Volovik effect in the $\pm$s-wave state for the iron-based superconductors

Abstract

We studied the field dependencies of specific heat coefficient $\gamma (H)={\lim }_{T\to 0}C(T,H)/T$ and thermal conductivity coefficient ${\lim }_{T\to 0}\kappa (T,H)/T$ of the $\pm$s-wave state in the mixed state. We found that it is a generic feature of the two band s-wave state with the unequal sizes of gaps, small ${\Delta }_S$ and large ${\Delta }_L$, that Doppler shift of the quasiparticle excitations (Volovik effect) creates a finite density of states, on the extended states outside of vortex cores, proportional to $H$ in contrast to the $\sqrt{H}$ dependence of the d-wave state. Impurity scattering effect on the $\pm$s-wave state, however, makes this generic $H$-linear dependence sublinear approaching to the $\sqrt{H}$ behavior. Our calculations of ${\lim }_{T\to 0}\kappa (T,H)/T$ successfully fit the experimental data of Ba(Fe${}_{1-x}$Co${}_x{)}_2$ As${}_2$ with different Co-doping $x$ by systematically varying the gap size ratio $R=|{\Delta }_S|/|{\Delta }_L|$. We also resolve the dilemma of a substantial value of $\gamma (H\to 0)$ but almost zero value of ${\lim }_{T\to 0}\kappa (T,H\to 0)/T$, observed in experiments.

5 pages, 2 figures accepted to Phys. Rev. Lett.

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