Relation between nodes and $2\Delta /T_c$ on the hole Fermi surface in iron-based superconductors

We analyze the interplay between the absence or presence of nodes in the superconducting gap along electron Fermi surfaces (FSs) in Fe pnictides and $2\Delta /T_c$ along hole FSs ($2{\Delta }_h/T_c$), measured by angle-resolved photoemission spectroscopy (ARPES). We solve the set of coupled gap equations for 4- and 5-pocket models of Fe pnictides and relate the presence of the nodes to $2{\Delta }_h/T_c$ being below a certain threshold. Using ARPES data for $2{\Delta }_h/T_c$, we find that the optimally doped ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$ and $\text{Ba}({\text{Fe}}_{1-x}{\text{Co}}_x){}_2{\text{As}}_2$ are likely nodeless, but isovalent ${\text{BaFe}}_2({\text{As}}_{1-x}{\text{P}}_x){}_2$ likely has nodes.

Figure 1

$2{\Delta }_h/T_c$ (relative to the BCS value) for the 4-pocket model A. (a) $2{\Delta }_h/T_c$ as a function of $\alpha$ and $\beta$. The black line separates nodal and nodeless regions. The colors indicate the gap magnitudes relative to the BCS value of 3.53. (b) $2{\Delta }_h/T_c$ vs $\beta$ for different values of $r$. $r>1$ [blue (dark gray)] are nodal lines, $r<1$ [yellow (light gray)] are nodeless lines, and $r=1$ (black) is the boundary line. The dashed lines indicate the boundaries of the “gray area” (see text). Outside of gray area the gap either definitely has nodes or is definitely non-nodal.

Figure 2

Gap structure strips for the 4- and 5-pocket models A and B. Each strip shows the regions of $2{\Delta }_h/T_c$ for the largest hole gap for which the gap along the electron FS definitely has nodes [blue (dark gray)], definitely has no-nodes [yellow (light gray)], or has/does not have nodes depending on $\alpha$ (gray). In the left panel, we show typical nodal and nodeless gap structures for A models. The symbols are the ARPES values for $2{\Delta }_h/T_c$. The symbols above the horizontal line should be compared with the 4-pocket models and those below the line with the 5-pocket models.