Gap structure probed by field-angle resolved thermal oscillations in $A_y$Fe$_2$Se$_2$ superconductors
We present a numerical study of the angle-resolved oscillations of the thermal conductivity and specific heat under rotated magnetic field in the $A_y$Fe$_2$Se$_2$ [$A$=K,Cs,(Tl,K)] superconductors, using realistic two-band Fermi surface parameterization. We find that even for isotropic pairing over an anisotropic Fermi surface, the thermodynamic quantities exhibit substantial oscillatory behavior in the superconducting state beyond that due to the anisotropy of the upper critical field. Furthermore, in multiband systems the competition of anisotropies between two Fermi surfaces can cause a double sign-reversal of the oscillations as a function of temperature, irrespective of gap anisotropy. Our findings put severe constraints on simple interpretations of field-angle resolved measurements used to identify the angular structure of the superconducting gap.