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Text: We model the Shiba bands by a low - energy model based on Ref . 10 for YSR impurities in a superconducting host with effective Rashba SOC ( see Methods ) . We derive Shiba band structures which closely resemble the experimental -and -YSR bands ( Fig . 4b , c and Supplementary Figures 6 and 7 ) using parameters which are consistent ( Supplementary Note 6 ) with the energies and particle - hole asymmetries of the respective single atom YSR states the bands emerge from ( Fig . 1d ) . In particular , Figs . 4b and 4c ( left panel ) show the according fit to the -YSR band . Originating from the non - degenerate single impurity YSR states ( Fig . 1 ) , the -YSR band is nondegenerate itself . A symmetry analysis of the system corroborates this result . We , therefore , conclude that the gap opened in the -YSR band is due to a p - wave contribution to the pairing mechanism . From the model calculations , we find that the topological index 1 of the -YSR band is nontrivial . Generally , the topological index can be derived from the experimental data assuming a weak superconducting pairing ( ∆ ind < < Shiba band width ) and if the band features a strong asymmetry in its respective particle - hole weight ( Supplementary Note 7 ) , which is both fulfilled for the -YSR band . We extrapolate to the fictitious case of a gapless band structure by setting the effective SOC to zero ( dashed line in Fig . 4b ) and count the number of Fermi level crossings c = 1 between k = 0 and k = π . This directly relates to Kitaev 's ℤ 2 -invariant 1 M = ( -1 ) c = -1 for this band . We thus find that the -YSR band carries a non - trivial topological index . In contrast , band structures with trivial gaps ( Fig . 4c , center & right panels ) , which can be simulated by changing the coupling of the individual impurity to the superconductor ( parametrized by A , see Methods ) , would have a strongly different appearance in conflict with the experiment .<|eot_id|><|start_header_id|>assistant<|end_header_id|>

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