Evidence for a universal Fermi-liquid scattering rate throughout the phase diagram of the copper-oxide superconductors

Abstract

The phase diagram of the cuprate superconductors continues to pose formidable scientific challenges. While these materials are typically viewed as doped Mott insulators, it is well known that they are Fermi liquids at high hole-dopant concentrations. It was recently demonstrated that at moderate doping, in the pseudogap (PG) region of the phase diagram, the charge carriers are also best described as a Fermi liquid. Nevertheless, the relationship between the two Fermi-liquid (FL) regions and the nature of the strange-metal (SM) state at intermediate doping have remained unsolved. Here we show for the case of the model cuprate superconductor HgBa 2 CuO 4+δ that the normal-state transport scattering rate determined from the cotangent of the Hall angle remains quadratic in temperature across the PG temperature, upon entering the SM state, and that it is doping-independent below optimal doping. Analysis of prior transport results for other cuprates reveals that this behavior is universal throughout the entire phase diagram and points to a pervasive FL transport scattering rate. These observations can be reconciled with a variety of other experimental results for the cuprates upon considering the possibility that the PG phenomenon is associated with the gradual, non-uniform localization of one hole per planar CuO 2 unit.

Extent of Fermi-surface reconstruction in the high-temperature superconductor HgBa 2 CuO 4+ δ

“…The pseudogap temperature T * is typically identified in electrical transport as the deviation from high-temperature linear-intemperature resistivity (ρ ∝ T ) termed strange-metal behavior. For Hg1201, we combine prior (34) and new measurements of the planar resistivity in zero-magnetic field to determine the doping dependence of T * , which is consistent other markers of T * as shown in SI Appendix Fig. S13.…”

“…The color contour represents the temperature exponent α of the zero-field planar resistivity of the form ρ = ρ0 + AT α , where A is a temperature independent coefficient. Black and grey squares along the top edge of the panel mark doping levels measured in this work and in Ref (16),. respectively, used to create the contour.…”

Low temperature hidden Fermi-liquid charge transport in under doped La x Sr1−x CuO2 infinite layer electron-doped thin films

“…To further analyze the normal state transport properties of our samples, we have also performed Hall measurements on typical under-doped samples (x ≈ 0.07). In figure 7(a)), it is shown the temperature behavior of ρ i (T) = ρ′(T) − A 0 □ − A log □log(T/1 K), figure 7(b)) presents 1/R H (where R H is the Hall coefficient) obtained after disentanglement of the logarithmic contribution [12,15] from the resitivity ρ′ and in figure 7(c)) the obtained temperature behavior for cot(θ H ) = ρ i / (HR H ) is displayed. As it is clear from figure 7(c)), the cot(θ H )(T) has a T 2 dependence up to temperatures of about 120 K, close to the T ** value and of the same order of the typical Neel temperatures observed in under-doped cuprates [2].…”

“…For the p doped compound presenting only one CuO 2 plane per unit cell, i.e. HgBa 2 CuO 4+δ , the cotangent of the Hall angle, cot(θ H ), has been found to follow a T 2 law independently of doping with no appreciable changes upon crossing the temperatures T ** and T * [12]. Moreover, the HgBa 2 CuO 4+δ paraconductivity has shown unusual exponential temperature dependence indicating that the emergence of SC in this system is dominated by the underlying intrinsic gap inhomogeneity [13].…”

“…The low temper ature resistivity upturn has been tentatively correlated to Kondo scattering [6] or weak localization (WL) effects [7], while the opening of the PG below T * has been attributed to non-Fermi liquid (FL) behavior in proximity of a quantum critical point generally identified as the quantum transition to the AF phase [4,5,8]. Nevertheless, recent developments have suggested that a FL behavior is present in a large part of the normal state phase diagram, at temperature T ** < T * [9][10][11][12][13]. In particular, p doped cuprates have shown, below T ** , quadratic temperature dependence of the resistivity per CuO 2 plane [9,14], a single relaxation scattering rate 1/τ ≈ T 2 , in agreement with the Kohler's rule for the magneto-resistivity [10] and a quadratic frequency dependence of the optical scattering rate with the temperature-frequency scaling expected in the case of FL [11].…”