Fermi Surface Analysis

The information gained from current investigations of Fermi surfaces is extraordinarily precise. It is therefore particularly valuable (quite apart from its direct value in the interpretation of transport properties, etc.) as a test of band structure theories, or as a reliable basis for semiempirical band theory. 

The principal technique for Fermi surface analysis is the use of the de Haas-van Alphen effect. The oscillations of the magnetization of a metal in a strong magnetic field are separated from the background and analyzed into component periodicities AH. Then each periodicity so detected is directly related to an extremal cross-sectional area A of the Fermi surface, perpendicular to the applied field. The effect may be explained in terms of the quantization of the energy associated with the motion of an electron in the applied field.  

By varying the direction of the applied field, the extremal cross sections can be determined as functions of this direction. Clearly for a simple centrosymmetric Fermi surface, such as that of an alkali metal 

The de Haas-van Alphen method is not always applicable. In particular, the effect is not detectable in alloys of concentration more than a fraction of a per cent. (The scattering time must be greater than the time necessary to complete an orbit in the magnetic field.) Other techniques, much less accurate, but applicable to cases where the de Haas-van Alphen effect fails, are of considerable current interest. Two examples are the use of positron annihilation and the identi- 

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Pattison, P. and Williams, B. (1976) Fermi surface parameters from fourier analysis of Compton profiles, Solid State Commun., 20, 585-588. 

Our analysis is, however, not complete in any respect. For instance, as the large difference in Fermi momenta renders the BCS-type condensation in the classical 2SC phase difficult, it seems to be worthwhile to consider other possibilities. Among others we thereby think of a crystalline phase, deformed Fermi surfaces [32, 35], spin-1 pairing [20] or the gapless 2SC [33, 34] or CFL phase [60], We conclude that whether quark matter exists in hybrid or... 

The transport properties of nanowires are of technological importance and have attracted significant attention in the recent years. Band structure gives simple solution to the analysis of the ballistic transport of periodic nanowires because the number of the bands crossing the Fermi surface is equal the number of quantum of conductance. However, the situation in nanocontacts is more complicated [112],... 

In the present contribution, we will examine the fundamentals of such an approach. We first describe some basic notions of the tight-binding method to build the COs of an infinite periodic solid. Then we consider how to analyze the nature of these COs from the viewpoint of orbital interaction by using some one-dimensional (ID) examples. We then introduce the notion of density of states (DOS) and its chemical analysis, which is especially valuable in understanding the structure of complex 3D sohds or in studying surface related phenomena. Later, we introduce the concept of Fermi surface needed to examine the transport properties of metallic systems and consider the different electronic instabilities of metals. Finally, a brief consideration of the more frequently used computational approaches to the electronic structure of solids is presented. 

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