Bulk Superconducting Phase with a Full Energy Gap in the Doped Topological Insulator ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$

The superconductivity recently found in the doped topological insulator ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ offers a great opportunity to search for a topological superconductor. We have successfully prepared a single-crystal sample with a large shielding fraction and measured the specific-heat anomaly associated with the superconductivity. The temperature dependence of the specific heat suggests a fully gapped, strong-coupling superconducting state, but the BCS theory is not in full agreement with the data, which hints at a possible unconventional pairing in ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$. Also, the evaluated effective mass of $2.6m_e$ ($m_e$ is the free electron mass) points to a large mass enhancement in this material.

Figure 1

(a) ${\rho }_{xx}(T)$ data of the ${\mathrm{Cu}}_{0.29}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ sample. (b) Temperature dependence of $R_H$; inset shows the ${\rho }_{yx}(B)$ data at 5 K. (c),(d) ${\rho }_{xx}(B)$ data for $B\parallel ab$ and $B\perp ab$, respectively. (e) $B_{c2}$ vs $T$ phase diagram determined from the midpoint in ${\rho }_{xx}(B)$ at various temperatures; solid lines show the WHH behavior. The midpoint definition for $B_{c2}$ gives $T_c=3.2\mathrm{K}$ consistent with the $M(T)$ data.

Figure 2

(a) Temperature dependence of the apparent shielding fraction of ${\mathrm{Cu}}_{0.29}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ measured in $B=0.2\mathrm{mT}\parallel ab$. (b) $M(B)$ curves at 1.8 and 2.4 K after subtracting the diamagnetic background. (c) Initial $M(B)$ behavior after ZFC to various temperatures. Arrows mark the position of $B_{c1,\parallel }$. Note the very small magnetic-field scale. (d) Plots of $\Delta M\equiv M-aB$, where $a$ is the initial slope, and the determination of $B_{c1,\parallel }$ shown by arrows. (e) $B_{c1,\parallel }$ vs $T$ phase diagram; the solid line is a fit within the local dirty limit.

Figure 3

(a) $c_p(T)/T$ data measured in 0 and 2 T applied along the $c$ axis; the latter represent the normal-state behavior. The dashed line is a fit to the 2-T data using the standard Debye formula. (b) Electronic term $c_{\mathrm{el}}/T$ in 0 T obtained after subtracting the phonon term determined in 2 T. The dotted line shows the calculated $c_{\mathrm{el}}/T$ curve given by strong-coupling BCS theory with $\alpha =1.9$; the dashed line is the BCS curve for $\alpha =2.3$, which is obtained from $B_c$, $N_0$, and $T_c$. The horizontal dash-dotted line denotes the value of ${\gamma }_n$, and its breakdown to ${\gamma }_s$ and ${\gamma }_{\mathrm{res}}$ is indicated.