Electronic topological transitions

ELECTRONIC TOPOLOGICAL TRANSITIONS AND COMPOSITIONAL ORDER IN CiiPd AND CuPt ALLOYS... 

I.A.Abrikosov, Yu.H.Vehkov, P.A.Korzhavyi, A.V.Ruban and L.E.Shilkrot, Ab-initio calculations of the electronic topological transition in Li-Mg alloys , Sohd State Commun. 83 867 (1992) ... 

Figure 1 2 1. The different types of 2.5 Lifshitz electronic topological transition (ETT) The upper panel shows the type (I) ETT where the chemical potential EF is tuned to a Van Hove singularity (vHs) at the bottom (or at the top) of a second band with the appearance (or disappearance) of a new detached Fermi surface region. The lower panel shows the type (II) ETT with the disruption (or formation) of a neck in a second Fermi surface where the chemical potential EF is tuned at a vHs associated with the gradual transformation of the second Fermi surface from a two-dimensional (2D) cylinder to a closed surface with three dimensional (3D) topology characteristics of a superlattice of metallic layers...

Bruno, E., Ginatempo, B., Guiliano, E. S., Ruban, A. V., and Vekilov, Yu. Kh., 1994, Fermi surfaces and electronic topological transitions in metallic solid solutions, Phys. Reports 249, 353-419. 

The topological transition (Fig. 1) from polymeric solids in compounds containing linked polyhedral homoatomic clusters to discrete molecular (soluble) clusters can be conveniently studied by using as examples compounds rich in elements of the main-groups 13 to 15. It is possible for main-group elements in the middle of the periodic table to form homoatomic molecules or ions with localized homonuclear 2c-2e bonds. At higher valence-electron concentrations, fewer bonding and more free-electron pairs are formed. As electron deficiency increases, however, the formation of delocalized bonds becomes necessary, a situation typical of elements on the left of the periodic table. 

Figure 1. Topological transition from a diamond network (left) to polyhedral homoatomic clusters (right). Some bonds between the tetravalent atoms break by adding electrons (middle). The formation of progressively more and more lone pairs eventually results in discrete cluster anions (right).

PMD color or the nature of the electron transitions produces the widest appHcation for PMDs. Depending on the polymethine chain length, the end-group topology, and the electron shell occupation, polymethines can absorb light in uv, visible, and near-ir spectral regions. 

Iversen, B.B., Larsen, F.K., Figgis, B.N. and Reynolds, P.A. (1997) X-N study ofthe electron density distribution in tra s-tetraammine-dinitronickel(II) at 9K transition metal bonding and topological analysis, J. Chem. Soc., Dalton Trans. 2227-2240. 

Figure 8.21 shows functions of the distorted topologies that are not pointed at the origin, and j (0) < 1. The reason is that the presented model is not an ideal two-phase system, because it considers smooth transitions of the electron density between the crystalline and the amorphous layers. 

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