Nodes versus Minima in the Energy Gap of Iron Pnictide Superconductors from Field-Induced Anisotropy

We develop the formalism for computing the oscillations of the specific heat and thermal transport under rotated magnetic field in multiband superconductors with anisotropic gap and apply it to iron-based materials. We show that these oscillations change sign at low temperatures and fields, which strongly influences the experimental conclusions about the gap structure. We find that recent measurements of the specific heat oscillations indicate that the iron-based superconductors possess an anisotropic gap with deep minima or nodes close to the line connecting electron and hole pockets. We predict the behavior of the thermal conductivity that will help distinguish between these cases.

Figure 1

Fermi surfaces and energy gaps in the two-band model of iron pnictides. The true structure is obtained by folding the FS sheets (blue [dark gray]) and SC gaps (red [medium gray]) along the sides of the square (full and dashed lines at $M$). The hole FS around $\Gamma$ has an isotropic gap. The $A_{1g}$ gap on the electronic FS may be isotropic, have deep minima along $\Gamma \mathrm{\text{−}}M$ line [panel (a), $r=0.45$ in Eq. (1)] or nodes along the [100] as in panel (b), $r=1$. We take the heat current along [100], as shown.

Figure 2

The anisotropy of $C/T$ (a),(b) and $\kappa /T$ (c),(d) for a gap with deep minima along $\Gamma \mathrm{\text{−}}M$ line (${\varphi }_0=45°$), as depicted in Fig. 1a. Except for the low-$T$, low-$H$ regime, the minima in the gap are marked by the maximum of $C$. For heat transport, note the same trend, and almost complete absence of the twofold anisotropy in $\kappa ({\varphi }_0)$ at low $H$ and $T\gtrsim 0.05T_{c0}$.

Figure 3

The anisotropy of $C/T$ (a),(b) and $\kappa /T$ (c),(d) for $r=0.55$, gap with a pair of nodes close to the $\Gamma \mathrm{\text{−}}M$ line. The overall behavior is similar to that for deep minima, Fig. 2. The additional structure in $C/T$ for near-nodal directions disappears already at low $T$, panels (a) and (b); Thermal transport shows additional structure to higher $T$, and the twofold component is dominant, panels (c) and (d).

Figure 4

Anisotropy of $C$ and $\kappa$ for $r=1$, nodes along [100], as in Fig. 1b. The nodal directions ${\varphi }_0=0$, 90°, are marked by minima of $C$ only at $T\lesssim 0.1T_c$. At higher $T$, $H$ the angle-dependence shows a maximum of $C$ for those directions, as well as additional structure.