Complex-hyperbolic Kleinian groups of large critical exponents

Using Livne's example, we construct a sequence of discrete isometry groups $(\Gamma_n)$ of the complex-hyperbolic plane whose critical exponents are strictly smaller than $4$, but converge to $4$, as $n\rightarrow\infty$. This shows there is no gap in the values of critical exponents for complex-hyperbolic Kleinian groups.