Universality of the Mott–Ioffe–Regel limit in metals

Abstract

The absence of resistivity saturation in many strongly correlated metals, including the hightemperature superconductors, is critically examined from the viewpoint of optical conductivity measurements. Coherent quasiparticle conductivity, in the form of a Drude peak centred at zero frequency, is found to disappear as the mean free path (at ω = 0) becomes comparable to the interatomic spacing. This basic loss of coherence at the so-called Mott-Ioffe-Regel (MIR) limit suggests that the universality of the MIR criterion is preserved even in the presence of strong electron correlations. We argue that the shedding of spectral weight at low frequencies, induced by strong correlation effects, is the primary origin of the extended positive slope of the resistivity to high temperatures observed in all so-called 'bad metals'.Moreover, in common with those metals which exhibit resistivity saturation at high temperatures, the scattering rate itself, as extracted from optical spectra, saturates at a value consistent with the MIR limit. We consider possible implications that this ceiling in the scattering rate may have for our understanding of transport within a wide variety of bad metals and suggest a better method for analysing their optical response.

Saturation of resistivity and Kohler's rule in Ni-dopedLa1.85Sr0.15CuO4cuprate

“…k F l min ≈ π, see Ref. [46,47]), where a is the lattice parameter in CuO 2 plane, one gets ρ small IRM =( √ 2π /e 2 )d/ √ n=0.68/ √ n mΩ cm [26]. This is clearly distinguishable from the large Fermi surface case, ρ large IRM =0.68/ √ 1 + n, inapplicable to the system.…”

“…The Ni-induced order-of-magnitude increase of a 0 /ρ sat ratio leaves the resulting ρ small IRM √ n intact. The revealed omnipresence of τ min even in bad metals points towards universality of the Ioffe-Regel-Mott criterion [46] rather than accidentalonly agreement between ρ IRM and saturation [27].…”

“…4(c) fails completely. Concluding, the signs of resistivity saturation both at the value ρ IRM and with n-dependence from Boltzmann theory reflect metallic-like character of transport despite small volume of Fermi surface and strong disorder in underdoped LSCO. A fully quantum-mechanical explanation of saturation is still lacking [26,46,[59][60][61]. Evidently however, strong electron-electron interactions [62] do not invalidate the ρ IRM limit [27].…”

Shear viscosity of strongly interacting fermionic quantum fluids

“…Also, a comparable limit η n was proposed by Eyring [4] almost 80 years ago. For a large class of strongly correlated systems such as 3d transition-metal oxide compounds, organic charge-transfer salts such as κ-(BEDT-TTF) 2 X, the MIR limit is violated [5][6][7] and the coherent quasiparticle-based transport picture breaks down, i.e., < a. Similarly, we might expect that in the incoherent regime of transport, the shear viscosity η could violate the quantum limit to coherent transport, i.e., η < η q .…”

Ong construction for the reconstructed Fermi surface of underdoped cuprates

“…According to Hartnoll [40], there are two universal bounds on the transport processes that occur in strongly correlated metals. One is the MIR bound described above, beyond which the quasiparticles are destroyed-resulting in a loss of (optical) spectral weight at low frequencies [41]. The other is a diffusivity bound (also known as the "Planckian" bound [42]) beyond which transport is driven by diffusion of charge and energy rather than by momentum relaxation.…”