Electron-hole gas density in different materials

[Stanley514]

If we connect a two metals with different Fermi levels electrons will start to flow from metal with higher Fermi level to a lower one. until metal with lower Fermi level will get negatively charged and the process will stop.
But what if we connect a two materials with different Fermi levels, but equal conductivity of both electrons and
holes? Will holes start to get transferred between these materials too, and if yes, how exactly?

 

[DrDu]

How do you define a hole in a metal?

 

[Stanley514]

I do not know, but does positive Hall coefficient in metals exists?

 

[DrDu]

It does, for example in aluminium. But this does not mean that the charge carriers are holes.

 

[Stanley514]

It does, for example in aluminium. But this does not mean that the charge carriers are holes.

What then?