Global counterexamples to uniqueness for a Calderón problem with $C^k$ conductivities

Let $\mathrm{\Omega }\subset R^n$, $n\ge 3$, be a fixed smooth bounded domain, and let $\gamma$ be a smooth conductivity in $\bar{\mathrm{\Omega }}$. Consider a non-zero frequency ${\lambda }_0$ which does not belong to the Dirichlet spectrum of $L_{\gamma }=-\mathrm{d}\mathrm{i}\mathrm{v}(\gamma \mathrm{\nabla }\cdot )$. Then, for all $k\ge 1$, there exists an infinite number of pairs of non-isometric $C^k$ conductivities $({\gamma }_1,{\gamma }_2)$ on $\bar{\mathrm{\Omega }}$, which are close to $\gamma$ such that the associated DN maps at frequency ${\lambda }_0$ satisfy \begin{equation*} Λ_{γ_1,λ_0} = Λ_{γ_2,λ_0}. \end{equation*}