Why would electrons cross a cross section when there is no potential difference?
First, there is a small change you need to make. 


  electrons going from left to right are more than the ones going from
  right to left, and then there will be NET NON-ZERO electrical current.


With that done, you should be aware that free electrons, like any particle, are incapable of being perfectly at rest (except at absolute zero). That is, they will exhibit random motion, usually called thermal motion. With no potential applied, the average overall, or net, motion will be zero, and so will the current.