Field dependence of the zero energy density of states of an anisotropic $s_{\pm}$ superconductor

The pairing symmetry in iron-based superconductors (SC) is generally believed to be an $s_{\pm}$-wave state. Although ARPES suggests a mainly isotropic gap on all Fermi surface sheets, different thermodynamic and transport measurements are still inconclusive about the existence and orientation of gap nodes. Specific heat measurements in a magnetic field showing a square root like dependence of the Sommerfeld coefficient $\gamma(B)$ have been reported, contradicting the linear behavior expected for a fully gapped system. For a $d$-wave SC, $\gamma(B)\propto\sqrt{B}$ is well-known as Volovik effect. For a fully gapped $s_{\pm}$-wave SC with $\Delta_+\ne\Delta_-$, a similar concave field dependence is expected. To distinguish these two effects we apply a two-band model using the Riccati parametrization of the Eilenberger equation to study the density of states around a single vortex and compare it with self-consistent calculations in the vortex lattice. Different models for the momentum dependence of the gap on each band relevant to the iron-based SC, ranging from isotropic to strongly anisotropic and nodal gaps are investigated. Partial support was provided by DOE DE-FG02-05ER46236 (PJH).