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First of all, this is something that is very difficult for me to conceptualize (k-space, the BZ, and related topics). Also, currently reading Kittel. I know that the Fermi surface is defined as the surface in k-space where all of the highest occupied electron states live. So, the surface represents the electrons states that are most easily excited. I also know that the shape can't be used to predict some important phenomena, such as superconductivity.

So why do we care about the shape–among other properties like nesting surfaces, crossings, etc.–of the Fermi surface?

Is it possible to look at a Fermi surface and say, "yep, this is going to have [insert macroscopic property here]"?

Tobias Fünke
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Kevmeister
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    Possibly of interest: https://chemistry.stackexchange.com/questions/58847/why-is-copper-a-better-conductor-than-iron and https://physics.stackexchange.com/questions/360204/notion-of-anisotropic-fermi-surface/489167#489167 and https://physics.stackexchange.com/questions/464381/can-i-consider-fermi-surface-as-a-band-diagram-drawn-in-3d/464906#464906 – Jon Custer Oct 29 '21 at 17:34

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