MottIoffeRegel limit and resistivity crossover in a tractable electronphonon model
Abstract
Many metals display resistivity saturation—a substantial decrease in the slope of the resistivity as a function of temperature that occurs when the electron scattering rate τ^{1} becomes comparable to the Fermi energy E_{F}/ℏ (the MottIoffeRegel limit). At such temperatures, the usual description of a metal in terms of ballistically propagating quasiparticles is no longer valid. We present a tractable model of a large number N of electronic bands coupled to N^{2} optical phonon modes, which displays a crossover behavior in the resistivity at temperatures where τ^{1}∼E_{F}/ℏ . At low temperatures, the resistivity obeys the familiar linear form, while at high temperatures, the resistivity still increases linearly, but with a modified slope (that can be either lower or higher than the lowtemperature slope, depending on the band structure). The hightemperature nonBoltzmann regime is interpreted by considering the diffusion constant and the compressibility, both of which scale as the inverse square root of the temperature.
 Publication:

Physical Review B
 Pub Date:
 February 2016
 DOI:
 10.1103/PhysRevB.93.075109
 arXiv:
 arXiv:1512.00041
 Bibcode:
 2016PhRvB..93g5109W
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 Phys. Rev. B 93, 075109 (2016)