  We consider the energy super critical nonlinear Schr\"odinger equation
$$i\pa_tu+\Delta u+u|u|^{p-1}=0$$ in large dimensions $d\geq 11$ with
spherically symmetric data. For all $p>p(d)$ large enough, in particular in the
super critical regime, we construct a family of smooth finite time blow up
solutions which become singular via concentration of a universal profile with
the so called type II quantized blow up rates. The essential feature of these
solutions is that all norms below scaling remain bounded. Our analysis fully
revisits the construction of type II blow up solutions for the corresponding
heat equation, which was done using maximum principle techniques following.
Instead we develop a robust energy method, in continuation of the works in the
energy and mass critical cases. This shades a new light on the essential role
played by the solitary wave and its tail in the type II blow up mechanism, and
the universality of the corresponding singularity formation in both energy
critical and super critical regimes.
