Tl:DR: These sorts of compound are extremely unstable largely due to ring strain, so it is unlikely that it will be synthesized.
Long Answer:
The study of the chemistry of experimentally known nitrogen homocycle was initially limited to two classes of compounds: 1.saturated three membered rings (triaziridines) 2. pentazoles (N,H). Later, the study was expanded to three nitrocycles: cyclotetrazene dianion ($\ce{N4^2-}$), the neutral 1,3-dihydrocyclotetrazene ($\ce{N2H2N2}$), and the cyclotetrazane dication
($\ce{N4H4^{2-}}$).
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/kOXyy.png)
These species were experimentally studied and because they are highly unstable, they study is confined to pure theory only. For more details, refer to the paper:
Zandwijk, van, G., Janssen, R. A. J., & Buck, H. M. (1990). 6pi Aromaticity in four-membered rings. Journal of the American Chemical Society, 112(11), 4155-4164. DOI: 10.1021/ja00167a009