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:

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