Plot graphs, shade areas and lines with Tikz

Question

How could I do the following plot with Tikz:

I'm new on Latex (and Tikz), thanks for your help!

Answer 1

You can do this real quick:

\documentclass{article}
\usepackage{tikz,enumitem,multicol}
\tikzset{axline/.style={-stealth}}
\begin{document}
    \begin{tikzpicture}[line width=1pt]
        \draw[dotted]
            (-1,1) --++ (-60:1.5)
            (-1,1) --++ (120:2)
            (1,1) --++ (-120:1.5)
            (1,1) --++ (60:2);
        \fill[olive!50] (-1,1) to[out=-60,in=180] (0,0) to[out=0,in=-120] (1,1) --cycle;
        \draw[axline] (-2,0) -- (2,0) node[below right]{$k$};
        \draw[axline] (0,0) -- (0,3) node[above right]{$E$};
        \draw
            (-1,1) -- (1,1)
            (-1,2pt) --++ (0,-4pt) node[below]{$-k_F$}
            (1,2pt) --++ (0,-4pt) node[below]{$k_F$};
        \draw (-1.7,2) to[out=-45,in=120] (-1,1) to[out=-60,in=180] (0,0) to[out=0,in=-120] (1,1) to[out=60,in=-135] (1.7,2);

    \begin{scope}[xshift=7cm]   
        \path (-1,1) node[left]{$-\nu_F^k$} --++ (-60:4) coordinate (1);
        \path (1,1) node[right]{$+\nu_F^k$}--++ (-120:4) coordinate (2);

        \fill[olive!50] (-1,1) --(1) -- (2) -- (1,1) --cycle;
        \draw[axline] (-2,0) -- (2,0) node[below right]{$k$};
        \draw[axline] (0,0) -- (0,3) node[above right]{$E$};
        \draw
            (-1,1) -- (1,1)
            (1) --++ (120:6) node[left]{$L$}
            (2) --++ (60:6) node[right]{$R$}
            (-1,2pt) --++ (0,-4pt) node[below]{$-k_F$}
            (1,2pt) --++ (0,-4pt) node[below]{$k_F$};

    \end{scope}
\end{tikzpicture}

\end{document}