Fermi surface

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. A ⊥ = 2 π e Δ H ℏ c {displaystyle A_{perp }={frac {2pi eDelta H}{hbar c}}} . 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. Consider a spin-less ideal Fermi gas of N {displaystyle N} particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy ϵ i {displaystyle epsilon _{i}} is given by ⟨ n i ⟩ = 1 e ( ϵ i − μ ) / k B T + 1 , {displaystyle langle n_{i} angle ={frac {1}{e^{(epsilon _{i}-mu )/k_{ m {B}}T}+1}},}