First-order Mott transition

The main effect of both types of electron localization, of course, is a crossover from metallic to nonmetalhc behavior (a M-NM transition). Nevertheless, it would be very beneficial to have a method of experimentally distinguishing between the effects of electron-electron Coulomb repulsion and disorder. In cases where only one or the other type of localization is present this task is relatively simpler. The Anderson transition, for example, is predicted to be continuous. That is, the zero-temperature electrical conductivity should drop to zero continuously as the impurity concentration is increased. By contrast, Mott predicted that electron-correlation effects lead to a first order, or discontinuous transition. The conductivity should show a discontinuous drop to zero with increasing impurity concentration. Unfortunately, experimental verification of a true first order Mott transition remains elusive. 

We have emphasised the distinction between localised and itinerant states. Under certain circumstances (governed by atomic properties) a given orbital is poised at the critical point where it can become either one or the other for small changes in the environment of the atom. In solid state physics, this gives rise to a first-order Mott transition. In the present context, such a situation is closely related to the problem of controlled orbital collapse (section 5.23) if a solid is built up from free atoms with a double well potential and the corresponding orbitals in the outer well, these may hybridise easily, the external part of the orbital going into itinerant states. If one forms a solid from atoms with collapsed orbitals, then they remain localised. 

In solid state physics, the first-order Mott transition is a phase transition between the metallic (delocalised or itinerant) and insulator (lo-... 

This table was derived from empirical data on conductivity and magnetism in solids. The shaded area maps the first order Mott transition between localised and itinerant behaviour in the solid, and the elements which lie on it have sensitive (e.g. pressure-dependent) properties. However, they are also remarkable in atomic physics for their giant resonances, are noted catalysts, or provide good materials for H storage, and then exhibit photon-stimulated desorption peaks which replicate the giant resonance profiles. Many of these properties seem to depend on the critical localisation of / and d electrons. 

These studies have led to the interesting proposal that this reversible metal-insulator transition represents a first-order Mott transition at room temperature. ... 

Marianetti CA, Kotliar G, Ceder G (2004) A first-order Mott transition in LixCo02. Nat Mater 3 627-631... 

The electronic bands of an infinite crystal can cross as a function of some parameter (pressure, concentration etc.). If one treats the e /r,2 term of the electron repulsion correctly, one sees that the crossing transition of the two bands is a first-order phase transition, between the metallic and insulating states. This transition was predicted by Mott in 1946 and has carried his name ever since. In fact, the original Mott criterion does not predict such a transition for Hg, but the criterion was derived for monovalent atoms. For divalent mercury it should not be applicable. Also the semiempirical Herzfeld criterion, which was very successful in predicting the insulator to metal transition in compressed xenon, predicts bulk Hg to be non-metallic. All this seems to imply that Hg is a rather special case. 

If, then, the low-temperature phase is semimetallic, we cannot interpret the first-order change at 260 K as a Mott transition caused by a discontinuous change in the number n of current carriers that theory predicts a discontinuous... 

An alternative way to clarify the nature of this state is to test its stability with respect to a metal-insulator transition. This has received a lot of theoretical attention recently. The JT singlet ground state makes these compounds free from the tendency towards a magnetic instability observed in so many Mott insulators. In fact, their ground state does not break any symmetry and Capone et al. explained [43] that it then has a zero entropy, which makes a direct connection with a metal impossible (it would violate the Luttinger theorem). These authors predict that the only way to go from the insulator to the metal would be through an exotic superconducting phase or a first-order transition. 

Pasternak MP, Taylor RD, Jeanloz R, Li X, Nguyen JH, McCanunon CA (1997) High pressure collapse of magnetism in Feo 94O Mossbauer spectroscopy beyond 100 GPa. Phys Rev Lett 79 5046-5049 Pasternak MP, Rozenberg GR, Machavariani GY, Naaman O, Taylor RD, Jeanloz R (1999) Breakdown of the Mott-Hubbard state in Fc203 A first order insulator-metal transition with collapse of magnetism at 50 GPa. Phys Rev Lett 82 4663-4666... 

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. 

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 ... 

We conclude that the Lai xSrxTi03 system exhibits a nearly classic Mott-Hubbard transition as the n band is filled toward an integral number of electrons per Ti atom. The transition is first-order and exhibits a volume... 

For the metals Co, Ni and Pd and perhaps others it appears to be a good approximation to assume, in spite of the hybridization, that part of the Fermi surface is s-like with mrff me, and part d-hke with meff me. The current is then carried by the former, and the resistance is due to phonon-induced s-d transitions. This model was first put forward by Mott (1935) and developed by many other authors (e.g. Coles and Taylor 1962) for reviews see Mott (1964) and Dugdale and Guenault (1966). Applications of the model have also been made to ordered alloys of the type Al6Mn, Al7Cr by Griiner et al (1974), where the width A of the d-band is the same as it would be for an isolated transitional-metal atom in the matrix, but most of the Fermi surface is assumed to be (s-p)-like. The behaviour of the disordered Pd-Ag alloy series is particularly interesting. The 4d-bands of the two constituents are well separated, as shown particularly by... 

We depart from the usual notation in two ways. The transfer integral, usually denoted by t, is written I, following our first edition and Mott and Davis (1979). Also, instead of transition metal , we write transitional metal (following J. Friedel), in order to avoid confusion with the former word as used in the title of this book. 

The theoretical treatment of a solid-state transition involving covalent (localized) vs. conduction (delocalized) electronic transformation was first enunciated by Mott [44], By considering the Pauli Exclusion Principle and the electron-electron interaction during the transformation, it was shown that such transition will be critically dependent upon the inter-atomic distances. The number of electrons already existing in the conduction state will in turn influence the critical inter-atomic distances and the transition therefore, it is necessarily a cooperative phenomenon. Later, in a theoretical treatment of the same subject, but based on a different context, Goodenough [45] has shown that the transition is likely to be second-order if the number of electrons per like atom is non-integral. Further, a crystallographic distortion is a prominent manifestation of such a transition. 

A fundamental question is whether the transition between localized and itinerant electronic behavior is continuous or discontinuous. Mott (1949) was the first to point out that an on-site electrostatic energy Ua > Wr, is needed to account for the fact that NiO is an antiferromagnetic insulator rather than a metal. Hubbard (1963) subsequently introduced U formally as a parameter into the Hamiltonian for band electrons his model predicted a smooth transition from a Pauli paramagnetic metal to an antiferromagnetic insulator as the ratio W/U decreased to below a critical value of order unity. This metal-insulator transition is known as the Mott-Hubbard transition. 

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