Anomalous suppression of the superfluid density in the Cu${}_x$Bi${}_2$Se${}_3$ superconductor upon progressive Cu intercalation

Cu${}_x$Bi${}_2$Se${}_3$ was recently found to be likely the first example of a time-reversal-invariant topological superconductor accompanied by helical Majorana fermions on the surface. Here we present that progressive Cu intercalation into this system introduces significant disorder and leads to an anomalous suppression of the superfluid density which was obtained from the measurements of the lower critical field. At the same time, the transition temperature $T_{\mathrm{c}}$ is only moderately suppressed, which agrees with a recent prediction for the impurity effect in this class of topological superconductors bearing strong spin-orbit coupling. Those unusual disorder effects give support to the possible odd-parity pairing state in Cu${}_x$Bi${}_2$Se${}_3$.

Figure 1

Cu content $x$ dependences of (a) critical temperature $T_{\mathrm{c}}$, (b) residual resistivity ${\rho }_0$, (c) superconducting shielding fraction, and (d) normal-state carrier density $n$. For comparison, the carrier density in pristine Bi${}_2$Se${}_3$ ($\lesssim$${10}^{19}$ cm${}^{-3}$) is shown with a diamond. Note that $n$ is essentially $x$ independent and remains low at $\sim$$1.5\times {10}^{20}$ cm${}^{-3}$. The dotted lines are guides to the eyes.

Figure 2

(a) Initial low-field $M_{\exp }$ vs $B$ curves for a sample with $x=0.26$ at various temperatures. (b) Reduced magnetization $\Delta M$ after subtracting the initial linear Meissner contribution $M_{\mathrm{lin}}$. The deviation points marked by arrows indicate $B_1$ at each temperature. (c) Plot of $B_1$ vs $T$ for $x=0.26$ together with a fit to the data. (d) Plots of $\Delta M$ vs $B$ at 1.8 K for various $x$.

Figure 3

$x$ dependences of (a) $B_{\mathrm{c}1}\left(0\right)$ for $B\parallel ab$ after the demagnetization correction, (b) corresponding penetration depth ${\lambda }_{\mathrm{av}}$, (c) $B_{\mathrm{c}2}\left(0\right)$ for fields parallel and perpendicular to the $ab$ planes, and (d) anisotropy factor $\gamma$. Dotted lines are guides to the eyes.

Figure 4

(a) Normalized superfluid density $n_s/n$ vs $x$, with $n$ the normal-state carrier density. For symbols without error bars, the estimated errors are smaller than the symbol size. (b), (c) Semilog plots of $n_s/n$ (b) and $T_{\mathrm{c}}$ (c) vs the mean free path $\ell$. The upper axis gives the corresponding $k_{\mathrm{F}}\ell$ value. To facilitate comparisons between (a) and (b) [(c)], data for different $x$ values are indicated by different symbols. The solid line $n_s^{\mathrm{BCS}}$ in (b) gives the expected disorder-induced suppression of $n_s/n$ for a conventional BCS superconductor. The inset shows $n_s^{\mathrm{BCS}}\to 1$ in the clean limit $\ell \to \infty$. The dotted lines in all panels are guides to the eyes.