Zooming on the Quantum Critical Point in Nd-LSCO
Recent studies of the high- superconductor LaNdSrCuO (Nd-LSCO) have found a linear- in-plane resistivity and a logarithmic temperature dependence of the thermopower at a hole doping , and a Fermi-surface reconstruction just below daou08 (); daou09 (). These are typical signatures of a quantum critical point (QCP). Here we report data on the -axis resistivity of Nd-LSCO measured as a function of temperature near this QCP, in a magnetic field large enough to entirely suppress superconductivity. Like , shows an upturn at low temperature, a signature of Fermi surface reconstruction caused by stripe order. Tracking the height of the upturn as it decreases with doping enables us to pin down the precise location of the QCP where stripe order ends, at .We propose that the temperature below which the upturn begins marks the onset of the pseudogap phase, found to be roughly twice as high as the stripe ordering temperature in this material.
keywords:cuprate superconductors, stripe order, quantum critical point, pseudogap phase, Nd-LSCO, c-axis resistivity 74.25.Fy, 74.72.Dn, 75.30.Kz
One of the central questions of high- superconductivity is the nature of the pseudogap phase. Recent quantum oscillation studies doiron07 () favour a scenario of competing order, as they reveal that the large hole-like Fermi surface of overdoped cuprates vignolle08 () transforms into small electron-like pockets in the pseudogap phase leboeuf07 (). This shows that there is some “hidden” order in the pseudogap phase which breaks translational symmetry and thus causes a reconstruction of the Fermi surface chakravarty08 (). In some cuprates, such as LaNdSrCuO (Nd-LSCO), there is clear evidence for charge / spin order, better known as “stripe order”, setting in at low temperature (see Ref. hunt01 () and references therein), and the pseudogap phase may be a precursor to that stripe phase.
The presence of an order in the phase diagram involves the presence of a quantum critical point (QCP) at a critical doping where the ordering temperature goes to zero. In Nd-LSCO at a hole-doping of , the in-plane resistivity is linear down to the lowest temperature daou08 (), and the thermopower has a dependence over a decade of temperature daou09 (). These are typical signatures of a quantum phase transition for a metal with two-dimensional antiferromagnetic fluctuations lohneysen07 (); paul01 (). They show that the QCP is close to but slightly below that doping, i.e. .
In this Letter, we present measurements of the -axis resistivity in Nd-LSCO as a function of temperature in the vicinity of the QCP. These out-of-plane measurements reveal the same behavior as found in the in-plane data, namely a linear- resistivity down to a temperature below which starts to deviate upwards daou08 (). In-plane data at and show that goes to zero between these two dopings (see Fig. 1). Here we use -axis samples at intermediate dopings to pin down with greater accuracy the critical doping where .
The four samples of Nd-LSCO used in this study were grown at the University of Texas, as described elsewhere daou08 (). They have a doping of and , respectively. The resistivity was measured at the National High Magnetic Field Laboratory in Tallahassee, in steady magnetic fields up to T.
Our data in a field of T is presented in Fig. 2. (Note that there is negligible magneto-resistance in all cases.) A linear fit to the data below 80 K is shown as a solid line. In the inset, we plot , the difference between data and fit. At , we see that remains linear down to the lowest temperature, as previously reported daou08 (). At lower doping, an upturn is observed below a temperature (see arrows in inset) which is plotted vs doping in Fig. 1 (red circles). The values of obtained from are seen to agree well with the overall doping dependence of obtained from (reproduced from ref. daou08 ()).
Another way to describe the evolution of the -axis resistivity data is to plot the magnitude of the upturn as a function of doping, defined as , the difference between data and fit in the limit of (red double-headed arrow in Fig. 2). Fig. 3 shows as a function of doping. It is clear that the height of the upturn goes down as the doping is increased, extrapolating to zero at . This accurately locates the quantum critical point below which Fermi-surface reconstruction begins. We infer that this is where translational symmetry is broken at .
As noted previously from in-plane data daou08 (); taillefer09 (), the upturn begins at a temperature significantly above the ordering temperature for stripe order, at (see Fig. 1), with . This suggests a two-step transformation of the electronic behaviour taillefer09 (): a first transformation at high temperature, detected in the resistivity and the quasiparticle Nernst signal below cyrchoiniere09 (), with , and a second transformation at the stripe ordering temperature, detected in the Hall daou08 () and Seebeck coefficients daou09 ().
We propose that the temperature is in fact the pseudogap temperature . The pseudogap phase would then most likely be a fluctuating precursor of the spin/charge density wave (stripe) order observed at lower temperature (below ). This QCP may be a generic feature of hole-doped cuprates. Indeed, recent measurements of -axis resistivity in overdoped Bi-2212 crystals show upturns below a temperature which also goes to zero at murata (). Moreover, a reconstruction of the Fermi surface by stripe-like order may also be a more general occurrence, given the very similar anomalies observed in YBCO in both the Hall taillefer09 () and Seebeck chang09 () coefficients.
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