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Register a new userDoping evolution of the electronic structure in the single-layer cuprates Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+delta}$: Comparison with other single-layer cuprates
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We have performed angle-resolved photoemission and core-level x-ray photoemission studies of the single-layer cuprate Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+delta}$ (Bi2201) and revealed the doping evolution of the electronic structure from the lightly-doped to optimally-doped regions. We have observed the formation of the dispersive quasi-particle band, evolution of the Fermi ``arc into the Fermi surface and the shift of the chemical potential with hole doping as in other cuprates. The doping evolution in Bi2201 is similar to that in Ca$_{2-x}$Na$_{x}$CuO$_{2}$Cl$_2$ (Na-CCOC), where a rapid chemical potential shift toward the lower Hubbard band of the parent insulator has been observed, but is quite different from that in La$_{2-x}$Sr$_{x}$CuO$_{4}$ (LSCO), where the chemical potential does not shift, yet the dispersive band and the Fermi arc/surface are formed around the Fermi level already in the lightly-doped region. The (underlying) Fermi surface shape and band dispersions are quantitatively analyzed using tight-binding fit, and the deduced next-nearest-neighbor hopping integral $t$ also confirm the similarity to Na-CCOC and the difference from LSCO.
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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.
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.
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.
How out-of-plane disorder affects the electronic structure has been investigated for the single-layer cuprates Bi$_2$Sr$_{1.6}$$Ln$$_{0.4}$CuO$_{6+delta}$ ($Ln$ = La, Nd, Gd) by angle-resolved photoemission spectroscopy. We have observed that, with increasing disorder, while the Fermi surface shape and band dispersions are not affected, the quasi-particle width increases, the anti-nodal gap is enhanced and the superconducting gap in the nodal region is depressed. The results indicate that the superconductivity is significantly depressed by out-of-plane disorder through the enhancement of the anti-nodal gap and the depression of the superconducting gap in the nodal region.
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