Fermi surface

▪ physics

      in solid-state physics, abstract interface that defines the allowable energies of electrons (electron) in a solid. Named for Enrico Fermi (Fermi, Enrico), who along with P.A.M. Dirac (Dirac, P.A.M.) developed the statistical theory of electrons, the Fermi surface is important for characterizing and predicting the thermal, electrical, magnetic, and optical properties of crystalline metals and semiconductors. It is closely related to the atomic lattice, which is the underlying feature of all crystalline solids, and to electron energy band theory in such materials.

      According to the theory, electrons in a solid lie within valence bands or conduction bands, where they are respectively bound into position or free to move. Each electron has a specific momentum and energy within a band. However, at absolute zero (−273.15 °C, or −459.67 °F), the energy may not exceed a value called the Fermi energy, which therefore divides allowed electronic states of momentum and energy from those that cannot be occupied. In an abstract three-dimensional space where the coordinate axes are the components of momentum, this condition defines a volume whose surface—the Fermi surface—separates occupied states within the volume from empty ones without it.

      The shape of the Fermi surface reflects the arrangement of atoms within a solid and is thus a guide to the properties of the material. In some metals, such as sodium and lithium, the Fermi surface is more or less spherical (a Fermi sphere), which indicates that the electrons behave similarly for any direction of motion. Other materials have Fermi surfaces that resemble American footballs or take on more-intricate shapes, typically with large bumps and depressions. In every case the dynamic behaviour of electrons residing at or near the Fermi surface is crucial in determining electrical, magnetic, and other properties and how they depend on direction within the crystal.

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