Semiclassical states for a magnetic nonlinear Schrödinger equation with exponential critical growth in $mathbb{R}^{2}$

This paper is devoted to the magnetic nonlinear Schr"{o}dinger equation [ Big(rac{arepsilon}{i} abla-A(x)Big)^{2}u+V(x)u=f(| u|^{2})u ext{ in } mathbb{R}^{2}, ] where $arepsilon>0$ is a parameter, $V:mathbb{R}^{2} ightarrow mathbb{R}$ and $A: mathbb{R}^{2} ightarrow mathbb{R}^{2}$ are continuous functions and $f:mathbb{R} ightarrow mathbb{R}$ is a $C^{1}$ function having exponential critical growth. Under a global assumption on the potential $V$, we use variational methods and Ljusternick-Schnirelmann theory to prove existence, multiplicity, concentration, and decay of nontrivial solutions for $arepsilon>0$ small.