From 549ba6f87a8862ae8f9b1321a293ad1b4d3110d2 Mon Sep 17 00:00:00 2001 From: Haonan Chen Date: Mon, 5 Jan 2026 16:55:02 +0800 Subject: [PATCH] =?UTF-8?q?=E8=B0=83=E6=95=B4=E5=86=85=E5=AE=B9?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- paper/result/perfect/default.typ | 62 ++++++++++++++++---------------- 1 file changed, 31 insertions(+), 31 deletions(-) diff --git a/paper/result/perfect/default.typ b/paper/result/perfect/default.typ index c48020c..2fa9a4a 100644 --- a/paper/result/perfect/default.typ +++ b/paper/result/perfect/default.typ @@ -4,10 +4,17 @@ Raman-active phonon modes were categorized into two groups, according to the distinct behaviors arising from different electrical polarities, - including eight negligible-polarity modes (i.e., having zero or very weak electrical polarity), + including eight negligible-polarity modes (possessing zero or very weak polarity), and three strong-polarity modes. The negligible-polarity modes should exhibit minimal dependence on the wavevector direction, - while the strong-polarity modes should show significant anisotropy. + whereas the strong-polarity modes should show significant anisotropy. +Consequently, the negligible-polarity modes were named + according to their irreducible representations at the #sym.Gamma point and in order of increasing frequency, + including A#sub[1]-1 to A#sub[1]-2, E#sub[1]-1 to E#sub[1]-2, and E#sub[2]-1 to E#sub[2]-4. +In contrast, the strong-polarity modes were designated based on their polarization relative to the wavevector. +Since the laser incidence direction was restricted to the x-z plane in this work, these modes were labeled as follows: + TO-xz (polarized in the x-z plane and roughly perpendicular to the wavevector), + TO-y (polarized along the y-axis), and LO (roughly parallel to the wavevector). // This distinction was clearly illustrated in @figure-discont, // where the phonon dispersion relations of negligible-polarity modes (gray solid lines) // were roughly continuous and flat at the #sym.Gamma point, @@ -16,12 +23,6 @@ The negligible-polarity modes should exhibit minimal dependence on the wavevecto // In contrast, the strong-polarity modes (colored solid lines) displayed discontinuities at the #sym.Gamma point, // resulting in #sym.tilde 10 cm#super[-1] frequency shifts and distinct different vibration patterns // under different incidence configurations. -Consequently, the negligible-polarity modes were named - according to their irreducible representations at the #sym.Gamma point and in order of increasing frequency, - including A#sub[1]-1 to A#sub[1]-2, E#sub[1]-1 to E#sub[1]-2, and E#sub[2]-1 to E#sub[2]-4. -In contrast, the strong-polarity modes were named according to their vibration directions and incidence configurations, - including TO-zOx (vibrating in the zOx plane and roughly perpendicular to the incidence direction), - TO-y (vibrating along the y-axis), and LO (vibrating roughly parallel to the incidence direction). Peaks corresponding to seven Raman-active negligible-polarity phonons were observed in our experiments (only the E#sub[2]-4 mode was not observed, see @figure-raman), @@ -50,17 +51,6 @@ However, the E#sub[1]-2 mode was observable in our experiments of y(zx)#overline Our experiments reported the observation of the E#sub[1]-2 peak for the first time, and explained the discrepancy among previous experiments and ours with the help of our calculations. -// TODO: 图中标注强调是拉曼活性的模式 -// TODO: b 图的标题歪了 - -#include "figure-raman.typ" - -#include "table-nopol.typ" - -#include "table-pol.typ" - -// TODO: 合并两个表格到一页，删除 polar 中的多余信息 - It is noteworthy that the large variation in Raman tensor magnitudes among different modes was not yet theoretically understood. For example, the Raman tensor of the E#sub[2]-3 mode was substantially larger @@ -77,25 +67,35 @@ By analyzing the local environment of individual atoms, denoted as $epsilon_i$, $eta_i$, and $zeta_i$，where $i in {1, 2, 5, 6}$, and $|epsilon_i| + |eta_i| + |zeta_i| << |a_i|$ was assumed). Detailed derivations were provided in @appd-predict, with results summarized in @table-nopol and @table-pol. -Notably, the E#sub[2]-3 mode was the only mode that retains the $a_i$ term, +Notably, the E#sub[2]-3 mode was the only mode that retains the $a_i$ term,determine which indicating a constructive interference of contributions from the local environment of individual atoms. This stood in contrast to other negligible-polarity modes where such contributions tend to cancel out, explaining the exceptionally high Raman tensor magnitude observed for the E#sub[2]-3 mode. +The mode frequency dependence on the wavevector were thoroughly investigated, + including both thoretical calculations (@figure-rev a), experimental measurements (@figure-rev b) + and their comparisons (@figure-rev c). +The E#sub[2]-3 mode frequency was calculated to remaine distinct in all incidence geometries (@figure-rev a), + making it an ideal calibration reference for experiments. +Meanwhile, + the E#sub[2]-1, E#sub[2]-2 and A#sub[1]-1 mode showed a relatively larger dependence on the incidence direction, + which is in good agreement with our experimental observations (@figure-rev c). + + +// TODO: 图中标注强调是拉曼活性的模式 +// TODO: b 图的标题歪了 + +#include "figure-raman.typ" + +#include "table-nopol.typ" + +#include "table-pol.typ" + +// TODO: 合并两个表格到一页，删除 polar 中的多余信息 + -模式频率在倒空间中的依赖性被仔细研究并展示在@figure-rev 中。 -各个模式在 gamma 点附近的色散关系被计算出来并被展示在图 a 中。 -在弱极性模式中，频率偏移在 1cm -1 以内；在极性模式中，频率的变化达到了 10 cm -1 量级。其中， -E2 模式没有极性，因此在 Gamma 点处无色散；离开 Gamma 点越远，频率对入射方向的依赖越大。 -这意味着相比于绿光，使用紫外光入射时，正入射与侧入射的频率差异会更大。 -A1 的极性不为零，它们的色散呈现瓣状，意味着无论使用什么激光波长，频率的变化都比较接近。 -E2-3 的频率几乎不变并且在任何角度的入射实验中都清晰可见 ，可以被选定为实验中的校准参考。 -图b给出了实验结果，其中 E2-1 由于较弱，导致样本标准差较大；E2-2 和 A1-1 的散射强度较强，因此标准差较小。 -图c对比了实验与计算的结果，可以看到两者吻合较好，只有 A1-1 的实验结果明显大于计算结果。 -这可以归结为一些原因。 -我们的研究对比了入射方向对极性较弱的声子模式的影响并在理论上进行了解释，以实现对拉曼光谱的更精确分析，并为掺杂和载流子对光谱影响的分析做了准备。