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 $C(\mathbf{H})$ 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, $C(\mathbf{H})$ has $\cos 4\varphi$ component, where $\varphi$ is the angle between $\mathbf{H}$ and the direction between hole and electron Fermi surfaces. The maxima of $C(\mathbf{H})$ are at $\pi \mathrm{/}4$, $3\pi \mathrm{/}4$, etc. if the applied field is smaller than $H_0\le 1T$, and at $\varphi =0,\pi \mathrm{/}2$, etc. if the applied field is larger than $H_0$. The angle-dependence of $C(\mathbf{H})$, 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 $\cos 4\varphi$ variation does not hold if the $s-$wave gap has accidental nodes along the two electron Fermi surfaces.