a Differential tunneling conductance (dI/dV) map showing star-shaped LDOS modulations of the YSR bound states around magnetic atoms. Tunneling parameters: IT = 1.0 nA, VS = −1.2 mV, 150 × 150 nm2, scale bar: 30 nm. (Inset: Atomically resolved STM constant-current image. Scale bar: 1.0 nm). The white arrows, a1(a2) and the yellow arrows, a1*(a2*) denote the lattice vector directions on the La(0001) surface extracted from the STM image and the corresponding reciprocal lattice vectors, respectively. b, c Zoomed-in dI/dV maps for an isolated magnetic atom YSR1 (white arrow in a) showing oscillatory beam-like extensions of the YSR bound state at b VS = −1.2 mV and c VS = +1.2 mV, 60 × 60 nm2, IT = 1.0 nA, scale bar: 15 nm. d Tunneling spectra measured on a single magnetic impurity (orange) and on the La(0001) surface (gray). A superconducting La-coated PtIr tip with a gap size of ΔT = 0.65 meV was used for taking STM images and differential tunneling conductance maps. A pair of the YSR bound states is indicated by red and blue arrows at ±|Δtip + EYSR | with EYSR = 0.55 meV (black arrows). e Differential tunneling conductance profiles taken across the center of a magnetic atom along two different directions, Q1 and Q2, as depicted in the inset. The profile along Q1 is plotted with an offset for clarity. f One-dimensional tunneling spectroscopic map across the YSR1 impurity along the Q2 direction.