By Florian Gebhard

The metal-insulator transition as a result of electron-electron interactions is among the so much celebrated yet least understood difficulties in condensed topic physics. right here this topic is comprehensively reviewed for the 1st time for the reason that Sir Nevill Mott's monograph of 1990. A pedagogical advent to the elemental options for the Mott transition, the Hubbard version, and diverse analytical techniques to correlated electron structures is gifted. a brand new category scheme for Mott insulators as Mott-Hubbard and Mott-Heisenberg insulators is proposed. conventional tools are severely tested for his or her power to explain the Mott transition. This publication will make an exceptional reference for scientists getting to know within the box of electron shipping in condensed topic.

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**Additional resources for The Mott Metal-Insulator Transition**

**Example text**

9. Magnetic ﬁeld versus temperature phase diagram for a twodimensional electron gas in GaAs/AlGaAs heterostructures; the system is a correlated electron liquid above the dotted curves, below it is a Wigner lattice (from [105]). “jellium” model [4, Chap. 5]) may localize at low densities. In three dimensions the average kinetic energy per particle of completely delocalized elec2/3 trons scales like Tˆ d=3 /Ne ∼ ne for low electron densities ne = Ne /V and thus goes faster to zero than the average potential energy of an electron’s Coulomb interaction with another electron at the average particle −1/3 1/3 distance ne , Vˆ /Ne ∼ ne .

The solution of the independent electron problem will provide us with a new set of electronic wave functions. Instead of working with plane waves in which Te is diagonal we can then work with a basis which already includes the electron–ion interaction. This is important because the ions’ nonretarded, barely screened Coulomb potential is rather singular both in its time and in its space dependence. In the new basis we can reanalyze the original problem Helectronic , which allows us to verify that the electron–ion interaction indeed dominates the electron–electron interaction.

1 Independent Electrons The seemingly crudest approximation we can make is to ignore totally the electron–electron interaction. This is not unreasonable since the electron– ion interaction and the delocalization of electrons are the main source of the lattice cohesion. Hence it is actually advisable to study independent electrons in the ﬁeld of the ions ﬁrst, HIE = Te + Ve−I . This approach also oﬀers a practical advantage: at least in principle we can exactly solve the problem of independent electrons in a periodic potential to arbitrary accuracy since we are left with a single-electron problem.