Normalized ground state solutions for Kirchhoff equations with critical exponential growth in <inline-formula><tex-math id="M1">$ \mathbb{R}^{2 } $</tex-math></inline-formula>

We are concerned with normalized solutions of the following Kirchhoff equation$\begin{align*} -M\left(\int_{\mathbb{R}^2}|\nabla u|^2\mathrm{\; d} x\right)\Delta u = \lambda u+b(x) f(u), x \in \mathbb{R}^2, \end{align*} $with $ L^2 $-constraint $ \int_{\mathbb{R}^2} u^2 \mathrm{\; d} x = a $, where $ a>0 $, $ M \in C([0, +\infty)) $, $ \lambda \in \mathbb{R} $ is a Lagrange multiplier, the potential $ b \in \mathcal{C}^1\left(\mathbb{R}^{2}, (0, \infty)\right) $ and the nonlinearity $ f \in \mathcal{C}(\mathbb{R}, \mathbb{R}) $ satisfies the critical exponential growth at infinity in the sense of the Trudinger-Moser inequality and the mass supercritical growth at the origin. By virtue of the variational approach, we prove the existence of ground state normalized solutions to the problem above for any $ a>0 $.