Anderson metal-insulator transition

Conductivities belohr cmin near the Anderson metal-insulator transition... 

Since oc in (81) is the reciprocal of the localization length , measurements of T0 near to the (Anderson) metal-insulator transition can determine how varies with nc—n. Thus Castner and co-workers (Shafarman and Castner 1986, Shafarman et al 1986) have made measurements in Si P and found, as expected, that for systems just below the Anderson transition varies as (nc— n)-v, with v l. 

Using a scaling theory of localization, adapted for anisotropic materials, Apel and Rice [76] find that the condition Le, c does correspond to the Anderson metal-insulator transition of a quasi-one-dimensional system. 

An Anderson metal-insulator transition [163], driven by a weak random disorder field, can also lead to electronic localization. 

Fig. 3.6 (a) The Anderson transition and (b) the form of the localized wave function in an Anderson metal-insulator transition, (c) The Fermi glass state where the Fermi level lies in the region of localized states, (From Refs. 64,65,80.)... 

For disordered systems, then, a quite different form of metal-insulator transition occurs—the Anderson transition. In these systems a range of energies exists in which the electron states are localized, and if at zero temperature the Fermi energy lies in this range then the material will not conduct, even though the density of states is not zero. The Anderson transition can be discussed in terms of non-interacting electrons, though in real systems electron-electron interaction plays an important part. 

For the subject matter of this book, it is of particular interest to consider the situation for a non-crystalline system analogous to that of crystalline ytterbium or strontium under pressure, namely that when a valence and conduction band are separate or overlap slightly. If the degree of overlap can be changed by varying the mean distance between atoms, the composition or the coordination number then a metal-insulator transition can occur. Many examples will be discussed in this book, particularly amorphous films of composition (Mgi- )j(By3, liquid mercury at low densities, and liquid tellurium alloys in which the coordination number changes with temperature. The transition is, we believe, of Anderson type. 

We discuss in this section the effect of short-range interaction on the Anderson-localized states of a Fermi glass described in Chapter 1, Section 7, and in particular the question of whether the states are singly or doubly occupied. Ball (1971) was the first to discuss this problem. In this section we consider an electron gas that is far on the metal side of the Wigner transition (Chapter 8) the opposite situation is described in Chapter 6, where correlation gives rise to a metal-insulator transition. We also suppose that Anderson localization is weak (cca 1) otherwise it is probable that all states are singly occupied. 

Impurity conduction can also be studied in compensated semiconductors, i.e. materials containing acceptors as well as donors, the majority carriers (or the other way round). For such materials, even at low concentrations, activated hopping conduction can occur (Chapter 1, Section 15), some of the donors being unoccupied so that an electron can move from an occupied to an empty centre. Here too a metal-insulator transition can be observed, which is certainly of Anderson type, the insulating state being essentially a result of disorder. 

Most amorphous metallic alloys do not show a metal-insulator transition. They do, however, show moderate changes in the resistivity with temperature, some of which can be interpreted in terms of the quantum interference effect, together with the interaction effect of Altshuler and Aronov (Chapter 5, Section 6). These will be described below. Amorphous alloys of the form Nb Six Au Six etc. do, however, show a metal-insulator transition of Anderson type, and some of those are treated in Chapter 1, Section 7. 

In this review, we have argued that the metallicity is intimately connected to the presence of JTD. We could speculate that the population of many different JTD states at high temperatures introduces a form of disorder that could trigger a metal-insulator transition of the Anderson type. It reveals conversely that cooperation is required between JTD and the electronic motion to establish coherent band-like properties. The transition at 250 K in K4C60 shows that the nature of the distortion can change, a situation close to that of the fulleride salt. A similar transition in metallic compounds might be responsible for the de-stabilization of the metallic state. 

N. F. Mott, Metal-Insulator Transitions, Taylor and Francis, London (1990) P. W. Anderson, Science 235, 1196 (1987). 

Anderson Localization spatial localization of electronic wavefunctions due to randomness of the electronic potential which causes a metal-insulator transition in sufficiently disordered materials. 

Anderson localization is only one possible way of inducing a transition from a localized to a delocalized state. Since the localized state is associated with insulating behavior and the delocalized state is associated with metallic behavior, this transition is also referred to as the metal-insulator transition. In the case of Anderson localization this is purely a consequence of disorder. The metal-insulator transition can be observed in other physical situations as well, but is due to more subtle many-body effects, such as correlations between electrons depending on the precise nature of the transition, these situations are referred to as the Mott transition or the Wigner crystallization. 

In addition to Mott-Hubbard localization, there is another common source of electron localization, which arises when a lattice is under a random potential (e.g. a random distribution of alkali metal ions in alkali metal containing transition metal oxides). For a metal, a practical consequence of a random potential is to open a band gap at the Fermi level. Insulating states induced by random potentials are referred to as Anderson localized states (see Anderson Localization)) ... 

An increase of the temperature may cause geometric changes and this may be enough to cause localization, as proposed in P. W. Anderson s model. However, metal-insulator (MI) transitions are not always caused by thermal disorder. 

In Chapter 7 we discussed the system La1 xSrxV03, which for x = 0 is an antiferromagnetic insulator and with increasing x undergoes a transition of Anderson type to metallic behaviour, with a decrease and ultimate disappearance... 

It has been seen in the previous section that the ratio of the onsite electron-electron Coulomb repulsion and the one-electron bandwidth is a critical parameter. The Mott-Hubbard insulating state is observed when U > W, that is, with narrow-band systems like transition metal compounds. Disorder is another condition that localizes charge carriers. In crystalline solids, there are several possible types of disorder. One kind arises from the random placement of impurity atoms in lattice sites or interstitial sites. The term Anderson localization is applied to systems in which the charge carriers are localized by this type of disorder. Anderson localization is important in a wide range of materials, from phosphorus-doped silicon to the perovskite oxide strontium-doped lanthanum vanadate, Lai cSr t V03. 

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