comparision of the Bruhat-tits tree with lattices in $\mathbb{R}^2$ || request for resources

Question

I am writing an expository paper on the comparision of the bruhat-tits tree with lattices in $\mathbb{R}^2$ which are in bijection with the upper half-plane modulo the group $PSL_2(\mathbb{Z})$. But so far I haven't been able to find any resources for the same, especially on "lattices in $\mathbb{R}^2$ which are in bijection with the upper half-plane modulo the group $PSL_2(\mathbb{Z})$". Would anyone happen to know any good papers / notes on the same?