Specific heat to H _c2: Evidence for nodes or deep minima in the superconducting gap of underdoped and overdoped Ba(Fe _1-xCo _x) ₂As ₂

Low-temperature specific heat, C, in magnetic fields up to H _c2 is reported for underdoped Ba(Fe _0.955Co _0.045) ₂As ₂ (T _c = 8 K) and for three overdoped samples Ba(Fe _1-xCo _x) ₂As ₂ (x = 0.103, 0.13, and 0.15; T _c = 17.2, 16.5, and 11.7 K, respectively). Previous measurements of thermal conductivity (as a function of temperature and field) and penetration depth on comparable-composition samples gave some disagreement as to whether there was fully gapped/nodal behavior in the under-/overdoped materials, respectively. The present work shows that the measured behavior of the specific heat γ (C/T as T → 0, i.e., a measure of the electronic density of states at the Fermi energy) as a function of field approximately obeys γ H0.5 ^±0.1, similar to the Volovik effect for nodal superconductors, for both the underdoped and the most overdoped Co samples. However, for the two overdoped compositions x = 0.103 and 0.13, the low-field (H ≤ 10 T) data show a Volovik-like behavior of γ H0.3 ^-0.4, followed by an inflection point, followed at higher fields by γ H1. We argue that, within the two-band theory of superconductivity, an inflection point may occur if the interband coupling is dominant.