From bc2c067fc11100c15d263f91f4aff8627ec60507 Mon Sep 17 00:00:00 2001 From: chn Date: Mon, 26 May 2025 11:50:07 +0800 Subject: [PATCH] --- test-typst/section/appendix/default.typ | 2 ++ .../non-polar => appendix}/predmode.typ | 0 .../section/perfect/non-polar/default.typ | 33 ++++++++++++------- 3 files changed, 24 insertions(+), 11 deletions(-) rename test-typst/section/{perfect/non-polar => appendix}/predmode.typ (100%) diff --git a/test-typst/section/appendix/default.typ b/test-typst/section/appendix/default.typ index 985f955..18e6348 100644 --- a/test-typst/section/appendix/default.typ +++ b/test-typst/section/appendix/default.typ @@ -1,6 +1,8 @@ #import "@preview/physica:0.9.5": pdv, super-T-as-transpose #show: super-T-as-transpose +#include "predmode.typ" + The center principle is to assign the Raman tensor (i.e., change of polarizability caused by atomic displacement) to each atom in the unit cell. This including the following steps: diff --git a/test-typst/section/perfect/non-polar/predmode.typ b/test-typst/section/appendix/predmode.typ similarity index 100% rename from test-typst/section/perfect/non-polar/predmode.typ rename to test-typst/section/appendix/predmode.typ diff --git a/test-typst/section/perfect/non-polar/default.typ b/test-typst/section/perfect/non-polar/default.typ index 0143483..ec7f4c5 100644 --- a/test-typst/section/perfect/non-polar/default.typ +++ b/test-typst/section/perfect/non-polar/default.typ @@ -38,17 +38,17 @@ However, whether a mode is sufficiently strong to be experimentally visible // TODO: maybe it is better to assign Raman tensor to each bond, instead of atom We propose a method to estimate the magnitudes of the Raman tensors of these phonons by symmetry analysis. -The method only takes the vibration directions of each atom in each phonon mode, - leaving the amplitudes unconsidered (see appendix for details), - and the result was summarized in @table-predmode. -In the Raman tensors in @table-predmode, - $a_i$ corresponding to the change of polarizability caused by movement of the Si atoms in A and C layers, - $epsilon_i$, $eta_i$ and $eta_i$ corresponding to the difference between different bilayers and different atoms. -Due to the similarity of environment in different bilayers and around different atoms, - the absolute values of $epsilon_i$, $eta_i$ and $zeta_i$ are expected to be much smaller than that of $a_i$, - thus the Raman tensors containing $a_i$ are expected to be much larger than those not containing $a_i$. - -#include "predmode.typ" +This method relies on the following two assumptions: +firstly, the change of polarizability caused by the movement of the atom in different locations + is mainly determined by its first- and second-nearest neighbors, + and the farther neighbors have relatively small contributions. +Secondly, the change of polarizability caused by Si atom and C atom is roughly connected by the reversal of the charge, + other factors (mass, bond length, etc.) contribute only a small value. +Therefore, the vibration mode with the most intense Raman intensity + could be estimated before the first-principle calculation and experiment, + and the Raman tensors of the calculated phonon modes could also be estimated + without further first-principle calculations. +Please see appendix for details. The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods, and the results are compared with experiment and theory (@table-nopol). @@ -74,6 +74,17 @@ The peek at 796 and 980 are caused by strong-polar phonons which will be discuss Besides, there are small peeks at xxx, which could not be explained in perfect 4H-SiC and will be discussed in the next section. +The method only takes the vibration directions of each atom in each phonon mode, + leaving the amplitudes unconsidered (see appendix for details), + and the result was summarized in @table-predmode. +In the Raman tensors in @table-predmode, + $a_i$ corresponding to the change of polarizability caused by movement of the Si atoms in A and C layers, + $epsilon_i$, $eta_i$ and $eta_i$ corresponding to the difference between different bilayers and different atoms. +Due to the similarity of environment in different bilayers and around different atoms, + the absolute values of $epsilon_i$, $eta_i$ and $zeta_i$ are expected to be much smaller than that of $a_i$, + thus the Raman tensors containing $a_i$ are expected to be much larger than those not containing $a_i$. + + // TODO: 将一部分 phonons 改为 phonon modes // 在论文中我们这样来称呼：phonon 对应某一个特征向量，而 modes 对应于一个子空间。 // 也就是说，简并的里面有两个或者无数个 phonon，但只有一个 mode