Lets say we have two pieces of metal with different electron-hole pressure. In both metals electrons and holes are NOT going to recombine. If we will connect those pieces of metal, will electron-hole density tend to equalize between the two? If yes how fast will it happen and which mechanism is responsible for it? If you ask how could we even in theory obtain such pieces of metal, I could give example. If metal has mixed electron-hole conductivity then when we heat one end of large metal piece both electrons and holes will flow to the cold end. Then we could cut the large piece in two with help of laser and obtain two smaller pieces with different electron-hole concentration.