Fermi surface

In condensed matter physics, the Fermi surface is an abstract boundary in reciprocal space useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. 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.

Consider a spinless ideal Fermi gas of ${\displaystyle N}$ particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy ${\displaystyle \epsilon _{i}}$ is given by

${\displaystyle \langle n_{i}\rangle ={\frac {1}{e^{(\epsilon _{i}-\mu )/k_{B}T}+1}},}$

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