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In this paper, we study the semiclassical limit for the stationary magneticnonlinear Schr\"odinger equation \begin{align}\label{eq:initialabstract}\left(i \hbar \nabla + A(x) \right)^2 u + V(x) u = |u|^{p-2} u, \quad x\in\mathbb{R}^{3},\end{align}where $p\textgreater{}2$, $A$ is a vector potentialassociated to a given magnetic field $B$, i.e $\nabla \times A =B$ and $V$ is anonnegative, scalar (electric) potential which can be singular at the originand vanish at infinity or outside a compact set.We assume that $A$ and $V$satisfy a cylindrical symmetry. By a refined penalization argument, we provethe existence of semiclassical cylindrically symmetric solutions of upperequation whose moduli concentrate, as $\hbar \to 0$, around a circle. Weemphasize that the concentration is driven by the magnetic and the electricpotentials. Our result thus shows that in the semiclassical limit, the magneticfield also influences the location of the solutions of$(\ref{eq:initialabstract})$ if their concentration occurs around a locus, nota single point.

Nonlinear Schr{\"o}dinger equation: concentration on circles driven by an external magnetic field