出不同的衬度, 标记的区域 I, II 和 III 分别对应于 ABC 堆叠、ABA 堆叠和混合 ABC+ABA 堆叠畴区, 红色箭头标记了在拉曼图中未显示出的额外混合 ABC + ABA 堆叠区域^[48]; (e)使用AFM接触模式对三层石墨烯畴壁进行操纵的示意图, 蓝色箭头表示尖端的移动方向; (f)—(i)三层石墨烯的两个区域在沿着黑色箭头对畴壁进行单线扫描前后, 畴壁形态变化的近场光学成像^[49]

Figure 7. Various domains of trilayer graphene. (a) AFM image and height profile of trilayer graphene on the substrate. (b), (c) Raman imaging of three-layer graphene samples before and after laser irradiation. (d) Near-field optical image of trilayer graphene after laser irradiation. Graphene domains with different stacking orders show different contrasts in near-field optical images. Marked regions I, II, and III correspond to ABC stacking, ABA stacking, and mixed ABC+ABA stacking domains, respectively. Red arrows highlight additional mixed ABC+ABA stacking domains not shown in the Raman map.^[48] (e) Schematic diagram of the manipulation of trilayer graphene domain walls using AFM contact mode. The blue arrow indicates the direction of movement of the tip. (f)–(i) Near-field optical images of domain walls with the reconstructed configuration before and after single-line scanning along the black arrows in trilayer graphene^[49].

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图 8 转角双层石墨烯的莫尔超晶格网络　(a)转角双层石墨烯不同堆叠构型, 分别用AB, BA, AA和SP标记; (b)转角双层石墨烯周期性三角形孤子畴壁的近场光学成像^[36]; (c)—(e)在不同激发频率下, hBN封装的转角双层石墨烯莫尔图案的近场光学成像, 转角为~0.05°; (f)—(h)在激励频率ω = 1560 cm^–1下, 分别为0.06°, 0.11°和0.21°的不同转角的近场光学成像, 标尺为500 nm^[53]; (i)转角双层石墨烯近场光电流成像的实验设置示意图, 叠层石墨烯中标记有AB和BA畴区; (j)转角双层石墨烯的光电流成像; (k)对应于图(j)中的黄色虚线矩形的近场光学相位图, 标尺为500 nm^[54]

Figure 8. Twisted bilayer graphene superlattice network. (a) Schematic diagram of twisted bilayer graphene showing different stacking configurations. They are marked with AB, BA, AA and SP respectively. (b) Near-field optical images of the periodic triangular soliton domain-wall lattice of twisted bilayer graphene. ^[36] (c)–(e) Near-field optical images of the normalized amplitude showing moiré pattern in buried twisted bilayer graphene encapsulated with hBN at different excitation frequencies. The twist angle is ~0.05°. (f)–(h) Near-field optical images showing different twist angles of 0.06°, 0.11° and 0.21° at excitation frequency ω = 1560 cm^–1. Scale bars are 500 nm. ^[53] (i) Schematic diagram of the experimental setup for near-field photocurrent images of twisted bilayer graphene with AB and BA labels in stacked graphene layers. (j) Photocurrent map of twisted bilayer graphene. (k) Near-field optical phase image corresponding to the yellow dashed rectangle in Fig. (j). Scale bar is 500 nm^[54].

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图 9 转角hBN超晶格网络　(a)频率为1368 cm^–1 处的转角hBN 畴结构的近场光学成像; (b)转角hBN 声子剩余极化带的近场光学信号的频率依赖关系图, 纵坐标表示畴区和畴壁的信号比值, 插图显示了对应的近场光学像^[59]; (c)转角hBN在石墨/SiO₂/Si衬底上的近场成像示意图, 该图展示了可能的堆叠构型(AA, AB, BA); (d)转角hBN的压电响应显微术(PFM)成像, 插图显示了直流静电力显微术(DC-EFM)成像; (e)—(j)在3个选定频率下拍摄的转角hBN的近场光学振幅和相位的图像, 对应图(d)中白色虚线矩形显示的区域, 所有实验都是在横向光学(TO)声子调谐频率附近进行的; (k), (l)不同堆叠构型的介电函数对频率的依赖关系; (m)相关拟合参数, 反映不同堆叠构型的频率偏移^[60]

Figure 9. Twisted hBN superlattice networks. (a) Near-field optical image of the twisted hBN domain structure at a frequency of 1368 cm^–1. (b) Frequency-dependent plot of the near-field optical signal of the phonon restrahlen band of the twisted hBN. The y-axis represents the signal ratio of the domain region and the domain wall. The inset shows the corresponding near-field optical image.^[59] (c) Schematic diagram of near-field optical imaging of twisted hBN on a graphite/SiO₂/Si substrate. The possible stacking configurations are drawn above (AA, AB, BA). (d) Piezo-force microscopy (PFM) image of twisted hBN. The inset shows DC electrical force microscopy (DC-EFM) imaging. (e)–(j) Images of the near-field optical amplitude and phase for twisted hBN at three selected frequencies, corresponding to the area marked with white dashed rectangle in Fig. (d). All experiments are performed at the transverse optical (TO) phonon frequency. (k), (l) Frequency dependence of the dielectric functions of different stacking configurations. (m) The fitting parameters, which reflect the frequency shift of the different stacking configurations^[60].

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图 10 转角双层α-MoO₃的声子极化激元的拓扑转变^[83]　(a)转角双层α-MoO₃ 示意图. 底层α-MoO₃ 的 [100] 和 [001] 方向分别定义为x 和 y 轴, 转角 Δθ 定义为顶层α-MoO₃ 相对于底层逆时针旋转角度; (b)—(e)和(j)—(m)显示了真实空间近场光学成像, 反映了声子极化激元色散作为转角的函数的拓扑性质, 频率为916 cm^–1(图(b)—(e)和986 cm^–1(图(j)—(m)); (f)—(i)和(n)—(q)对应计算的电场分布z分量的实数部分, Re(E_z)

Figure 10. Topological transition of phonon polaritons in the twisted bilayer α-MoO₃. ^[83] (a) Schematic diagram of the twisted bilayer α-MoO₃. The [100] and [001] directions of the bottom α-MoO₃ are defined as the x and y axes, respectively. The twist angle Δθ is defined as the counterclockwise rotation angle of the top layer α-MoO₃ relative to the bottom layer. (b)–(e) and (j)–(m) Near-field optical images reflecting the topological properties of the phonon polariton dispersion as a function of the twist angle at a frequency of 916 cm^–1 (Fig. (b)–(e)) and 986 cm^–1 (Fig. (j)–(m)); (f)–(i) and (n)–(q) corresponds to calculated real parts of z-components of the electric field distributions, Re(E_z).

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