Pair breaking caused by magnetic impurities in the high-temperature superconductor Bi${}_{2.1}$Sr${}_{1.9}$Ca(Cu${}_{1-x}$Fe${}_x$)${}_2$O${}_y$

Conventional superconductivity is robust against the addition of impurities unless the impurities are magnetic in which case superconductivity is quickly suppressed. Here we present a study of the cuprate superconductor Bi${}_2$Sr${}_2$Ca${}_1$Cu${}_2$O${}_{8+\delta }$ that is intentionally doped with the magnetic impurity, Fe. Through the use of our tomographic density of states technique, we find that while the superconducting gap magnitude is essentially unaffected by the inclusion of iron, the onset of superconductivity, $T_{\mathrm{C}}$, and the pair-breaking rate are strongly dependent and correlated. These findings suggest that, in the cuprates, the pair-breaking rate is critical to the determination of $T_{\mathrm{C}}$ and that magnetic impurities do not disrupt the strength of pairing but rather the lifetime of the pairs.

Figure 1

Panels (a1)–(a3) show raw nodal ARPES of Bi2212 across the measured Fe concentrations. Each spectrum was taken in $\Gamma Y$ orientation at the node and at low temperature. Panel (b) shows the energy dependence of the MDC widths for all the doping levels studied. Panel (c) shows the MDCs at E${}_{\mathrm{F}}$ for different dopings. Panel (d) shows the Im $\Sigma$ extracted from the MDC at $E_{\mathrm{F}}$ for every individual sample studied.

Figure 2

A selection of TDoS spectra for different Fe concentrations and the corresponding TDoS fit results. Panels (a1)–(a3) show TDoS curves (open circles) and the individual TDoS fits (black lines) for selected angles from the node. The inset in (a2) shows the $k$-space cuts and our definition of $\theta$. Panels (b1)–(b3) show the $\Delta$ and ${\Gamma }_{\mathrm{TDoS}}$ values exacted from the TDoS fits. The fit to $\Delta$ is a $d$-wave gap with the node and gap maximum as the only fitting parameters. The fit to ${\Gamma }_{\mathrm{TDoS}}$ is a simple average.

Figure 3

${\Gamma }_0$ and ${\Delta }_{\max }$ vs Fe impurity concentration. Panel (a) shows ${\Gamma }_0$, which is extracted from the angular average of ${\Gamma }_{\mathrm{TDoS}}$ for a given Fe concentration. ${\Gamma }_0$ shows a linear dependence on Fe concentration, as shown by the dashed line. Panel (b) shows ${\Delta }_{\max }$, which is extrapolated from the $d$-wave gap fit shown in Fig. 2. ${\Delta }_{\max }$ shows very little dependence on Fe concentration, decreasing less than 1$\%$ according to the linear fit (dashed line). The inset shows T${}_c$ vs Fe concentration, which changes from 91 K to 67 K, a 26$\%$ change over the full Fe range.

Figure 4

Segregating the effects of Fe impurities from native defects using our simple model of impurity scattering. ${\Gamma }_0^{\mathrm{Native}}$ is the pair-breaking rate for all the combined native defects not including any Fe impurities, while $\alpha$ is a dimensionless parameter that represents the pair-breaking scattering cross section (in units of Cu-Cu spacing) for Fe impurities.