Nesting, Fermi surface

Besides magnetic perturbations and electron-lattice interactions, there are other instabilities in solids which have to be considered. For example, one-dimensional solids cannot be metallic since a periodic lattice distortion (Peierls distortion) destroys the Fermi surface in such a system. The perturbation of the electron states results in charge-density waves (CDW), involving a periodicity in electron density in phase with the lattice distortion. Blue molybdenum bronzes, K0.3M0O3, show such features (see Section 4.9 for details). In two- or three-dimensional solids, however, one observes Fermi surface nesting due to the presence of parallel Fermi surface planes perturbed by periodic lattice distortions. Certain molybdenum bronzes exhibit this behaviour. 

Thus, measurements of k and Cp provided first hints for possible nodes in the energy gap. More detailed investigations, however, point to different scenarios, in particular those based on Fermi-surface nesting. Also there are discrepancies between experimental data and the (s + g)-wave description. 

Figure 7.7. The Peierls distortion of a one-dimensional metallic chain, (a) An undistorted chain with a half-filled band at the Fermi level (filled levels shown in bold) has an unmodulated electron density, (b) The Peierls distortion lowers the symmetry of the chain and modulates the electron density, creating a CDW and opening a band gap at the Fermi level, (c) The Fermi surface nesting responsible for the electronic instability.

The concept of Fermi surface does not only play a key role in understanding the dimensionality of the transport properties of metals but also in explaining the electronic instabilities of partially filled band systems. When a piece of a Fermi surface can be translated by a vector q and superimposed on another piece of the Fermi surface, this Fermi surface is said to be nested by the vector q. Since the Fermi surface of (92a) consists of two parallel fines, it is nested by an infinite number of wave vectors, two examples of which are shown in (96). In discussing Fermi surface nesting, it is important to consider Fermi surfaces in the entire reciprocal space, which is achieved by repeating the Fermi surface pattern of the first... 

In discussing metal-to-insulator and metal-to-supercon-ductor transitions, it is convenient to describe the insulating and the superconducting states as a consequence of a perturbation on the metallic state. In the following, we first examine why Fermi surface nesting is likely to induce a metal-to-insulator transition from the viewpoint of band... 

Metals and semiconductors have positive and negative slopes in their electrical resistivity p) vs. temperature (T) curves as schematically shown in (109) and (110), respectively. By definition, the Fermi surface disappears when a band gap opens at the Fermi level. If the Fermi surface nesting is complete, all the Fermi surface is removed by the appropriate orbital mixing. However, if the Fermi surface nesting is incomplete, only the nested portion of the surface is removed by orbital mixing. The unnested portion is left as small Fermi surface pockets. The system will thus retain its metallic properties although the number of carriers (i.e. those electrons at the Fermi level) will be... 

D-ACAR measurements (Mosley et al. 1994) have led to the identification of a Fermi surface in Bai j Kj Bi03. It is a cubic structure, centered around F, with rounded corners. Its location is in excellent agreement with that predicted by band-structure calculations. The observed large, parallel sheets of Fermi surface suggest the presence of effects due to Fermi surface nesting which may drive the superconducting state. 

---