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In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied electron states from unoccupied electron states at zero temperature. [1] 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 periodicity of these oscillations can be measured, and in turn can be used to determine the cross-sectional area of the Fermi surface. [8] If the axis of the magnetic field is varied at constant magnitude, similar oscillations are observed. The oscillations occur whenever the Landau orbits touch the Fermi surface.
The Pomeranchuk instability is an instability in the shape of the Fermi surface of a material with interacting fermions, causing Landau’s Fermi liquid theory to break down. It occurs when a Landau parameter in Fermi liquid theory has a sufficiently negative value, causing deformations of the Fermi surface to be energetically favourable.
The Fermi momentum can also be described as =, where = /, called the Fermi wavevector, is the radius of the Fermi sphere. [ 4 ] n {\displaystyle n} is the electron density. These quantities may not be well-defined in cases where the Fermi surface is non-spherical.
Here, E is measured with respect to the Fermi level E F, and E k with respect to vacuum so = + where , the work function, is the energy difference between the two referent levels. The work function is material, surface orientation, and surface condition dependent.
The border between occupied and unoccupied momentum states, the Fermi surface, is arguably the most significant feature of the electronic structure and has a strong influence on the solid's properties. [2] In the free electron model, the Fermi surface is a sphere. With ACAR it is possible to measure the momentum distribution of the electrons.
The concept of a nesting vector is illustrated in the Figure for the famous case of chromium, which transitions from a paramagnetic to SDW state at a Néel temperature of 311 K. Cr is a body-centered cubic metal whose Fermi surface features many parallel boundaries between electron pockets centered at and hole pockets at H.
The "frequency" of the magnetoresistance oscillations indicate areas of extremal orbits around the Fermi surface. The area of the Fermi surface is expressed in teslas. More accurately, the period in inverse Teslas is inversely proportional to the area of the extremal orbit of the Fermi surface in inverse m/cm.