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\begin{document}

\preprint{APS/123-QED}

\title{Title Title Title}

\author{Ann Author}\altaffiliation[Also at ]{Physics Department, XYZ University.}

\begin{abstract}
An article usually includes an abstract, a concise summary of the work
covered at length in the main body of the article. 
\end{abstract}

\maketitle

\section{Introduction}\label{sec_introduction}

SiC has many excellent properties and wide applications.

Phonons in SiC are important. They can influence the properties of SiC and can be used to characterize the materials.

There are many existing studies on phonons in SiC, but they have some shortcomings.

In this paper, we do some things. We do something for the first time.

\section{Methods}\label{sec_methods}

\section{Results}\label{sec_results}

\subsection{Phonons in Perfect 4H-SiC}

% 拉曼活性的声子模式对应于 Gamma 点附近的声子模式。
% 根据这些声子模式在拉曼实验中的表现，我们将这些声子分成三个部分。

Raman scattering peeks correspond to phonons located near $\Gamma$ point in reciprocal space.
We classified these phonons into three categories according to their behavior in Raman scattering:
  (1) phonons could not be observed in Raman scattering spectrum,
    either because they are Raman inactive or their scattering intensity is too weak;
  (2) phonons could be observed in Raman scattering spectrum and with weak or no polarities,
    their frequencies were independent of the direction of the incident light;
  (3) strong polar phonons,
    which were visible in Raman scattering spectrum,
    and their frequencies depend on the direction of the incident light.

% 我们计算了 4H-SiC 在 A-Gamma 和 Gamma-M 上的声子频率，如图和附录1所示。
% 在拉曼散射中，起作用的模式都是那些非常接近于 Gamma 的模式
%   （如图中的点所示，分为位于 1/50 和 1/100 处，这两条线分别对应于拉曼散射在 z 方向入射/散射和 y 方向入射/散射）。
% 大多数声子模式在 Gamma 附近都是连续的，这使得它们的频率对入射光的方向不敏感；
%   然而，少数声子具有较强的极性，这使得声子之间存在长程的库伦相互作用（引用文献），并导致 gamma 附近的频率不同，如图中的某两条线所示。
% 据此，我们将无缺陷的 4H-SiC 的声子分成三类：
%   无拉曼活性或拉曼散射强度太弱的模式，它们在拉曼散射谱上不可见；
%   拉曼散射强度足够大且极性不强的模式，它们在拉曼散射谱上可以看到，且频率与拉曼入射光方向无关；
%   极性声子，它们在拉曼散射谱上可以看到，不仅频率与入射光方向有关，而且可与载流子发生一些相互作用。

Phonons in defect-free 4H-SiC are calculated at A-$\Gamma$ and $\Gamma$-M,
  as shown in Figure \ref{fig:phonon} and Table \ref{tab:phonon}.
Raman active phonons are very close to $\Gamma$,
  as indicated by the points in the figure.
Because of the consistency of the most phonon modes near $\Gamma$,
  most of the phonon frequencies are insensitive to the direction of the incident light.
However, some phonons have strong polarities,
  which leads to long-range Coulomb interactions between phonons,
  and results in different frequencies near $\Gamma$,
  as shown by the two lines in the figure.
Thus, we divide the phonons of defect-free 4H-SiC into three categories:
  (1) Raman inactive or too weak Raman intensity,
    which are invisible in the Raman scattering spectrum;
  (2) Raman active phonons with strong polarities,
    which are visible in the Raman scattering spectrum,
    and their frequencies are independent of the direction of the incident light;
  (3) Polar phonons,
    which are visible in the Raman scattering spectrum,
    and their frequencies depend on the direction of the incident light,
    and can interact with carriers.

