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The Fermi surface is something that separates unfilled orbitals from filled orbitals. I found in some documents that electrical properties are related to the shape of the Fermi surfaces. I am not clear about the significance of the Fermi surface shape. Can anyone explain and give examples or introduce more documents about Fermi surface? When we explore electrical properties, do we need to consider only the Fermi surface near the Fermi level?

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Many electronic properties, particularly of metals, are directly related to the Fermi surface shape. Screening properties and conductivity are especially affected by the Fermi surface. For example, the explanation for why copper is a better conductor than iron involves the disconnected nature of iron's Fermi surface, see e.g. this Chem.SE answer. Recall that the low-energy excitations dominate transport properties (at least in the linear response regime), and these are near the Fermi surface by definition. For more examples of the impact of Fermi surface shapes you may have a look at S B Dugdale: Life on the edge: a beginner's guide to the Fermi surface. Phys. Scr. 91, 053009 (2016).

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