Determining gap nodal structures in Fe-based superconductors: Theory of the angle dependence of the low-temperature specific heat in an applied magnetic field

Since the discovery of high-$T_c$ ${\mathrm{LaO}}_{1-x}{\mathrm{F}}_x\mathrm{FeAs}$ and other such systems based on $\mathrm{FeAs}$ layers, several proposals have been made for the superconducting order parameter ${\Delta }_{\mathbf{k}}$, on both phenomenological and microscopic grounds. Here we discuss how the symmetry of ${\Delta }_{\mathbf{k}}$ in the bulk can be determined, assuming that single crystals will soon be available. We suggest that a measurement of the dependence of the low-temperature specific heat on the angle of a magnetic field in the $\mathrm{FeAs}$ plane is the simplest such method, and calculate representative specific heat vs field angle oscillations for the various candidate states, using a phenomenological band structure fitted to the density functional theory Fermi surface.

Figure 1

(Color online) The two hybridized bands of our model. The white region depicts the narrow energy window around the Fermi energy (dashed line) where the model reproduces the semiquantitative aspects of the local-density approximation band structure. The momenta refer to points in the two-dimensional effective large Brillouin zone (see Fig. 2).

Figure 2

(Color online) The different FS sheets in the large effective BZ calculated within our two-band model. The two hybridized bands result in two sets of Fermi surface sheets, centered around the $\Gamma$ point (blue) and the $M$ point (red) of the real BZ (dashed black line). Backfolding of the large into the small BZ produces the dashed sheets in the small zone. The black crosses show the FS of the paramagnetic ground state determined by DFT (Ref. 14).

Figure 3

(Color online) Candidate order parameter states considered in this work. (a) $d_{x^2-y^2}$ state; (b) $d_{xy}$ state; (c) extended $s$ state; (d) generalized extended $s$; (e) $p_x$ state $({\Delta }_{\mathbf{k}}\propto \sin k_x)$; (f) nodeless state with symmetry $p_x+i{p}_y$ $({\Delta }_{\mathbf{k}}=\sin k_x+i\sin k_y)$. Solid and dashed red and blue lines correspond to sheets of the Fermi surface as in Fig. 2. The dashed orange line denotes the small Brillouin zone and the green line denotes locus of gap nodes.

Figure 4

(Color online) Residual density of states $N(\omega =0,\mathbf{H})$ vs $\alpha$, the angle $\mathbf{H}$ makes with the $x$ axis for the different superconducting states shown in Fig. 3. $N(\omega =0,\mathbf{H})$ is proportional to the linear specific heat coefficient at low temperature. Note all curves have been offset by a constant amount for clarity.