Metallization and metallicity: Universal conductivity limits

The Mott–Ioffe–Regel minimum metallic conductivity based on a minimum mean free path of inter-atomic spacing has been used as a robust criterion for signalling Fermi liquid behaviour. Instead we examine the conductivity of a system in universal terms of the excitation energy, Eexc, of a charge carrier bound to its hole. The expression for conductivity depends simply on probability of charge transfer expressed as Eexc/ℏ. The minimum conductivity for Fermi liquid state is obtained as σ min ( FL ) = CE exc max / ℏ = 11 , 360 S cm−1 (C = 1; E exc max = 6.8 eV is the maximum excitonic binding energy for a mobile exciton). From simple considerations in the t–J model of the Larmor precession time, τ L int , due to an internal exchange magnetic field and the residence time, τW, for a charge carrier with energy EW, we express condition for Fermi liquid ( τ L int / τ W > 1 ) and non-Fermi liquid behaviour ( τ L int / τ W < 1 ). For such NFL liquids, we find that one requires CNFL = (1/π2π2/3) ∼ 1/21.2 to account for the reduced probability of charge transfer with conservation of spin in NFL systems. The maximum value of the conductivity, σ±, at which the temperature coefficient of resistance (TCR) changes sign at an insulator metal transition is given by σ max ± ( IM ) = C NFL σ min ( FL ) ≈ 536 S cm−1. This value is close to that observed in several systems. We discuss these universal values of the conductivity in the context of the Herzfeld criterion, Mooij criterion, exciton transfer rates, chemical reaction rate theory, universal sheet resistance at insulator–superconductor transition, as well as the changes in resistivity during the metallization of molecular hydrogen, oxygen and iodine.