Eigler, D. M. & Schweizer, E. K. Positioning single atoms with a scanning tunnelling microscope. Nature 344, 524–526 (1990).

Article 
ADS 

Google Scholar
 

Choi, D.-J. et al. Colloquium: atomic spin chains on surfaces. Rev. Mod. Phys. 91, 041001 (2019).

Article 
ADS 

Google Scholar
 

Khajetoorians, A. A., Wegner, D., Otte, A. F. & Swart, I. Creating designer quantum states of matter atom-by-atom. Nat. Rev. Phys. 1, 703–745 (2019).

Article 

Google Scholar
 

Piquero-Zulaica, I. et al. Engineering quantum states and electronic landscapes through surface molecular nanoarchitectures. Rev. Mod. Phys. 94, 045008 (2022).

Article 
ADS 

Google Scholar
 

Crommie, M. F., Lutz, C. P. & Eigler, D. M. Confinement of electrons to quantum corrals on a metal surface. Science 262, 218–220 (1993).

Article 
ADS 

Google Scholar
 

Moon, C. R. et al. Quantum phase extraction in isospectral electronic nanostructures. Science 319, 782–787 (2008).

Article 
ADS 
MathSciNet 

Google Scholar
 

Gomes, K. K., Mar, W., Ko, W., Guinea, F. & Manoharan, H. C. Designer Dirac fermions and topological phases in molecular graphene. Nature 483, 306–310 (2012).

Article 
ADS 

Google Scholar
 

Shockley, W. On the surface states associated with a periodic potential. Phys. Rev. 56, 317–323 (1939).

Article 
ADS 

Google Scholar
 

Gartland, P. O. & Slagsvold, B. J. Transitions conserving parallel momentum in photoemission from the (111) face of copper. Phys. Rev. B 12, 4047–4058 (1975).

Article 
ADS 

Google Scholar
 

Heimann, P., Neddermeyer, H. & Roloff, H. F. Ultraviolet photoemission for intrinsic surface states of the noble metals. J. Phys. C: Solid State Phys. 10, L17–L21 (1977).

Article 
ADS 

Google Scholar
 

Manoharan, H., Lutz, C. P. & Eigler, D. Quantum mirages formed by coherent projection of electronic structure. Nature 403, 512–515 (2000).

Article 
ADS 

Google Scholar
 

Fiete, G. A. et al. Scattering theory of Kondo mirages and observation of single Kondo atom phase shift. Phys. Rev. Lett. 86, 2392–2395 (2001).

Article 
ADS 

Google Scholar
 

Porras, D., Fernández-Rossier, J. & Tejedor, C. Microscopic theory for quantum mirages in quantum corrals. Phys. Rev. B 63, 155406 (2001).

Article 
ADS 

Google Scholar
 

Agam, O. & Schiller, A. Projecting the Kondo effect: theory of the quantum mirage. Phys. Rev. Lett. 86, 484–487 (2001).

Article 
ADS 

Google Scholar
 

Weissmann, M. & Bonadeo, H. A simple interpretation of quantum mirages. Physica E 10, 544–548 (2001).

Article 
ADS 

Google Scholar
 

Aligia, A. A. Many-body theory of the quantum mirage. Phys. Rev. B 64, 121102 (2001).

Article 
ADS 

Google Scholar
 

Hallberg, K., Correa, A. A. & Balseiro, C. A. Spectroscopic and magnetic mirages of impurities in nanoscopic systems. Phys. Rev. Lett. 88, 066802 (2002).

Article 
ADS 

Google Scholar
 

Lobos, A. & Aligia, A. A. One- and many-body effects on mirages in quantum corrals. Phys. Rev. B 68, 035411 (2003).

Article 
ADS 

Google Scholar
 

Schmid, M. & Kampf, A. Mirages, anti-mirages, and further surprises in quantum corrals with non-magnetic impurities. Ann. Phys. 515, 463–470 (2003).

Article 

Google Scholar
 

Morr, D. K. & Stavropoulos, N. A. Quantum corrals, eigenmodes, and quantum mirages in s-wave superconductors. Phys. Rev. Lett. 92, 107006 (2004).

Article 
ADS 

Google Scholar
 

Fu, Z.-G., Zhang, P., Wang, Z. & Li, S.-S. Quantum corrals and quantum mirages on the surface of a topological insulator. Phys. Rev. B 84, 235438 (2011).

Article 
ADS 

Google Scholar
 

Gadzuk, J. W. & Plihal, M. Quantum mirages in scanning tunneling spectroscopy of Kondo adsorbates: vibrational signatures. Phys. Rev. B 68, 235413 (2003).

Article 
ADS 

Google Scholar
 

Fransson, J. & Balatsky, A. V. Imaging spin-inelastic Friedel oscillations emerging from magnetic impurities. Phys. Rev. B 85, 161401 (2012).

Article 
ADS 

Google Scholar
 

Balatsky, A. V., Vekhter, I. & Zhu, J.-X. Impurity-induced states in conventional and unconventional superconductors. Rev. Mod. Phys. 78, 373–433 (2006).

Article 
ADS 

Google Scholar
 

Heinrich, B. W., Pascual, J. I. & Franke, K. J. Single magnetic adsorbates on s-wave superconductors. Prog. Surf. Sci. 93, 1–19 (2018).

Article 
ADS 

Google Scholar
 

Kim, H., Rózsa, L., Schreyer, D., Simon, E. & Wiesendanger, R. Long-range focusing of magnetic bound states in superconducting lanthanum. Nat. Commun. 11, 4573 (2020).

