- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Intramolecular variations of Andreev reflection

Ankur Das, Nicolas Néel, and Jörg Kröger*

  • *Contact author: joerg.kroeger@tu-ilmenau.de
PDF

Phys. Rev. B 113, 085427 – Published 19 February, 2026

DOI: https://doi.org/10.1103/lybh-5fn2

Abstract

Andreev reflection is probed with a scanning tunneling microscope using a gold-coated normal-metal tip and a single nickel-phthalocyanine molecule adsorbed on superconducting Pb(111). Spectroscopy of the differential conductance at tip-molecule separations ranging from tunneling to contact distances unveils the evolution of Andreev reflection at the central Ni ion and its neighboring pyrrole moieties. Both molecular sites behave similarly in the tunneling range, while at contact separations deviations occur. The efficiency of Andreev reflection rises in a less pronounced manner for Ni than for the pyrrole groups. In addition, across Ni the Andreev reflection rate stays well below the maximal achievable value, while across the pyrrole groups it is nearly reached. This difference is associated with the energy shift of the lowest unoccupied molecular orbital, which reflects the progressive hybridization of the molecule with the approaching tip. The orbital energy remains above the Fermi level for Ni and dives below for the pyrrole groups, which is accompanied by the absence (Ni) and presence (pyrrole) of the molecular Kondo effect. A possible interplay of Andreev reflection and Kondo screening is suggested.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (89)

  1. P. de Gennes and D. Saint-James, Elementary excitations in the vicinity of a normal metal-superconducting metal contact, Phys. Lett. 4, 151 (1963).
  2. A. F. Andreev, The thermal conductivity of the intermediate state in superconductors, Sov. Phys. JETP 19, 1228 (1964).
  3. G. Deutscher, Andreev–Saint-James reflections: A probe of cuprate superconductors, Rev. Mod. Phys. 77, 109 (2005).
  4. K. Mendelssohn and J. L. Olsen, Anomalous heat flow in superconductors, Phys. Rev. 80, 859 (1950).
  5. J. K. Hulm, Thermal resistivity of mercury in the intermediate state, Phys. Rev. 90, 1116 (1953).
  6. S. Strässler and P. Wyder, Thermal conductivity and electron scattering at interphase boundaries in a superconductor, Phys. Rev. Lett. 10, 225 (1963).
  7. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  8. P. G. De Gennes, Boundary effects in superconductors, Rev. Mod. Phys. 36, 225 (1964).
  9. S. Artemenko, A. Volkov, and A. Zaitsev, On the excess current in microbridges S-c-S and S-c-N, Solid State Commun. 30, 771 (1979).
  10. N. Agraït, A. L. Yeyati, and J. M. van Ruitenbeek, Quantum properties of atomic-sized conductors, Phys. Rep. 377, 81 (2003).
  11. A. Martín-Rodero and A. L. Yeyati, Josephson and Andreev transport through quantum dots, Adv. Phys. 60, 899 (2011).
  12. G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion, Phys. Rev. B 25, 4515 (1982).
  13. G. E. Blonder and M. