The Mott Metal-Insulator Transition Models and Methods
The metal-insulator transition due to electron-electron interactions is one of the most celebrated but least understood problems in condensed matter physics. Here this subject is comprehensively reviewed for the first time since Sir Nevill Mott's monograp
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In the first section we specify an insulator as a substance with a vanishing electrical conductivity in a (weak) static electrical field at zero temperature. The transport of electrical charge in the solid state is provided by electrons that are subjected to the Coulomb interaction with the ions and the other electrons. Correspondingly, in the first category of insulators we find band, Peierls, and Anderson insulators, which can be understood in terms of single electrons that interact with the electrostatic field of the ions. Mott insulators constitute the second category, where the insulating behavior is understood as a cooperative many-electron phenomenon. In the absence of electron pairing an insulator may be characterized by a gap for charge excitations into states in which the wave functions of the excitations spatially extend over the whole specimen (gap criterion). This zero-temperature gap sets an energy scale that allows us to distinguish in practical terms between good conductors (“metals”) and bad conductors (“insulators”) at finite temperature. In the second section we describe quantum and thermodynamic phase transitions as possible scenarios for the formation of a gap. In quantum phase transitions the gap opens as a consequence of the competition between the carriers’ kinetic and interaction energy. The notion of a gap that separates two bands remains valid at all temperatures (“robust gap”). In thermodynamic phase transitions the gap opens as a consequence of the formation of longrange order (symmetry breaking) at some finite temperature (“soft gap”). In the third section we briefly describe band, Peierls, and Anderson insulators and their corresponding transitions. Pressure-induced metal–band insulator transitions and the metal–Anderson insulator transition upon doping provide examples for quantum phase transitions in which the formed charge gap is robust. The Peierls transition provides an example for a thermodynamic phase transition (symmetry breaking) in which the gap is the consequence of the formation of a charge-density wave. In the fourth section we discuss Mott’s correlated electron view of the metal–insulator transition. Mott emphasized the importance of magnetic moments as a signature of electron correlations, regardless of whether or not they are ordered. Correspondingly, we propose to distinguish between Mott– Hubbard and Mott–Heisenberg insulators. In the quantum phase transition from the metal into the Mott–Hubbard insulator the moments need not order.
Florian Gebhard: The Mott Metal-Insulator Transition, STMP 137, 1–48 (2000) c Springer-Verlag Berlin Heidelberg 2000
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1. Metal–Insulator Transitions
They order in a thermodynamic phase transition into the Mott-Heisenberg insulator. The concept of the Mott–Heisenberg insulator resembles Slater’s views on the metal-to-insulator transition as an ordering phenomenon. His approach is conceptually different since the magnetic moments form and order at the same temperature in Slater’s one-electron picture, whereas pre-formed moments order at the tr
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