Evidence for a Competition between the Superconducting State and the Pseudogap State of $(\mathrm{BiPb}{)}_2(\mathrm{SrLa}{)}_2{\mathrm{CuO}}_{6+\delta }$ from Muon Spin Rotation Experiments

The in-plane magnetic penetration depth ${\lambda }_{ab}$ in optimally doped $(\mathrm{BiPb}{)}_2(\mathrm{SrLa}{)}_2{\mathrm{CuO}}_{6+\delta }$ (OP Bi2201) was studied by means of muon-spin rotation. The measurements of ${\lambda }_{ab}^{-2}(T)$ are inconsistent with a simple model of a $d$-wave order parameter and a uniform quasiparticle weight around the Fermi surface. The data are well described assuming the angular gap symmetry obtained in ARPES experiments [Phys. Rev. Lett. 98, 267004 (2007)], which suggest that the superconducting gap in OP Bi2201 exists only in segments of the Fermi surface near the nodes. The remaining parts of the Fermi surface, which are strongly affected by the pseudogap state, do not contribute significantly to the superconducting condensate.

Figure 1

(a) Dependence of ${\sigma }_{\mathrm{sc}}$ of OP Bi2201 on the applied magnetic field measured at $T=1.6\mathrm{K}$. The black solid line corresponds to ${\sigma }_{\mathrm{sc}}(H)$ obtained by using the numerical calculations of Brandt [20] ($\lambda =360\mathrm{nm}$, $\kappa =140$) for a superconductor with an isotropic energy gap. The solid red line represents ${\sigma }_{\mathrm{sc}}(H)$ expected in case of a $d$-wave superconductor. The blue dotted curves show the local magnetic field distribution $P(B)$ calculated by means of the maximum entropy Fourier-transform technique at $T=1.6\mathrm{K}$ and ${\mu }_{0}H=5$, 40, and 640 mT. (b) Field dependence of the skewness parameter ${\alpha }_s$. The solid line is the average value ${\alpha }_s=0.84(2)$.

Figure 2

(a) Dependence of ${\sigma }_{\mathrm{sc}}$ of OP Bi2201 on $T$ measured at ${\mu }_{0}H=40\mathrm{mT}$. Lines represent the theoretical ${\sigma }_{\mathrm{sc}}(T)$ curves obtained by assuming different symmetries of the superconducting energy gap [see Fig. 3a]. The errors in ${\sigma }_{\mathrm{sc}}$ are smaller than the size of data points. (b) Dependence of the skewness parameter ${\alpha }_s$ on $T$. The blue dotted curves represent $P(B)$ distributions below ($T=27\mathrm{K}$) and above ($T=30\mathrm{K}$) the VL melting temperature.

Figure 3

(a) Angular dependence of the energy gap of OP Bi2201 obtained in ARPES experiments [3]. Lines represent the various models of the gap symmetries used to analyze the experimental ${\sigma }_{\mathrm{sc}}(T)$ data [see Fig. 2a]. The inset shows schematically a part of the Fermi surface. The points “$A$” and “$B$” are close to the nodal ($\phi \sim 45°$) and the antinodal ($\phi \sim 0°$) region, respectively. (b) Temperature dependence of the energy gap in the nodal (curve $A$) and the antinodal (curve $B$) regions.