Article 
ADS 

Google Scholar
 

Ménard, G. C. et al. Coherent long-range magnetic bound states in a superconductor. Nat. Phys. 11, 1013–1016 (2015).

Article 

Google Scholar
 

Machida, K. & Shibata, F. Bound states due to resonance scattering in superconductor. Prog. Theor. Phys. 47, 1817–1823 (1972).

Article 
ADS 

Google Scholar
 

Schneider, L. et al. Proximity superconductivity in atom-by-atom crafted quantum dots. Nature 621, 60–65 (2023).

Article 
ADS 

Google Scholar
 

Ortuzar, J., Pascual, J. I., Bergeret, F. S. & Cazalilla, M. A. Theory of a single magnetic impurity on a thin metal film in proximity to a superconductor. Phys. Rev. B 108, 024511 (2023).

Article 
ADS 

Google Scholar
 

Tomanic, T., Schackert, M., Wulfhekel, W., Sürgers, C. & v. Löhneysen, H. Two-band superconductivity of bulk and surface states in Ag thin films on Nb. Phys. Rev. B 94, 220503 (2016).

Article 
ADS 

Google Scholar
 

Ruby, M., Peng, Y., von Oppen, F., Heinrich, B. W. & Franke, K. J. Orbital picture of Yu-Shiba-Rusinov multiplets. Phys. Rev. Lett. 117, 186801 (2016).

Article 
ADS 

Google Scholar
 

Farinacci, L. et al. Tuning the coupling of an individual magnetic impurity to a superconductor: quantum phase transition and transport. Phys. Rev. Lett. 121, 196803 (2018).

Article 
ADS 

Google Scholar
 

Huang, H. et al. Quantum phase transitions and the role of impurity-substrate hybridization in Yu-Shiba-Rusinov states. Commun. Phys. 3, 199 (2020).

Article 

Google Scholar
 

Liebhaber, E. et al. Yu-Shiba-Rusinov states in the charge-density modulated superconductor NbSe2. Nano Lett. 20, 339–344 (2020).

Article 
ADS 

Google Scholar
 

Moro-Lagares, M. et al. Quantifying the leading role of the surface state in the Kondo effect of Co/Ag(111). Phys. Rev. B 97, 235442 (2018).

Article 
ADS 

Google Scholar
 

Aapro, M., Kipnis, A., Lado, J. L., Kezilebieke, S. & Liljeroth, P. Tuning spinaron and Kondo resonances via quantum confinement. Phys. Rev. B 109, 195415 (2024).

Article 
ADS 

Google Scholar
 

Chiappe, G. & Aligia, A. A. Interaction between Kondo impurities in a quantum corral. Phys. Rev. B 66, 075421 (2002).

Article 
ADS 

Google Scholar
 

Correa, A., Hallberg, K. & Balseiro, C. A. Mirages and enhanced magnetic interactions in quantum corrals. Europhys. Lett. 58, 899–905 (2002).

Article 
ADS 

Google Scholar
 

Stepanyuk, V. S., Niebergall, L., Hergert, W. & Bruno, P. Ab initio study of mirages and magnetic interactions in quantum corrals. Phys. Rev. Lett. 94, 187201 (2005).

Article 
ADS 

Google Scholar
 

Stepanyuk, V. S., Negulyaev, N. N., Niebergall, L. & Bruno, P. Effect of quantum confinement of surface electrons on adatom-adatom interactions. New J. Phys. 9, 388 (2007).

Article 
ADS 

Google Scholar
 

Brovko, O. O., Hergert, W. & Stepanyuk, V. S. Quantum confinement on nanoislands as a tool for tailoring exchange interaction: an ab initio study. Phys. Rev. B 79, 205426 (2009).

Article 
ADS 

Google Scholar
 

Ngo, A. T., Kim, E. H. & Ulloa, S. E. Single-atom gating and magnetic interactions in quantum corrals. Phys. Rev. B 95, 161407 (2017).

Article 
ADS 

Google Scholar
 

Mishra, A., Simon, P., Hyart, T. & Trif, M. Yu-Shiba-Rusinov qubit. PRX Quantum 2, 040347 (2021).

Article 
ADS 

Google Scholar
 

Lo Conte, R., Wiebe, J., Rachel, S., Morr, D. K. & Wiesendanger, R. Magnet-superconductor hybrid quantum systems: a materials platform for topological superconductivity. Riv. Nuovo Cim. 47, 453–554 (2024).

Article 
ADS 

Google Scholar
 

Gharavi, K., Hoving, D. & Baugh, J. Readout of Majorana parity states using a quantum dot. Phys. Rev. B 94, 155417 (2016).

Article 
ADS 

Google Scholar
 

Steiner, J. F. & von Oppen, F. Readout of Majorana qubits. Phys. Rev. Res. 2, 033255 (2020).

Article 

Google Scholar
 

Löptien, P., Zhou, L., Khajetoorians, A. A., Wiebe, J. & Wiesendanger, R. Superconductivity of lanthanum revisited: enhanced critical temperature in the clean limit. J. Phys.: Condens. Matter 26, 425703 (2014).

ADS 

Google Scholar
 

Ruby, M., Heinrich, B. W., Pascual, J. I. & Franke, K. J. Experimental demonstration of a two-band superconducting state for lead using scanning tunneling spectroscopy. Phys. Rev. Lett. 114, 157001 (2015).

Article 
ADS 

Google Scholar
 

Ton, K. T. et al. Data for the article entitled: ‘Non-local detection of coherent Yu-Shiba-Rusinov quantum projections’. Zenodo https://doi.org/10.5281/zenodo.17341988 (2025).