Anomalous Fermi-Surface Dependent Pairing in a Self-Doped High-$T_c$ Superconductor

We report the discovery of a self-doped multilayer high $T_c$ superconductor ${\mathrm{Ba}}_2{\mathrm{Ca}}_3{\mathrm{Cu}}_4{\mathrm{O}}_8{\mathrm{F}}_2$ (F0234) which contains distinctly different superconducting gap magnitudes along its two Fermi-surface sheets. While formal valence counting would imply this material to be an undoped insulator, it is a self-doped superconductor with a $T_c$ of 60 K, possessing simultaneously both electron- and hole-doped Fermi-surface sheets. Intriguingly, the Fermi-surface sheet characterized by the much larger gap is the electron-doped one, which has a shape disfavoring two electronic features considered to be important for the pairing mechanism: the van Hove singularity and the antiferromagnetic ($\pi /a$, $\pi /a$) scattering.

Figure 1

(a) Crystal structure of ${\mathrm{Ba}}_2{\mathrm{Ca}}_3{\mathrm{Cu}}_4{\mathrm{O}}_8({\mathrm{O}}_{\delta }{\mathrm{F}}_{1-\delta }{)}_2$. There are four ${\mathrm{CuO}}_2$ layers in a unit cell with the outer two having apical F atoms (b) Laue pattern of the sample shows the tetragonal symmetry without superstructure. (c) LEED pattern on the cleaved surface after ARPES measurement confirms no surface reconstruction. (d) $T_c$ vs F-substitution ratio with SQUID measurement of the measured sample (inset).

Figure 2

(a) FS map ($T=20\mathrm{K}$) by integrating spectral intensity from $E_b=20\mathrm{meV}$ to $E_f$. White double arrow shows photon polarization. Red and blue symbols give FS contours of bands $P$ and $N$ extracted by the method described in text. (b) Derivative map by integrating the derivative of the spectral density from $E_b=20\mathrm{meV}$ to $E_f$. Red and blue symbols are defined as in (a). (c)–(f) MDC (c),(d) and image (e),(f) plots of raw data along cuts marked by green arrows in (a). Arrows in (c),(d) show the $P$ and $N$ contributions in MDC curves. Band maxima ($k_f$) positions are indicated by arrows in (e),(f) marked as $P$ and $N$, respectively. Dotted lines superimposed on (e),(f) are MDC fit dispersions of both bands. Insets in (e),(f) illustrate one (above) and two (below) Lorentzian peaks fits of the MDCs at $E_b=150\mathrm{meV}$.

Figure 3

Raw data image (top) and EDC stack (bottom) plots along cuts indicated in the inset. Red and blue broken lines in EDC plots are guides to the eye that follow the band dispersions. Red and blue bold EDCs represent the EDCs at $k_f$ positions for a pair of $P$ and $N$ bands, which are also indicated by arrows in the image plots.

Figure 4

Temperature dependent EDCs from points a–f along both FSs (see inset); $T=80\mathrm{K}(\mathrm{\text{red}})$ and 20 K (blue) data are measured on two cleaves of the same sample.

Figure 5

(a) FS contours from two samples show good agreement. Black double arrow shows the ($\pi /a$, $\pi /a$) scattering vector. Angle $\theta$ gives the definition of horizontal axis in (b). (b) Leading edge gap along $k$-space angle from the two FS contours. (c),(d) Three representative EDCs from both FS contours (labeled as 1–3, blue for band $N$ and red for $P$, respectively, measured at $T=20\mathrm{K}$) that give the corresponding points in (b). Black lines superimposed on EDCs are empirical fits to the data; the fit peaks’ positions from both bands are indicated by black arrows.