I understand that superconductors have zero resistivity, however, I wonder if there is a relation between resistivity and the work function of a specific material so that a superconductor has zero (or a low value) work function. If so, photons with very long wavelengths can release electrons from the surface of a superconductor. Am I right?


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The work function is a measure of how much energy it takes to completely remove an electron from a material and send it into free space, and costs on the order of 1000-5000 meV of energy. The resistance is a measure of how much energy is needed to move electrons infinitesimally ($\omega\sim0$) within the material where any individual electron will only receive an energy many, many orders of magnitude lower than the work function, unless you drive with very high currents/voltages.

In superconductors, the resistance is zero until you excite electrons at energies on the order of a few meV (thousands of times smaller than the work function). So no, super conductors do not have zero work function. In fact, if they did, they would be inherently unstable because electrons would constantly leave the superconductor and go into free space.

However, your question is still a good one. The energy cost for jumping from one superconductor to another can be negligibly small and fully coherent. This type of effect lays at the heart of Josephson junctions and tunneling of electrons between two superconductors


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