Universal sheet resistance and revised phase diagram of the cuprate high-temperature superconductors

Abstract

Upon introducing charge carriers into the copper-oxygen sheets of the enigmatic lamellar cuprates, the ground state evolves from an insulator to a superconductor and eventually to a seemingly conventional metal (a Fermi liquid). Much has remained elusive about the nature of this evolution and about the peculiar metallic state at intermediate hole-carrier concentrations (p). The planar resistivity of this unconventional metal exhibits a linear temperature dependence (ρ ∝ T) that is disrupted upon cooling toward the superconducting state by the opening of a partial gap (the pseudogap) on the Fermi surface. Here, we first demonstrate for the quintessential compound HgBa 2 CuO 4+δ a dramatic switch from linear to purely quadratic (Fermi liquid-like, ρ ∝ T 2 ) resistive behavior in the pseudogap regime. Despite the considerable variation in crystal structures and disorder among different compounds, our result together with prior work gives insight into the p-T phase diagram and reveals the fundamental resistance per copper-oxygen sheet in both linear (ρ ☐ = A 1☐ T) and quadratic (ρ ☐ = A 2☐ T 2 ) regimes, with A 1☐ ∝ A 2☐ ∝ 1/p. Theoretical models can now be benchmarked against this remarkably simple universal behavior. Deviations from this underlying behavior can be expected to lead to new insight into the nonuniversal features exhibited by certain compounds.

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

“…While α 1 vanishes for all specimens with y 0.035, the T 2 -coefficient a 2 changes linearly with 1/n (compare Ref. [3]) in the whole studied y range (Fig. 2d).…”

“…Fermi-Dirac statistic underlying the quantum oscillations [1], single-parameter -quadratic in energy ω and temperature T -scaling in optical conductivity σ(ω, T ) (Ref. [2]), T 2 resistivity behavior extending over substantial Tregion in clean systems [3] and fulfillment of typical for conventional metals Kohler's rule in magnetotransport [4] are observations in favor of Fermi-liquid scenario.…”

“…On the other hand, in cuprates with significant disorder manifested by large residual resistivity ρ res , pure T 2 resistivity dependence has not been reported so far as for Bi 2 Sr 2 CuO 6+δ [3,5,6] or observed only at relatively narrow doping-and T-region as in La 2−x Sr x CuO 4 (LSCO) [3,7]. The clear violation of Kohler's scaling in underdoped LSCO and YBa 2 Cu 3 O 7 [8,9] (although not necessarily meaning breakdown of Fermi-liquid description [10]) has served almost as a hallmark of their peculiar normal-state properties for two decades.…”

Conductivity in Cuprates Arises from Two Different Sources: One-Electron Exchange and Disproportionation

“…Similarly, the resistivity increases with T as T 2 in the overdoped region [33][34][35][36]. Here, conductivity should be caused by electron pair transfer, since there are no Cu(II) ions available.…”

Hidden Fermi-liquid Charge Transport in the Antiferromagnetic Phase of the Electron-Doped Cuprate Superconductors

“…In a new development, the hole-doped cuprates were found to exhibit FL properties in an extended temperature range below the characteristic temperature T * * (T * * < T * ; T * is the PG temperature): (i) the resistivity per CuO 2 sheet exhibits a universal, quadratic temperature dependence, and is inversely proportional to the doped carrier density p, ρ ∝ T 2 /p [15]; (ii) Kohler's rule for the magnetoresistvity, the characteristic of a conventional metal with a single relaxation rate, is obeyed, with a Fermi-liquid scattering rate, 1/τ ∝ T 2 [16]; (iii) the optical scattering rate exhibits the quadratic frequency dependence and the temperature-frequency scaling expected for a Fermi liquid [17]. In this part of the phase diagram, the Hall coefficient is known to be approximately independent of temperature and to take on a value that corresponds to p, R H ∝ 1/p [18].…”