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METALS, SUPERCONDUCTORS... 2009Anomalous criticality in the electrical resistivity of a high-T c cuprateAn important theme in strongly correlated electron systemsis quantum criticality and the associated quantum phasetransitions that occur at zero temperature upon tuning anon-thermal control parameter g (e.g. pressure, magneticfield H or composition) through a critical value g c . Onefeature of such a system is the influence that critical fluctuationshave on the physical properties over a wide region inthe (T , g) phase diagram above the quantum critical point(QCP), inside which the system shows marked deviationsfrom conventional Landau Fermi-liquid behaviour. A numberof candidate non-Fermi-liquid systems have emerged,particularly in the heavy-fermion family, though there areothers, e.g. certain transition metal-oxides, that displaysimilar characteristics.The physics of copper-oxide high temperature superconductorsmay also be governed by proximity to a QCP.The generic temperature-doping (T , p) phase diagram resemblesthat seen in the heavy-fermions, with an apparentfunnel-shaped region that either pierces or skirts the superconductingdome. Above this region, cuprates display anin-plane resistivity ρ ab that varies linearly with temperatureover a wide temperature yet narrow doping range. ThisT -linear resistivity has been widely interpreted, in tandemwith other anomalous transport properties, as a manifestationof scale-invariant physics borne out of proximity to theQCP. This viewpoint has remained untested, largely due tothe high upper critical field H c2 values in hole-doped high-T c cuprates that restrict access to the important limiting lowtemperatureregion below T c (p).In our experiment, we employed a combination of persistentand pulsed high magnetic fields to expose the normalstate of La 2−x Sr x CuO 4 (LSCO) over a wide dopingand temperature range and studied the evolution of ρ ab (T )with carrier density, from the slightly underdoped (p =0.15) to the heavily overdoped (p = 0.33) region of thephase diagram. Our measurements revealed the preservationof the T -linear resistivity in all superconducting samplesto temperatures as low as 1.5 K [Cooper et al., Science323, 603 (2009)]. Indeed, for all dopings, the ρ ab (T )curves for T < 200 K could be fitted either to the expressionρ ab (T ) = α 0 + α 1 T + α 2 T 2 or to a parallel-resistorformalism1/ρ ab (T ) = 1/[α 0 + α 1 T + α 2 T 2 ] + 1/ρ max withρ max (= 900 ± 100µΩcm). The inclusion of ρ max helps toaccount smoothly for the escalation of ρ ab (T ) to highertemperatures and makes the values of α 1 and α 2 insensitiveto the temperature range of fitting.Figure 75: Doping evolution of the temperature-dependent coefficientsof ρ ab (T ). (A) Doping dependence of α 1 , the coefficientof the T -linear resistivity component. (B) Doping dependenceof α 2 , the coefficient of the T 2 resistivity component. Inboth panels, solid squares are coefficients obtained from least--square fits of the ρ ab (T ) curves for T < 200 K to the expressionρ ab (T ) = α 0 + α 1 T + α 2 T 2 , whilst the filled circles are obtainedfrom fits over the same temperature range to a parallel-resistor-formalism1/ρ ab (T ) = 1/[α 0 +α 1 T +α 2 T 2 ]+1/ρ max withρ max = 900± 100 µΩcm. The open symbols are obtained fromcorresponding fits made to the ρ ab (T ) data of [Ando et al., Phys.Rev. Lett. 93, 267004 (2004)] between 70 K and 200 K. Thedashed lines are guides to the eye.As shown in the top panel of figure 75, for both sets ofdata and analysis, α 1 is seen to grow rapidly with decreasingp, attaining a maximum value of around 1 µΩcm/K atp c = 0.185 ± 0.005. The preservation of T -linear resistivityin LSCO over such a wide doping range is wholly unexpectedand contrasts markedly with what is observed inother candidate quantum critical systems. Our analysis alsoreveals (figure 75) that the magnitude of the T -linear termscales monotonically with T c on the strongly overdopedside but saturates, or is maximal, at a critical doping levelp crit ∼ 0.19 at which superconductivity itself is most robust.The observation of a singular doping concentration inLSCO close to p = 0.19 at which a bulk transport propertyundergoes a fundamental change at low T lends support toearlier thermodynamic studies that showed the pseudogaptemperature T ∗ or energy scale ∆ g vanishes inside the superconductingdome, rather than at its apex. The magnitudeof α 1 at p = p crit , coupled with other features of the data,suggests that the opening of the pseudogap coincides withthe loss of quasiparticle coherence for states near the zoneboundaries.B. Vignolle, C. ProustR. A. Cooper, Y. Wang, N. E. Hussey (University of Bristol, Bristol, UK)56