Fermi Surface. The properties of a material is guided by the arrangement of atoms within the material, which reflects the shape of a Fermi surface, thus the Fermi surface has a direct correlation with properties of materials.

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Fermi Surface

A Fermi surface is a term used in solid state physics that describes a theoretical interface which defines the allowable energy states of electrons in a solid. In otherwords it describes a surface of constant energy in k-space. It was derived by the Italian physicist Enrico Fermi, who along with the English physicist P.A.M Dirac developed the statistical theory of electrons [1]. Fermi surfaces are of great interest due to their beneficial nature of being able to predict the electrical, thermal, optical and magnetic properties of crystalline metals, semiconductors being the most valuable. Fermi surfaces can be seen as being closely related to the atomic lattice [1], which is the underlying feature of all crystalline solid, and to energy band theory, which depicts the distribution of electrons in such crystals.

Electrons within a solid can only lie within two areas, the valence band, where they are bound into a specific position and the conduction band where they are free to move. However electrons may only enter the conduction band at higher energies. Each electron has a specific energy within a band, which can be related to its momentum. At absolute zero, the energy