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In the Peltier effect, current through a 2-metal junction will cause an increase or decrease in temperature as electrons traveling through 1 metal are higher in energy than metals in the other level, and the increase or decrease in electron energy crossing the junction will come out of or contribute to the thermal energy of the system.

Assuming these are both metals and not semiconductors, why would the conduction band energy levels of the 2 metals be different? When we first touched the 2 metals together, their fermi levels became equal, and because there's no valence-conduction band separation (or, in some sense, they're the same thing), there are conducting states for both metals available at/ directly above the fermi level. For this reason, I expect the conducting electrons in both metals to be identically close to the fermi level energy because there's no gap between the fermi level and the conducting states.

It's not clear to me, then, why the conducting electron energy levels between both metals would be discontinuous, as the Peltier effect seems to require.

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