% insert fig1.svg
\begin{figure}[h]
  \centering
  \includegraphics{../画图/声子不连续/整体图.pdf}
  \caption{Phonon dispersion of defect-free 4H-SiC.}
  \label{fig:phonon}
\end{figure}


\subsubsection{}

\appendix

\section{A little more on appendixes}

\begin{sidewaystable}
  \centering
  \caption{Title}
  \begin{tabular}{ | C{2cm} | C{2cm} | C{2.5cm} | C{3cm} | C{3cm} | C{3cm} | C{3cm} | C{2cm} | C{2cm} | }
    \hline
    \textbf{Number of Phonon} \
      & \textbf{Vibration Direction} \
      & \textbf{Representation in Group $\mathrm{C_{6v}}$} \
      & \textbf{Might Visible in Polarization} \
      & \textbf{Raman Intensity (a.u.)} \
      & \textbf{Wavenumber (Simulation) ($\mathrm{cm^{-1}}$)} \
      & \textbf{Wavenumber (Experiment) ($\mathrm{cm^{-1}}$)} \
      & \textbf{Electrical Polarity} \
      & \textbf{Visible in Common Raman Experiment} \\
    \hline
    % E2
    1 & x & \tworow{$\mathrm{E_2}$} & xy & \tworow{0.17} & \tworow{190.51} & \tworow{195.5} &
      \tworow{None} & \tworow{Yes} \\ \cline{1-2} \cline{4-4}
    2 & y & & xx \& yy & & & & & \\ \hline
    % E2
    3 & x & \tworow{$\mathrm{E_2}$} & xy & \tworow{1.13} & \tworow{197.84} & \tworow{203.3} &
      \tworow{None} & \tworow{Yes} \\ \cline{1-2} \cline{4-4}
    4 & y & & xx \& yy & & & & & \\ \hline
    % E1
    5 & x & \tworow{$\mathrm{E_1}$} & xz & \tworow{2.43} & \tworow{257.35} & \tworow{265.7} &
      \tworow{Weak} & \tworow{Yes} \\ \cline{1-2} \cline{4-4}
    6 & y & & yz & & & & & \\ \hline
    % 2B1
    7 & z & $\mathrm{B_1}$ & - & 0 & 389.96 & - & None & No \\ \hline
    8 & z & $\mathrm{B_1}$ & - & 0 & 397.49 & - & None & No \\ \hline
    % A1
    \tworow{9} & \tworow{z} & \tworow{$\mathrm{A_1}$} & xx \& yy & 2.83 &
      \tworow{591.90} & \tworow{609.5} & \tworow{Weak} & \tworow{Yes} \\ \cline{4-5}
    & & & zz & 1.79 & & & & \\ \hline
    % E1
    10 & x & \tworow{$\mathrm{E_1}$} & xz & \tworow{0.09} & \tworow{746.91} & \tworow{-} &
      \tworow{Weak} & \tworow{No} \\ \cline{1-2} \cline{4-4}
    11 & y & & yz & & & & & \\ \hline
    % E2
    12 & x & \tworow{$\mathrm{E_2}$} & xy & \tworow{88.54} & \tworow{756.25} & \tworow{776} &
      \tworow{None} & \tworow{Yes} \\ \cline{1-2} \cline{4-4}
    13 & y & & xx \& yy & & & & & \\ \hline
    % E2
    14 & x & \tworow{$\mathrm{E_2}$} & xy & \tworow{0.50} & \tworow{764.33} & \tworow{-} &
      \tworow{None} & \tworow{No} \\ \cline{1-2} \cline{4-4}
    15 & y & & xx \& yy & & & & & \\ \hline
    % A1
    \tworow{16} & \tworow{z} & \tworow{$\mathrm{A_1}$} & xx \& yy & 0.01 &
      \tworow{812.87} & \tworow{839} & \tworow{Weak} & \tworow{Yes} \\ \cline{4-5}
    & & & zz & 1.78 & & & & \\ \hline
    % 2B1
    17 & z & $\mathrm{B_1}$ & - & 0 & 885.68 & - & None & No \\ \hline
    18 & z & $\mathrm{B_1}$ & - & 0 & 894.13 & - & None & No \\ \hline
    % E1+A1
    19-21 & \multicolumn{6}{c|}{Depend on direction of incident and scattered light} & Strong & Yes \\ \hline
  \end{tabular}
  \label{tab:phonon}
\end{sidewaystable}


\end{document}

