I want to draw the following picture. And so far my code is the following:
\begin{tikzpicture}[xscale=1.5,yscale=1.5]
\draw [->] (0,-2) --(0,2) node [left] {${\rm Im}(p)$};
\draw [->] (-2,0) -- (2,0) node [below] {${\rm Re}(p)$};
\draw [thick] (1,-1.8) --(1,1.8);
\draw [fill] (0,-1.8) --(1,-1.8); \draw [fill] (0,1.8) --(1,1.8);
\draw [black] (0,1.8) arc [radius=1.8, start angle=90, end angle = 270];
\draw [fill] (0.5,1) circle [radius=.05];
\draw [fill] (0.5,0.5) circle [radius=.05];
\draw [fill] (0.5,-0.5) circle [radius=.05];
\draw [fill] (0.5,-1) circle [radius=.05];
\node at (1.15,-0.15) [] {$\sigma$};
\draw [fill] [<-] (0.65,1.1)--(1.5,1.5);
\end{tikzpicture}
I would appreciate if anyone could help me draw the direction arrows and is it possible to include text in the graph?
Thank you in advance for your help.