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The helicity of Raman scattered light: principles and applications in two-dimensional materials

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  • ReceivedAug 10, 2021
  • AcceptedSep 7, 2021
  • PublishedNov 23, 2021

Abstract


Funding

the Ministry of Science and Technology of China(2016YFA0200100,2018YFA0703502)

the National Natural Science Foundation of China(52021006,51720105003,21790052,21974004)

Beijing National Laboratory for Molecular Sciences(BNLMS-CXTD-202001)

the Strategic Priority Research Program of CAS(XDB36030100)


Acknowledgment

This work was supported by the Ministry of Science and Technology of China (2016YFA0200100, 2018YFA0703502), the National Natural Science Foundation of China (52021006, 51720105003, 21790052, 21974004), Beijing National Laboratory for Molecular Sciences (BNLMS-CXTD-202001) and the Strategic Priority Research Program of Chinese Academy of Sciences (XDB36030100).


Interest statement

The authors declare no conflict of interest.


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  • Figure 1

    Schematic illustration of the researches on the helicity of Raman scattered light for 2D materials (color online).

  • Figure 2

    Schematic of the Raman scattering process excited by circularly polarized light. Reproduced with permission from Ref. [13]. Copyright 2018 American Physical Society (color online).

  • Figure 3

    (a) Phonon dispersion relation of a honeycomb AB lattice. The insets show phonon vibrations for sublattices A and B in one unit cell at K and K′, numbers 1 to 4 denote four bands. The circles represent the vibrations of A and B, including the vibration amplitudes, phase and rotation directions. (b) Phase correlation of the phonon nonlocal part for sublattice A (upper two panels) and sublattice B (lower two panels) at K′ (left panels) and K (right panels). (c) Phonon pseudoangular momentum (PAM) for bands 1 to 4 at valleys K and K′. Reproduced with permission from Ref. [28]. Copyright 2015 American Physical Society. (d) The vibration of the in-plane degenerate modes at Γ point of graphene. εvj1  and εvj2  are the two degenerate eigenvectors. εvj1+iεvj2 and εvj1+iεvj2  are the reconstructed vibrations of the two orthogonal eigenvectors εvj1  and εvj2. The red and blue arrows denote the real and imaginary parts, respectively. Reproduced with permission from Ref. [13]. Copyright 2018 American Physical Society (color online).

  • Figure 4

    Schematic of the experimental setup for HRRS. The green (red) path represents the incident (scattered) light. Reproduced with permission from Ref. [14]. Copyright 2015 American Chemical Society (color online).

  • Figure 5

    (a) The HRRS for the G band of monolayer graphene. Adapted with permission from Ref. [15]. Copyright 2017 American Physical Society. Inset shows the vibration modes of the iTO and iLO phonons at the Γ point of the Brillouin zone of graphene. Reproduced with permission from Ref. [12]. Copyright 2018 MDPI. (b) HRRS of graphene with varying layer numbers. (c) The polarization degree for the G mode of graphene as a function of layer number. Adapted with permission from Ref. [37]. Copyright 2021 American Physical Society (color online).

  • Figure 6

    (a) Schematic diagrams of the two first-order Raman modes (IMC, OC) of monolayer TMDC. HRRS of the IMC and OC modes of WS2 (b) and MoS2 (c) with various thicknesses. Inset in (c) shows the polar plot of the normalized intensities of Rayleigh (green), IMC (blue), and OC phonon (orange) scattering for MoS2. (d) Schematic diagrams of interlayer shear and breathing vibration modes of bilayer TMDC. HRRS for shear (S) and breathing (B) modes of WS2 (e) and MoS2 (f) with various thicknesses. Adapted with permission from Ref. [14]. Copyright 2015 American Chemical Society (color online).

  • Figure 7

    (a, b) The HRRS of WSe2 with different layer numbers for the (a) σ+σ− or (b) σ+σ+ configurations. The Davydov-split peaks of the A1g mode are resolved in (b). Reproduced with permission from Ref. [19]. Copyright 2017 IOP Publishing. The HRRS of (c) MoSe2 and (d) Mo(S0.3Se0.7)2. Reproduced with permission from Ref. [51]. Copyright 2017 American Physical Society (color online).

