Dependence of superconductivity in ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ on quenching conditions

Topological superconductivity, implying gapless protected surface states, has recently been proposed to exist in the compound ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$. Unfortunately, low diamagnetic shielding fractions and considerable inhomogeneity have been reported in this compound. In an attempt to understand and improve on the finite superconducting volume fractions, we have investigated the effects of various growth and postannealing conditions. With a melt-growth (MG) method, diamagnetic shielding fractions of up to 56% in ${\mathrm{Cu}}_{0.3}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ have been obtained, the highest value reported for this method. We investigate the efficacy of various quenching and annealing conditions, finding that quenching from temperatures above ${560}^{\circ }\mathrm{C}$ is essential for superconductivity, whereas quenching from lower temperatures or not quenching at all is detrimental. A modified floating zone (FZ) method yielded large single crystals but little superconductivity. Even after annealing and quenching, FZ-grown samples had much less chance of being superconducting than MG-grown samples. From the low shielding fractions in FZ-grown samples and the quenching dependence, we suggest that a metastable secondary phase having a small volume fraction in most of the samples may be responsible for the superconductivity.

Figure 1

(a) Resistance vs temperature for a single crystal of $x=0.35$. (b) Magnetic susceptibility $\chi$ vs temperature for a single crystal with $x=0.25$, 2.2 mg, and $\sim 30\%$ shielding fraction at 1.7 K. The applied field was 2 Oe with $H\perp c$, with both zero field cooling (ZFC) and field cooling (FC) shown. (c) Magnetization curve for a single crystal with $x=0.35$ near 1.7 K for both $H\perp c$ and $H\parallel c$ under ZFC; the shielding fraction was found to be 48% at 1.7 K. The best-fit line used for shielding fraction calculation has been plotted. In (b) and (c), two measurements were taken at each field and temperature, respectively, then averaged and plotted. (d) and (e) Composition as determined by EDX measurements for samples taken from different sections of an $x=0.25$ FZ ingot. The sections are ordered by increasing height. (d) Atomic percents of Cu, Bi, and Se. (e) $x$ for the ratio ${\mathrm{Cu}}_x$:${\mathrm{Bi}}_2$ for the first three sections. (f) Photo of crystals cleaved from section 3 of the same ingot. The smallest division of the grid is 1 mm.

Figure 2

(a) Shielding fractions obtained for samples of ${\mathrm{Cu}}_{0.3}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ obtained for various growth and annealing conditions. See text for description of conditions. The numbers of samples plotted in each row from top to bottom are 19, 12, 18, 31, 6, 6, and 18. (b) Shielding fractions for MG ${\mathrm{Cu}}_{0.3}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ samples obtained after annealing and quenching at the displayed temperatures. The numbers of samples plotted in each row from top to bottom are 11, 31, 6, 6, 6, and 6. In (a) and (b), for each distribution of shielding fractions (including nonsuperconducting samples), the box plot indicates the median, quartiles, and the most extreme values not greater than 1.5 times the interquartile range from the median; the triangles represent samples with negligible diamagnetic response.