The Hall effect includes the transverse (to the flow of current) electric field set up by the charges which accumulate on the edges, to counter the magnetic component of the Lorentz force acting on them to move towards the edges. These charges can be both positive holes and negative electrons in semiconductors. If the concentration of any one kind of carriers is very high as compared to other(n-type and p-type), the electric field set up can be understood from the accumulation of charges (negative for n-type and vice versa) at one edge due to the Lorentz force acting on it. But if the intrinsic semiconductors contain the same density of the positive holes and the electrons, both move in opposite directions to contribute to the current but the lorentz force acting on them is in the same direction. And hence their deflection owing to the magnetic field is in the same direction.
This means, both the positive and negative charges are deflected towards the same edge and hence cannot produce a net charge density and therefore should not be able to set up an countering electric field and the Hall potential. Does this mean that they will continuosly keep being deflected towards one of the edge and keep annihilating at that edge, never setting up a counter electric field?
If the difference in mobility (or the effective mass) makes any difference, what would happen if they have the same mobility and consequently the same effective mass?