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Register a new userTransport signatures of the pseudogap critical point in the cuprate superconductor Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+delta}$
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M. Lizaire
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Five transport coefficients of the cuprate superconductor Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+delta}$ were measured in the normal state down to low temperature, reached by applying a magnetic field (up to 66T) large enough to suppress superconductivity. The electrical resistivity, Hall coefficient, thermal conductivity, Seebeck coefficient and thermal Hall conductivity were measured in two overdoped single crystals, with La concentration $x = 0.2$ ($T_{rm c}=18$K) and $x = 0.0$ ($T_{rm c}=10$K). The samples have dopings $p$ very close to the critical doping $p^{star}$ where the pseudogap phase ends. The resistivity displays a linear dependence on temperature whose slope is consistent with Planckian dissipation. The Hall number $n_{rm H}$ decreases with reduced $p$, consistent with a drop in carrier density from $n = 1+p$ above $p^{star}$ to $n=p$ below $p^{star}$. This drop in $n_{rm H}$ is concomitant with a sharp drop in the density of states inferred from prior NMR Knight shift measurements. The thermal conductivity satisfies the Wiedemann-Franz law, showing that the pseudogap phase at $T = 0$ is a metal whose fermionic excitations carry heat and charge as do conventional electrons. The Seebeck coefficient diverges logarithmically at low temperature, a signature of quantum criticality. The thermal Hall conductivity becomes negative at low temperature, showing that phonons are chiral in the pseudogap phase. Given the observation of these same properties in other, very different cuprates, our study provides strong evidence for the universality of these five signatures of the pseudogap phase and its critical point.
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The specific heat $C$ of the cuprate superconductors La$_{2-x}$Sr$_x$CuO$_4$ and Bi$_{2+y}$Sr$_{2-x-y}$La$_x$CuO$_{6+delta}$ was measured at low temperature (down to $0.5~{rm K}$), for dopings $p$ close to $p^star$, the critical doping for the onset of the pseudogap phase. A magnetic field up to $35~{rm T}$ was applied to suppress superconductivity, giving direct access to the normal state at low temperature, and enabling a determination of $C_e$, the electronic contribution to the normal-state specific heat, at $T to 0$. In La$_{2-x}$Sr$_x$CuO$_4$ at $x=p = 0.22$, $0.24$ and $0.25$, $C_e / T = 15-16~{rm mJmol}^{-1}{rm K}^{-2}$ at $T = 2~{rm K}$, values that are twice as large as those measured at higher doping ($p > 0.3$) and lower doping ($p < 0.15$). This confirms the presence of a broad peak in the doping dependence of $C_e$ at $p^starsimeq 0.19$, as previously reported for samples in which superconductivity was destroyed by Zn impurities. Moreover, at those three dopings, we find a logarithmic growth as $T to 0$, such that $C_e / T sim {rm B}ln(T_0/T)$. The peak vs $p$ and the logarithmic dependence vs $T$ are the two typical thermodynamic signatures of quantum criticality. In the very different cuprate Bi$_{2+y}$Sr$_{2-x-y}$La$_x$CuO$_{6+delta}$, we again find that $C_e / T sim {rm B}ln(T_0/T$) at $p simeq p^star$, strong evidence that this $ln(1/T)$ dependence - first discovered in the cuprates La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ - is a universal property of the pseudogap critical point. All four materials display similar values of the $rm B$ coefficient, indicating that they all belong to the same universality class.
The electrical resistivity $rho$ and Hall coefficient R$_H$ of the tetragonal single-layer cuprate Nd-LSCO were measured in magnetic fields up to $H = 37.5$ T, large enough to access the normal state at $T to 0$, for closely spaced dopings $p$ across the pseudogap critical point at $p^star = 0.235$. Below $p^star$, both coefficients exhibit an upturn at low temperature, which gets more pronounced with decreasing $p$. Taken together, these upturns show that the normal-state carrier density $n$ at $T = 0$ drops upon entering the pseudogap phase. Quantitatively, it goes from $n = 1 + p$ at $p = 0.24$ to $n = p$ at $p = 0.20$. By contrast, the mobility does not change appreciably, as revealed by the magneto-resistance. The transition has a width in doping and some internal structure, whereby R$_H$ responds more slowly than $rho$ to the opening of the pseudogap. We attribute this difference to a Fermi surface that supports both hole-like and electron-like carriers in the interval $0.2 < p < p^star$, with compensating contributions to R$_H$. Our data are in excellent agreement with recent high-field data on YBCO and LSCO. The quantitative consistency across three different cuprates shows that a drop in carrier density from $1 + p$ to $p$ is a universal signature of the pseudogap transition at $T=0$. We discuss the implication of these findings for the nature of the pseudogap phase.
Interlayer van der Waals (vdW) coupling is generic in two-dimensional materials such as graphene and transition metal dichalcogenides, which can induce very low-energy phonon modes. Using high-resolution inelastic hard x-ray scattering, we uncover th
e ultra-low energy phonon mode along the Cu-O bond direction in the high-$T_c$ cuprate (Bi,Pb)$_2$(Sr,La)$_2$CuO$_{6+delta}$ (Bi2201). This mode is independent of temperature, while its intensity decreases with doping in accordance with an increasing c-axis lattice parameter. We compare the experimental results to first-principles density functional theory simulations and identify the observed mode as a van der Waals phonon, which arises from the shear motion of the adjacent Bi-O layers. This shows that Bi-based cuprate has similar vibrational properties as graphene and transition metal dichalcogenides, which can be exploited to engineer novel heterostructures.
We observe apparent hole pockets in the Fermi surfaces of single-layer Bi-based cuprate superconductors from angle-resolved photoemission (ARPES). From detailed low-energy electron diffraction measurements and an analysis of the ARPES polarization-dependence, we show that these pockets are not intrinsic, but arise from multiple overlapping superstructure replicas of the main and shadow bands. We further demonstrate that the hole pockets reported recently from ARPES [Meng et al, Nature 462, 335 (2009)] have a similar structural origin, and are inconsistent with an intrinsic hole pocket associated with the electronic structure of a doped CuO$_2$ plane. The nature of the Fermi surface topology in the enigmatic pseudogap phase therefore remains an open question.
Using Cu-$L_3$ edge resonant inelastic x-ray scattering (RIXS) we measured the dispersion and damping of spin excitations (magnons and paramagnons) in the high-$T_mathrm{c}$ superconductor (Bi,Pb)$_{2}$(Sr,La)$_{2}$CuO$_{6+delta}$ (Bi2201), for a large doping range across the phase diagram ($0.03lesssim plesssim0.21$). Selected measurements with full polarization analysis unambiguously demonstrate the spin-flip character of these excitations, even in the overdoped sample. We find that the undamped frequencies increase slightly with doping for all accessible momenta, while the damping grows rapidly, faster in the (0,0)$rightarrow$(0.5,0.5) nodal direction than in the (0,0)$rightarrow$(0.5,0) antinodal direction. We compare the experimental results to numerically exact determinant quantum Monte Carlo (DQMC) calculations that provide the spin dynamical structure factor $S(textbf{Q},omega)$ of the three-band Hubbard model. The theory reproduces well the momentum and doping dependence of the dispersions and spectral weights of magnetic excitations. These results provide compelling evidence that paramagnons, although increasingly damped, persist across the superconducting dome of the cuprate phase diagram; this implies that long range antiferromagnetic correlations are quickly washed away, while short range magnetic interactions are little affected by doping.
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