How would you define "super inductor" as being different from a standard inductor :?: - perhaps one with a very large inductance for its size?
The only special inductor I'm aware of is a superconducting inductor which has a pure inductance with no series resistance. But the available ones need to be cooled to cryogenic temperatures to achieve the zero resistance, and I don't think they are particularly small for their value of inductance.
I know that - in some cases - the active and artificial unit "FDNR" is also called "super-capacitor". The impedance of this two-opamp circuit is Z=-1/(D*w^2).
(Thus, it is negative and real).
In a similar way one could define and realize an active circuit (with two opamps) that has an impedance Z=-L*w^2. Such a circuit could be called "super-inductor".
Active inductors can be made to have a value of thousands of henries.
An active inductor can be constructed around an op amp and capacitor. A real coil would have to be large and bulky in order to have such a high henry value.
The active inductor provides the response of an inductor in the sense that it impedes a change in current flow.
It cannot create the 'kick' (elevated voltage spike) which a coil can deliver.
Nevertheless, even a thousands-of-Henrys-inductor behaves like an inductor.
In contrast, the active circuit "super-inductor" (also called "frequency-dependent negative conductanc", FDNC) has an impedance that
a) is negative, and
b) is proportional to the sqare of the frequency (therefore: super...)