Visualizing Pairing Symmetry in Nematic Superconductors using spin-polarized spectroscopy of magnetic impurities

We study the spin-polarized spectral properties of Yu-Shiba-Rusinov resonance states induced by magnetic impurities in 2- and 3-dimensional nematic superconductors: few layer Bi$_2$Te$_3$ grown on FeTe$_{0.55}$Se$_{0.45}$ (2-dimensional) and Cu$_x$Bi$_2$Se$_3$ (3-dimensional). We focus on the relationship between pairing symmetry and the topograph of spin-polarized spectroscopy. We calculate the spin-polarized local density of states (SP LDOS) and the corresponding Fourier transformation using the $T$-matrix method for both the 2- and 3-dimensional materials. Various situations with different impurity orientations and different SP LDOSs have been investigated. We find that, like the quasiparticle interference spectrum, the SP LDOS can be applied to distinguish other pairings which preserve the threefold rotation symmetry of $D_3$ point group and nematic pairings in these materials.