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In this paper, using variational methods, we establish the existence and multiplicity of multi-bump solutions for the following nonlinear magnetic Schrödinger equation    $$\begin{aligned} -(\nabla +\mathrm{i} A(x))^2 u+(\lambda V(x)+Z(x))u=f(\vert u\vert ^{2})u\quad \text {in}\, \,{\mathbb {R}}^{2}, \end{aligned}$$  - ( ∇ + i A ( x ) ) 2 u + ( λ V ( x ) + Z ( x ) ) u = f ( | u | 2 ) u in R 2 , where    $$\lambda &gt;0$$  λ &gt; 0 ,  f ( t ) is a continuous function with exponential critical growth, the magnetic potential    $$A:{\mathbb {R}}^2\rightarrow {\mathbb {R}}^2$$  A : R 2 → R 2 is in    $$L^{2}_{loc}({\mathbb {R}}^2)$$  L loc 2 ( R 2 ) and the potentials  V ,    $$Z:{\mathbb {R}}^{2}\rightarrow {\mathbb {R}}$$  Z : R 2 → R are continuous functions verifying some natural conditions. We show that if the zero set of the potential  V  has several isolated connected components    $$\Omega _{1}, \ldots , \Omega _{k}$$  Ω 1 , … , Ω k such that the interior of    $$\Omega _{j}$$  Ω j is non-empty and    $$\partial \Omega _{j}$$  ∂ Ω j is smooth, then for    $$\lambda &gt;0$$  λ &gt; 0 large enough, the equation has at least    $$2^{k}-1$$  2 k - 1 multi-bump solutions.

Multi-bump solutions for the nonlinear magnetic Schrödinger equation with exponential critical growth in $${\mathbb {R}}^{2}$$