Is there a connection on $\mathbb{R}^2 \setminus \{0\}$ for which all operators of parallel transports are in the form $$\begin{pmatrix}a&-b\\b&a \end{pmatrix}$$

but the parallel transport along circles with center at origin depends on the radius of the circle. That is two different circle have different parallel transports.

This question is motivated by this paper.