Amorphous Fermi surface

In an imperfect crystal or amorphous material the wavenumber k is not a good quantum number, and if Ak/k becomes comparable to unity then the concept of a Fermi surface has little meaning. Nevertheless, at zero temperature a sharp Fermi energy must still exist. 

The rest of this section is devoted to a discussion of amorphous semiconductors, which play a special role within the field of the electronic structures of disordered materials for two reasons. First, as discussed below, the transport properties of amorphous semiconductors are dominated by carriers within kT of the transition energy where the states are uniquely characteristic of disordered materials. Secondly, the amorphous semiconductors are all covalent, and it is the electronic structures of the covalent materials which should be most sensitive to disorder. Simple metals, where the electrons interact weakly with the atoms via small pseudopotentials are free-electron-like near the Fermi surface both as solids and liquids. Insulating materials with large band gaps but narrow bands again have electronic structures relatively insensitive to order. The covalent semiconductors correspond to intermediate cases of maximal sensitivity of electronic structure to atomic structure and composition. 

In two recent papers Allgaier (1969 1970) has emphasised the dangers in extrapolating ideas particular to ordered solids into the liquid and amorphous states. For example, suppose that a liquid exists in which it is permissible to use an energy-momentum description of the electron state. Since the E-k relationship is the same in all directions, the Fermi surface is a sphere enclosing all the valence (free) electrons. Within this framework, the Hall coefficient is given by... 

The electronic properties of simple metal amorphous alloys are expected to behave according to the free-electron model since the spatial isotropy that should exist in homogeneous amorphous alloys would lead to a spherical Fermi surface. However, substitution of A1 by R and/or M species raises the fundamental question as to how... 

A.K. Singh and Srivastava (1979-1983, 1985) have obtained results similar to those of Schiffmacher (1983) and Gasgnier (1982). They showed that such polytypic structures migh be not only formed with pure Gd, Tb, Ho, Er and Y elements, but also with (Gd, Tb), (Gd, Ho) and (Gd, Er) intermetalhcs. However the conclusions of Singh and Srivastava do not appear to be clearly established. Indeed, they explain the formation of modulated phases in terms of the reduction of electron energies which is manifested in the type of contact between the Fermi surface and the Brillouin zone. But since the films are initially amorphous and crystallize instantaneously under a focused e-beam such a hypothesis seems irrelevant first because the Fermi surface does not exist for an amorphous material, and second, because in their theory the aufiiors claim that this Fermi surface is spherical, which is far from being true. 

Various interesting properties of 4f-electron systems such as CK and HF compounds have been generally studied using crystalline materials, where there is also periodicity of 4f electrons. The formation of the Fermi surface from 4f-electron bands is essential to many, if not all of these cooperative properties. Therefore, such behaviors are not expected to occur in disordered alloys without translational symmetry where the 4f electrons have non-Bloch-type states. However, interesting behaviors have recently been observed in Ce-based structurally disordered materials. Here, we introduce amorphous CeRu system as a typical example. Crystalline CeRu2 compoimd is one of the famous itinerant 4f-electron materials to show SC (T = 6.3 K, y = 27 mj/mol K ) (Hedo et al., 1998 Matthias et al., 1958). On the other hand, amorphous fl-CeRu also shows FlF-like behavior in the Ce-rich side and SC in the Ru-rich side (Homma et al., 1997). 

In addition, quasicrystal material is also a promising thermoelectric material. Quasicrystals have special fivefold and tenfold symmetries which cannot exist in crystal and amorphous materials. A large number of small gaps near the Fermi surface exist in these compounds, which can be destroyed with the temperature variation. Then the shape of the Fermi surface will change, and finally enhance the... 

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