Is it possible to have a flowing current of positive particles? Hydrogen ions are basically protons, can protons flow in a current?

A beam of protons would be a good example.

 

You should also be aware of the notion of a hole, which is a positively charged quasi-particle,

There are proton conducting materials used in hydrogen fuel cells. Unfortunately the only thing I know about them is that they exist.

 

My lab did a side project assisting another group in characterizing some exciton conducting materials though. Excitons are bound states of electron hole quasiparticles and electrons. Some pretty interesting stuff IMO.

Thanks guys, gives me some more places to look while surfing.