Normalized ground state solutions of nonlinear Schrödinger equations involving exponential critical growth

We are concerned with the following nonlinear Schrödinger equation \begin{eqnarray*} \begin{aligned} \begin{cases} -Δu+λu=f(u) \ \ {\rm in}\ $\mathbb{R}$^{2},\ u\in H^{1}($\mathbb{R}$^{2}),~~~ \int_{$\mathbb{R}$^2}u^2dx=ρ, \end{cases} \end{aligned} \end{eqnarray*} where $\rho >0$ is given, $\lambda \in \mathbb{R}$ arises as a Lagrange multiplier and $f$ satisfies an exponential critical growth. Without assuming the Ambrosetti-Rabinowitz condition, we show the existence of normalized ground state solutions for any $\rho >0$. The proof is based on a constrained minimization method and the Trudinger-Moser inequality in ${\mathbb{R}}^2$.