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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク fermi surface ： ウィキペディア英語版 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.〔N. Ashcroft and N.D. Mermin, ''Solid-State Physics'', ISBN 0-03-083993-9〕〔W.A. Harrison, ''Electronic Structure and the Properties of Solids'', ISBN 0-486-66021-4〕 〔(VRML Fermi Surface Database )〕〔J. M. Ziman, ''Electrons in Metals: A short Guide to the Fermi Surface'' (Taylor & Francis, London, 1963), ASIN B0007JLSWS.〕 ==Theory== Consider a spinless ideal Fermi gas of $N$ particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy $\backslash epsilon\_i$ is given by $\backslash langle\; n\_i\backslash rangle\; =\backslash frac,$ where, *$\backslash left\backslash langle\; n\_i\backslash right\backslash rangle$ is the mean occupation number of the $i^$ state *$\backslash epsilon\_i$ is the kinetic energy of the $i^$ state *$\backslash mu$ is the ''internal chemical potential'' (at zero temperature, this is the maximum kinetic energy the particle can have, i.e. Fermi energy $\backslash epsilon\_F$) *$T$ is the absolute temperature *$k\_B$ is the Boltzmann constant Suppose we consider the limit $T\backslash to\; 0$. Then we have, By the Pauli exclusion principle, no two fermions can be in the same state. Therefore, in the state of lowest energy, the particles fill up all energy levels below $\backslash epsilon\_F$, which is equivalent to saying that ''$\backslash epsilon\_F$ is the energy level below which there are exactly $N$ states. In momentum space, these particles fill up a sphere of radius $p\_F$, the surface of which is called the Fermi surface〔K. Huang, ''Statistical Mechanics'' (2000), p. 244〕 The linear response of a metal to an electric, magnetic or thermal gradient is determined by the shape of the Fermi surface, because currents are due to changes in the occupancy of states near the Fermi energy. Free-electron Fermi surfaces are spheres of radius $k\_F\; =\; \backslash frac$ determined by the valence electron concentration where $\backslash hbar$ is the reduced Planck's constant. A material whose Fermi level falls in a gap between bands is an insulator or semiconductor depending on the size of the bandgap. When a material's Fermi level falls in a bandgap, there is no Fermi surface. Materials with complex crystal structures can have quite intricate Fermi surfaces. The figure illustrates the anisotropic Fermi surface of graphite, which has both electron and hole pockets in its Fermi surface due to multiple bands crossing the Fermi energy along the $\backslash vec\_z$ direction. Often in a metal the Fermi surface radius $k\_F$ is larger than the size of the first Brillouin zone which results in a portion of the Fermi surface lying in the second (or higher) zones. As with the band structure itself, the Fermi surface can be displayed in an extended-zone scheme where $\backslash vec$ is allowed to have arbitrarily large values or a reduced-zone scheme where wavevectors are shown modulo $\backslash frac$ (in the 1-dimensional case) where a is the lattice constant. In the three-dimensional case the reduced zone scheme means that from any wavevector $\backslash vec$ there is an appropriate number of reciprocal lattice vectors $\backslash vec$ subtracted that the new $\backslash vec$ now is closer to the origin in $\backslash vec$-space than to any $\backslash vec$. Solids with a large density of states at the Fermi level become unstable at low temperatures and tend to form ground states where the condensation energy comes from opening a gap at the Fermi surface. Examples of such ground states are superconductors, ferromagnets, Jahn–Teller distortions and spin density waves. The state occupancy of fermions like electrons is governed by Fermi–Dirac statistics so at finite temperatures the Fermi surface is accordingly broadened. In principle all fermion energy level populations are bound by a Fermi surface although the term is not generally used outside of condensed-matter physics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「fermi surface」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.