  The thermal conductivity kappa of the iron-arsenide superconductor
Ba1-xKxFe2As2 was measured for heat currents parallel and perpendicular to the
tetragonal c axis at temperatures down to 50 mK and in magnetic fields up to 15
T. Measurements were performed on samples with compositions ranging from
optimal doping (x = 0.34; Tc = 39 K) down to dopings deep into the region where
antiferromagnetic order coexists with superconductivity (x = 0.16; Tc = 7 K).
In zero field, there is no residual linear term in kappa(T) as T goes to 0 at
any doping, whether for in-plane or inter-plane transport. This shows that
there are no nodes in the superconducting gap. However, as x decreases into the
range of coexistence with antiferromagnetism, the residual linear term grows
more and more rapidly with applied magnetic field. This shows that the
superconducting energy gap develops minima at certain locations on the Fermi
surface and these minima deepen with decreasing x. We propose that the minima
in the gap structure arise when the Fermi surface of Ba1-xKxFe2As2 is
reconstructed by the antiferromagnetic order.
