Specific heat of Bi2Sr2CuO6 and Bi2Sr2CaCu2O8 in the superconducting state

Abstract

We have measured the specific heat $C\left(T\right)\mathrm{}$ of single-phase samples of the cuprate superconductors ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Cu}{\mathrm{O}}_{6-\delta }$ (2:2:0:1; $T_c=12.5\mathrm{}$ K) and ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8-\delta }$ (2:2:1:2; $T_c=84\mathrm{}$ K) in the temperature range 3-11 K. Bulk superconductivity with a Meissner fraction of about 25% is observed for both materials. We find no strong evidence for a term in $C\left(T\right)\mathrm{}$ linear in the temperature $T$; rather, $\frac{C\left(T\right)\mathrm{}}{T}$ is a linear function of $T^2$ in this temperature range. A least-squares fit gives an upper bound of 0.35 mJ/Cu${\mathrm{K}}^2$ for any linear term. This result appears to rule out gapless pairing and gap functions with lines of nodes in these materials. Though gap functions with point nodes are not excluded by our results, we demonstrate that possibility to be unlikely in these materials. We suggest further experiments to test whether such $T^3$ electronic contribution to the specific heat exists for the 2:2:0:1 material.