Concept

Fermi surface

Summary
In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called fermiology. Theory Consider a spin-less ideal Fermi gas of N particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy \epsilon_i is given by :\langle n_i\rangle =\frac{1}{e^{(\epsilon_i-\mu)/k_{\rm B}T}+1}, where, *\left\langle n_i\right\rangle is the mean occupation number of the i^{th} state *\epsilon_i is the kinetic energy of the i^{th
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