Possible Pairing Symmetry of BaPtAs${}_{1-x}$Sb${}_x$ with an Ordered Honeycomb Network

We investigate the possible pairing symmetry of superconducting ${\mathrm{B}\mathrm{a}\mathrm{P}\mathrm{t}\mathrm{A}\mathrm{s}}_{1-x}{\mathrm{S}\mathrm{b}}_x$ solid solution with an ordered-honeycomb network of Pt and pnictogens. A spontaneous internal magnetic field below the superconducting transition temperature is observed in BaPtSb ($x=1$) via the muon-spin relaxation measurement. We then pursue a scenario where the pairing symmetry is changed from a time-reversal symmetry-breaking (TRSB) state to another one by changing the Sb-concentration utilizing the effective tight-binding model obtained from the first principles calculations for $x=0$ and $x=1$, at which we see a significant difference in the shape of the dominant Fermi surfaces. We find that the chiral $d$-wave state with TRSB is most stable at $x=1$, whereas the nodal $f$-wave or the conventional $s$-wave states without TRSB are competitive at $x=0$.