Topological superconductivity, implying gapless protected surface states, has recently been proposed to exist in the compound CuxBi2Se3. 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 Cu0.3Bi2Se3 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 degrees 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.
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