Non-quasiparticle transport and resistivity saturation: a view from the large-N limit

The electron dynamics in metals are usually well described by the semiclassical approximation for long-lived quasiparticles. However, in some metals, the scattering rate of the electrons at elevated temperatures becomes comparable to the Fermi energy; then, this approximation breaks down, and the full quantum-mechanical nature of the electrons must be considered. In this work, we study a solvable, large-N electron–phonon model, which at high temperatures enters the non-quasiparticle regime. In this regime, the model exhibits “resistivity saturation” to a temperature-independent value of the order of the quantum of resistivity—the first analytically tractable model to do so. The saturation is not due to a fundamental limit on the electron lifetime, but rather to the appearance of a second conductivity channel. This is suggestive of the phenomenological “parallel resistor formula”, known to describe the resistivity of a variety of saturating metals. Resistivity saturates as a function of temperature in some metals; this happens in a regime in which the usual description of a metal in terms of ballistically propagating quasiparticles does not apply. In this work Yochai Werman and co-workers from Weizmann Institute of Science in Israel and Stanford University in the US introduce a tractable microscopic model which allows a fully quantum mechanical treatment of the electrons. In the non-quasiparticle regime, the single-particle lifetime decreases without bound, yet the resistivity saturates. The saturation of the resistivity is due to the appearance of a distinct conductivity channel, in accordance with experimental evidence. Beyond the implications for resistivity of metals, the current analysis may be extended to other problems of unconventional metallic transport.