The metal-insulator transition in mesoscopic and macroscopic systems

3 The metal-insulator transition in mesoscopic and macroscopic systems 

In a series of seminal contributions beginning in 1949, Sir Nevill Mott first posed the key question of how such an insulating, non-metallic system could naturally evolve into a metallic system. His conclusion, that such a system could undergo an insulator-to-metal transition, was perhaps not surprising what was remarkable, however, was Mott s proposal that at the very transition from insulator to metal, all the outer (valence) electrons would become free at once, not just a few 

The ramifications for a Gedanken experiment at T = 0 K are sketched in Fig. 4a, revealing the d.c. electrical conductivity for a macroscopic system such as Si P in which d, the average distance between one-electron centers, can be continuously tuned by changes in the composition of the system. For values of d below a critical distance, dc, i.e. d 4) the system is metallic and the electronic wave-function is completely delocalized over the entire sample. For very large d d dfj, we have an insulator with a valence electron wavefunction that is completely localized at the individual atomic sites. At a critical distance, d we then have, according to Mott, a first-order (discontinuous) metal-insulator transition. Thus, at r = 0 K one either has a non-metal or an insulator, for which the limiting (low temperature) d.c. electrical conductivity is zero, or a metal, with a finite conductivity at this base temperature. Whether the metal-insulator transition in Si P (Fig. 4a) is continuous or discontinuous is still a source of controversy. 

There is therefore a clear distinction to be made here between the nature of the metal insulator transition in a macroscopic system such as Si P and our (assumed) inevitable metal-insulator transition occurring solely within an isolated microscopic cluster or particle, typically containing between 10 and 10 atoms (Fig. 1). 

In his celebrated papeF of 1961, The Transition to the Metallic State , Mott also alluded to the fundamental differences between these two situations. Concerning the proposed first-order (discontinuous) nature of the metal-insulator transition in macroscopic systems, he noted ... the sharp transition described here is only expected in an infinite lattice. It goes without saying that for a finite number of atoms there will be a gradual decrease in the weight of the ionized states in the wave function as the interatomic distance is increased, or, in other words, a gradual transition  

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