In this paper, we study the following fractional nonlinear Schrödinger equation \(\begin{aligned} (-\Delta )^{s}u+V(x)u=\lambda u+a|u|^{q}u, \quad \hbox {in } \mathbb {R}^2, \end{aligned}\) where \(s\in (\frac{1}{2}, 1)\) , \(q\in (0, 2s)\) , \(V: \mathbb {R}^{2}\rightarrow \mathbb {R}\) is a trapping potential, \(\lambda \in \mathbb {R}\) and \(a>0\) . For any fixed \(a>a^{*}:=\Vert Q\Vert _{2}^{2s}\) , where Q is the unique positive radial solution of \((-\Delta )^{s}u+su-|u|^{2s}u=0\) in \(\mathbb {R}^{2}\) , by constructing a suitable trial function to analyze the precise energy estimates, we obtain the concentration behaviour and symmetry breaking of the normalized solutions of the above equation as \(q\nearrow 2s\) .