  • Figure 8

    (a) The schematic diagram of the three-dimensional orientation of a graphene sheet expressed by the Euler angle (θ, φ, ε). The left part is the schematic diagram of VG array on a substrate with a tilting angle α. (b) HRRS of VG array with θ=0°. Inset shows the sample’s scanning electron microscopy (SEM) image. (c) HRRS of VG array with 0°<θ<90°. (d) Correlation of ρ for G mode with the tilting angle α. The inset is a cross-sectional SEM image of VG array with an oblique angle θ0. Adapted with permission from Ref. [21]. Copyright 2021 American Chemical Society (color online).

  • Figure 9

    (a) The absorption spectrum of monolayer MoS2 from a supercontinuum light source. The peak positions of A and B excitons are at 655 and 610 nm. The laser excitation wavelengths at 633 and 532 nm are used for HRRS measurements. The on-resonance 633 nm excitation is close to both the A and B exciton peaks, while the off-resonance 532 nm excitation is far from both exciton peaks. HRRS of exfoliated monolayer MoS2 for (b) off-resonance 532 nm excitation and (c) on-resonance 633 nm excitation. Adapted with permission from Ref. [15]. Copyright 2017 American Physical Society (color online).

  • Figure 10

    (a) Illustration of the movement of the atoms for the LO phonon mode of MoS2. The resulting electric field is indicated with red arrows. The Fröhlich interaction means the interaction between the macroscopic electric field and an exciton. (b) Schematic of the Raman scattering processes for monolayer MoS2 excited by circularly polarized light with specific helicity and the helicities of the Raman scattering light for off-excitonic resonance (left) and on-resonance (right) excitations. Reproduced with permission from Ref. [17]. Copyright 2020 American Chemical Society. The HRRS of monolayer MoS2 in a field-effect device with polymer electrolyte gate at T=300 K under (c) off-resonance excitation, low charge carrier density; (d) on-resonance excitation, low charge carrier density; (e) on-resonance excitation, high charge carrier density. The filled curves are Lorentzian fits to the data. (f–h) Polar plots of the normalized amplitude of the fitted peaks are shown in the panel above the respective plot versus the rotation of the quarter-wave plate. The black arrows mark 0°. 0° and 90° correspond to the σ+σ+ and σ+σ− configurations, respectively. Figure (a, c–h) reproduced with permission from Ref. [16]. Copyright 2019 Springer Nature (color online).

  • Figure 11

    (a–c) HRRS of the out-of-plane A1g vibration mode of monolayer CrI3 at 60 K (a), and the two ferromagnetic states, spin-up (b) and spin-down (c) at 15 K. Adapted with permission from Ref. [73]. Copyright 2020 Springer Nature. HRRS of the out-of-plane Ag mode of VI3 thin layer for the two parallel configurations (σ+σ+ and σσ−) measured at 60 K (d) and 1.7 K (e). (f) The variation of Raman helicity polarization (ρ=(Iσ+σ+Iσσ)/(Iσ+σ++Iσσ)) as a function of temperature. Inset shows the tuning of Raman helicity polarization by a full cycle of the magnetic field. The arrows show the field sweep direction. Adapted with permission from Ref. [74]. Copyright 2020 American Chemical Society (color online).

  • Figure 12

    (a) Illustration of the experimental design and the mechanism. The chiral Raman scattered light of WS2 couples to the SPPs in Ag nanowire. (b) The HRRS of WS2, excited by 633 nm laser. The Raman imaging of the A1g mode under excitation of (c) left-handed and (d) right-handed circularly polarized light for different excitation spot positions. Adapted with permission from Ref. [23]. Copyright 2019 American Physical Society (color online).

  • Table 1   The conservation law of PAM for the helicity change of the first-order Raman modes for several point groups. Adapted with permission from Ref. [13]. Copyright 2018 American Physical Society

    Point group

    Vibration mode

    N

    Nv

    Degeneracy

    mvph

    p for the helicity change

    D2h

    Ag

    2

    2

    Nondegenerate

    0

    ±1

    D2h

    B1g

    2

    2

    Nondegenerate

    0

    ±1

    D3h

    E′

    3

    1

    Degenerate

    0, ±1

    ±1, ±2, ±3

    D4h

    B1g

    4

    2

    Nondegenerate

    0

    ±1

    D4h

    B2g

    4

    2

    Nondegenerate

    0

    ±1

    D6h

    E2g

    6

    2

    Degenerate

    0, ±1

    ±1

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