# How do I make a straight skeleton with qtree?

I have the following tree:

\documentclass{article}
\usepackage{qtree}

\begin{document}

\Tree [.A [.a ] [.B [.A ] [.a ] ] ]

\end{document}


and I would like the A -> B -> A skeleton to be a straight line (meaning, the angle between the branches should be different, so that A -> B -> A goes straight down).

Also, I would like to have a dashed curvy line connecting between the two "a"s. Are those two things possible?

(I don't mind using tikz-qtree instead if needed.)

I did this with Forest because it makes it easy. Perhaps tikz-qtree offers something similar, but Forest is generally more capable in this regard.
\documentclass[border=10pt]{standalone}