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@@ -75,40 +75,28 @@ E#sub[1]-2 和 E#sub[2]-4 模式位于最强模式 E#sub[2]-3 附近,且具有
使得它们在实验光谱中难以区分。
此外A#sub[1]-2 模式在基面极化配置xx yy仅为 0.01)中具有非常弱的拉曼强度,这导致它在正入射的拉曼实验中通常不可见;
但当偏振沿 z 轴时1.78)则显示出可观测的强度。
E#sub[1]-1 模式在理论上无法在正入射中观察到,但在实验中仍然可以看到一个小峰。
这被认为是因为入射光并非完全沿z轴入射由于衬底斜切和共聚焦汇聚角。通过向不同方向倾斜衬底我们可以使这个峰变高或变低如附图所示这印证了我们的猜想。
// E#sub[1]-1 模式在理论上无法在正入射中观察到,但在实验中仍然可以看到一个小峰。
// 这被认为是因为入射光并非完全沿z轴入射由于衬底斜切和共聚焦汇聚角。通过向不同方向倾斜衬底我们可以使这个峰变高或变低如附图所示这印证了我们的猜想。
The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods,
and the results are compared with both experimental data and theoretical predictions (@table-nopol).
The calculated phonon frequencies are in good agreement with experimental values,
and the results were compared with both experimental data and theoretical predictions (@table-nopol).
The calculated phonon frequencies were in good agreement with experimental values,
with a slight underestimation of 2-5%,
which may be attributed to the known tendency of the PBE functional underestimation interatomic forces (cite).
The calculated Raman tensors are also consistent with both experimental and theoretical results.
Among negligible-polar modes, the E#sub[2] mode at 776 cm#super[-1] in experiment (mode 8)
exhibits the highest Raman intensity,
followed by four modes with lower intensities that are also experimentally visible,
including the E#sub[2] modes at 195.5 cm#super[-1] (mode 1) and 203.3 cm#super[-1] (mode 2),
the E#sub[1] mode at 269.7 cm#super[-1] (mode 3), and the A#sub[1] mode at 609.5 cm#super[-1] (mode 6).
The E#sub[1] mode calculated at 746.91 cm#super[-1] (mode 7)
and the E#sub[2] mode calculated at 756.25 cm#super[-1] (mode 9)
are predicted to have much weaker Raman intensities and are located close to the most intense mode (mode 8),
making them indistinguishable in experimental spectra.
Additionally, the A#sub[1] mode calculated at 812.87 cm#super[-1] (mode 10)
exhibits a very weak Raman intensity in the basal-plane polarized configurations (xx and yy, only 0.01)
but shows an observable intensity when the polarization is along the z-axis (1.78).
Since most Raman experiments are performed in a back-scattering configuration with light incident along the z-direction
(i.e., with in-plane polarization)
and with photon energies much lower than the band gap,
this mode is typically not observed (cite).
However, it should become detectable if the incident light has a polarization component along the z-direction
(as in our experiment),
or when the excitation wavelength approaches resonance conditions (cite).
The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods, and the results are compared with both experimental data and theoretical predictions (@table-nopol). The calculated phonon frequencies are in good agreement with experimental values, with a slight underestimation of 25%, which may be attributed to the known tendency of the PBE functional to underestimate interatomic forces (cite). The computed Raman tensor magnitudes are also consistent with both experimental and theoretical results.
Among the negligible-polar modes, the E#sub[2] mode at 776 cm#super[-1] (mode 8, experimental value) exhibits the highest Raman intensity. Four additional modes with lower but clearly observable intensities are also identified: the E#sub[2] modes at 195.5 cm#super[-1] (mode 1) and 203.3 cm#super[-1] (mode 2), the E#sub[1] mode at 269.7 cm#super[-1] (mode 3), and the A#sub[1] mode at 609.5 cm#super[-1] (mode 6). The E#sub[1] mode at 746.91 cm#super[-1] (mode 7) and the E#sub[2] mode at 756.25 cm#super[-1] (mode 9) are predicted to have much weaker Raman intensities and are located close to the most intense mode (mode 8), making them difficult to resolve in experimental spectra.
Additionally, the A#sub[1] mode at 812.87 cm#super[-1] (mode 10) exhibits a very weak Raman intensity in the basal-plane polarization configurations (xx and yy, only 0.01), but shows a significantly higher intensity (1.78) when the polarization is aligned along the z-axis. Since most Raman measurements are performed in a backscattering geometry with incident light along the z-direction (i.e., in-plane polarization) and photon energies well below the band gap, this mode is typically not observed (cite). However, it may become detectable if the incident light has a polarization component along the z-direction (as in our experiment), or under resonance excitation conditions (cite).
which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
The calculated Raman tensors were also consistent with both experimental and theoretical results.
Among negligible-polar modes, the E#sub[2]-3 mode exhibited the highest Raman intensity,
followed by four modes with lower intensities that were also visible in normal incidence Raman experiments,
including the E#sub[2]-1 mode, the E#sub[2]-2 mode, the E#sub[1]-1 mode, and the A#sub[1]-1 mode.
The E#sub[1]-2 mode and E#sub[2]-4 mode were not visible in our Raman experiments,
as they were located close to the most intense E#sub[2]-3 mode (only about 10 cm#super[-1] away)
with very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively).
Additionally,
the A#sub[1]-2 mode exhibited a very weak Raman intensity under the incident light with in-plane polarization
(only 0.01),
but showed an observable intensity when the polarization is along the z-axis (1.78).
Thus, it was not typically observed in normal incidence Raman experiments (cite),
but could be clearly detected in edge incidence configurations in our experiments.
// TODO: 这里缺两个引用
非零长度的波矢i.e. 参与散射的声子不在 Gamma 点)导致不同入射配置的峰位具有微小但可观测的差异,如色散图所示。
相比于正入射肩入射时E2-1与E2-2的间距会减小、E2-2会展宽E2-3会展宽同时略微蓝移动。我们的计算结果为xxx实验结果为xxx。