Hello, I have a question about conduction in metals.(adsbygoogle = window.adsbygoogle || []).push({});

I guess you all know a common pedagogical picture where an electron bands are drawn as ~ cosine curves in 1D or E_0 - cos(k_x) - cos(k_y) in 2D.

Now, in metals , we were told that the Fermi surface passes through the band. Therefore, electrons "under" Fermi surface can go to states above Fermi surface and thus conduct electricity. That sounds good so far.

We also defined an effective mass as m* ~ [itex](\frac{d^2E}{dk^2})^{-1}[/itex]. But what happens if Fermi surface crosses the cosine band exactly in the middle (or where it is linear locally), then the double derivative is zero, and m* = infinity. How can these electrons move anywhere or even conduct? I see possible resolutions to this question:

1) electrons further away from such surface can still move to other states, but this will be a bad conductor (because m* for those nearby electrons will be huge)

2) in real metals Fermi surface doesn't cross bands where there is no curvature?

3) maybe conduction in not related to m*, but to how many electrons go above the Fermi surface ?

4) maybe m* definition breaks down far away from Brillouin zone boundaries?

5) maybe we don't define effective mass for metals? only for semiconductors?

6) something else?

Thanks in advance

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# Infinite effective mass in metals

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