实验与计算对比的文字
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@@ -13,10 +13,11 @@ This approximation is based on the fact that
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the dispersion of these phonons is continuous and very close to the #sym.Gamma point,
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and has been widely adopted in the literature @_n-sic_2008.
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Symmetry analysis pointed out that
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these phonons correspond to twelve irreducible representations of the C#sub[6v] point group
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(2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2], see appendix for details).
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In which the B#sub[1] representation is Raman inactive,
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while other phonons are potentially observable in Raman experiments.
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these phonons correspond to twelve irreducible representations of the C#sub[6v] point group and were named accrodingly
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(A#sub[1]-1 to A#sub[1]-2, B#sub[1]-1 to B#sub[1]-4, E#sub[1]-1 to E#sub[1]-2, and E#sub[2]-1 to E#sub[2]-4,
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see appendix for details).
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Among which the B#sub[1] representation is Raman inactive,
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while other eight modes are potentially observable in Raman experiments.
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However, it should be noted that the intensity of Raman scattering from each mode
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cannot be inferred from symmetry considerations alone.
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@@ -39,73 +40,50 @@ Furthermore, the absolute amplitude differences among atoms of the same type wit
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and only their vibrational directions were considered.
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This enables a preliminary estimation of the Raman tensor magnitudes prior to expensive first-principles calculations,
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with the results summarized in @table-nopol.
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Our analysis gave the result that the E#sub[2]-3 mode
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should possess a much higher Raman scattering intensity than the others,
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which is consistent with experimental and first-principles calculation results in the following text.
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Our analysis gave the result that the E#sub[2]-3 mode possess a much higher Raman intensity
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and should be clearly observable in Raman experiments,
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while the observability of other modes depends on their frequencies were well-separated or not
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and could only be confirmed by further first-principles calculations or experiments.
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Our result showed that
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the high Raman intensity of this mode arises from the constructive interference of contributions from all bonds,
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in contrast to other negligible-polar modes where contributions tend to cancel each other out.
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#include "table-nopol.typ"
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我们做了计算，估计哪些峰可以看到、哪些峰看不到。
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实验看到了7个峰，比别人多。
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使用第一性原理计算得到了声子频率和拉曼张量的大小。
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我们的计算表明，E#sub[2]-1 E#sub[2]-2 E#sub[1]-1 A#sub[1]-1 E#sub[2]-3 模式的拉曼强度较高，并且被报道在绝大多数的拉曼实验中可以看到。
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A#sub[1]-2 被报道在一些实验中可以观测到而在另外一些实验中不可以观测到(cite)。
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我们的计算表明它在面内偏振下拉曼散射强度非常弱，但在 z 轴偏振下有可观测的强度；
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因此在正入射拉曼实验中可能难以看到，但在侧入射时通过选取合适的偏振配置应该可以观察到。
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E#sub[1]-2 和 E#sub[2]-4 模式位于最强模式 E#sub[2]-3 附近，且具有很弱的拉曼强度（分别为最强模式的0.1%和0.6%），在报道的实验中都不可见。
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E#sub[1]-2 与最强模式 E#sub[2]-3 表示不同，我们认为，通过选取合适的偏振配置，可能可以在实验中观察到。
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我们做了实验，看到了其中 7 个峰，比别人的实验要多。
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为了解释实验结果，我们进行了第一性原理计算。
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E#sub[2]-1 E#sub[2]-2 E#sub[1]-1 A#sub[1]-1 E#sub[2]-3 这几个模式在大多数实验中都可以看到，这是因为它们有较高的拉曼强度且位置比较分散。
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A#sub[1]-2 在一些实验中可以观察到而在另外一些实验中不可以观察到(cite)，这是因为它在面内偏振下拉曼散射强度非常弱，但在 z 轴偏振下有可观测的强度；
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因此在我们的正入射拉曼实验中它很难被看到，但在侧入射时通过选取合适的偏振配置应该可以观察到。
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E#sub[1]-2 和 E#sub[2]-4 距离最强模式 E#sub[2]-3 很近，且具有很弱的拉曼强度，在报道的实验中都不可见。
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在我们的实验中，通过选取合适的偏振配置和延长积分时间，E#sub[2]-3 被压制后，E#sub[1]-2 也被观察到了。
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我们的实验第一次指出了 E#sub[1]-2 峰，并且与计算和理论吻合较好。
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The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods.
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The results showed that
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the E#sub[2]-1, E#sub[2]-2, E#sub[1]-1, A#sub[1]-1, and E#sub[2]-3 modes possess relatively high Raman intensities
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The calculated phonon frequencies were in good agreement with experimental values,
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with a slight underestimation of 2-5%,
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which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
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The calculated Raman tensors were also consistent with both experimental and theoretical results.
