Correction to: Scientific Reports https://doi.org/10.1038/s41598-023-28106-0, published online 30 January 2023


The original version of this Article contained errors in the Results and discussion section.


“Wurde et al.5 predicted that there two surface resonance (SR) states near TBBE and BBBE at \({\overline{\text{M}}}_{{Pb\left( {111} \right)}}\) [S1 and S2 of Fig. 3 in Ref. 5].”


now reads:


“Wurde et al.5 predicted that there are two surface resonance (SR) states near BBBE and TBBE at \({\overline{\text{M}}}_{{Pb\left( {111} \right)}}\) [S1 and S2 of Fig. 3 in Ref. 5].”


Additionally,


“However, their surface weights are not as large as those of S2 and S3 so the intensity of the extra band is substantially lower than them in Fig. 3c.”


now reads:


“However, their surface weights are not as large as those of S2 and S3 so the intensity of the extra band is substantially lower than them in Fig. 3d.”


And,


“The blue dashed-dot curves in Fig. 3c, d represent the calculated SR bands of Pb(111), extracted from Fig. 3 of Ref. 5 in two symmetry directions.”


now reads:


“The blue dashed-dot curves in Fig. 3d, f represent the calculated SR bands of Pb(111), extracted from Fig. 3 of Ref. 5 in two symmetry directions.”


Finally,


“Figure 6 shows the calculated charge distribution of S1 state at \(M_{3 \times 3}^{1} \left( {M_{{Pb\left( {111} \right)}} } \right)\) in the Au and six Pb layers below, for the three cases.”


now reads:


“Figure 6 shows the calculated charge distribution of S1 state at \(M_{3 \times 3}^{1} \left( {M_{{Pb\left( {111} \right)}} } \right)\) in the Au, Cu, Ag and six Pb layers below, for the three cases.”


The original Article has been corrected.