Angular resolved specific heat in iron-based superconductors: the case for nodeless extended $s$-wave gap

We consider the variation of the field-induced component of the specific heat $C({\bf H})$ with the direction of the applied field in $Fe-$pnictides within quasi-classical Doppler-shift approximation, with special emphasis to recent experiments on FeSe$_{0.4}$Te$_{0.6}$ [Zheng et al., arXiv:1004.2236]. We show that for extended $s-$wave gap with no nodes, $C({\bf H})$ has $\cos 4 \phi$ component, where $\phi$ is the angle between ${\bf H}$ and the direction between hole and electron Fermi surfaces. The maxima of $C({\bf H})$ are at $\pi/4$, $3\pi/4$, etc. if the applied field is smaller than $H_0 \leq 1T$, and at $\phi =0, \pi/2$, etc. if the applied field is larger than $H_0$. The angle-dependence of $C({\bf H})$, the positions of the maxima, and the relative magnitude of the oscillating component are consistent with the experiments performed in the field of $9T >> H_0$. We show that the observed $\cos 4 \phi$ variation does not hold if the $s-$wave gap has accidental nodes along the two electron Fermi surfaces.