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Among negligible-polar modes, the E#sub[2]-3 mode showed the highest Raman intensity,
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followed by four modes with lower intensities that were also visible in normal incidence Raman experiments,
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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.
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The E#sub[1]-2 mode and E#sub[2]-4 mode were not visible in our Raman experiments,
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as they were located close to the most intense E#sub[2]-3 mode (only about 10 cm#super[-1] away)
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with very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively).
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Additionally,
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the A#sub[1]-2 mode had only a very weak Raman intensity under the incident light with in-plane polarization
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(only 0.01),
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but showed an observable intensity when the polarization is along the z-axis (1.78).
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Thus, it was not typically observed in normal incidence Raman experiments (cite),
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but could be clearly detected in edge incidence configurations in our experiments.
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我们做了实验，比别人多看到了几个峰；和计算结果比对良好。
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拉曼散射实验在衬底上进行，并与第一性原理计算结果进行了比较。
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在我们的实验中，除了 E#sub[2]-4 以外的弱极性模式对应的拉曼散射峰都被观察到，多于其它实验；
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这包括 A#sub[1]-2 在 xzzx 下可以观察到，
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以及 E#sub[1]-2 在 xzyx 下通过额外延长积分时间而观察到。
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计算的声子频率与实验数据有很好的吻合，误差在 2-5% 之间，这个误差可能是由于 PBE 泛函对原子间力的低估（cite）。
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计算的拉曼张量也与实验和理论结果基本一致。
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The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods,
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and the results were compared with both experimental data and theoretical predictions (@table-nopol).
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The calculated phonon frequencies were in good agreement with experimental values,
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with a slight underestimation of 2-5%,
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which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
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The calculated Raman tensors were also consistent with both experimental and theoretical results.
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Among negligible-polar modes, the E#sub[2]-3 mode showed the highest Raman intensity,
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followed by four modes with lower intensities that were also visible in normal incidence Raman experiments,
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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.
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The E#sub[1]-2 mode and E#sub[2]-4 mode were not visible in our Raman experiments,
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as they were located close to the most intense E#sub[2]-3 mode (only about 10 cm#super[-1] away)
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with very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively).
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Additionally,
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the A#sub[1]-2 mode had only a very weak Raman intensity under the incident light with in-plane polarization
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(only 0.01),
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but showed an observable intensity when the polarization is along the z-axis (1.78).
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Thus, it was not typically observed in normal incidence Raman experiments (cite),
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but could be clearly detected in edge incidence configurations in our experiments.
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Raman experiments were established and seven negligible-polar phonon peaks were observed,
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which is more than all previous experiments (where only five or six peaks were typically reported).
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To further understand our experimental results,
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first-principles calculations were performed,
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and the result was compared with experimental data.
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Our calculation showed that the mode of E#sub[2]-1, E#sub[2]-2, E#sub[1]-1, A#sub[1]-1 and E#sub[2]-3
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had relatively high Raman intensities and well-separated frequencies,
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making them observed in our experiments as well as most previous experiments.
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The A#sub[1]-2 mode had only a very weak Raman intensity with in-plane polarization (e.g., zyy#overline[z]),
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while showed an observable intensity when the polarization is along the z-axis (e.g., xzzx).
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Thus, it could be observed clearly in our edge incidence experiments (xzzx),
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but hardly seen in normal incidence configurations.
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This peek was reported to be observable in some experiments (cite) but not in others (cite),
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our calculation provided an explanation for this discrepancy.
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The E#sub[1]-2 and E#sub[2]-4 modes are calculated
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to be located close to the most intense E#sub[2]-3 mode (< 10 cm#super[-1] away)
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and exhibit very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively),
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making them hard to observe in reported experiments.
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However, in our experiments,
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with edge incidence configuration (zxy#overline[z]) and extended integration time,
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the E#sub[2]-3 peek was suppressed and the E#sub[1]-2 mode was also observed.
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Our experiments reported the E#sub[1]-2 peak for the first time,
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and the experimental results were in good agreement with both calculations and theoretical analysis.
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#include "figure-raman.typ"
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@@ -48,6 +48,10 @@
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// E2 E2 A1 E2
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[0.228 #pm 0.051], [-0.260 #pm 0.025], m2[-0.279 #pm 0.016], [0 #linebreak() (used for calibration)],
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)},
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caption: [Negaligible-polarized Phonons at $Gamma$ Point.],
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caption: [
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Negaligible-polarized Phonons at $Gamma$ Point.
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The calculated phonon frequencies had a slight underestimation of 2-5% comparing to experimental values,
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which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
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],
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)<table-nopol>]
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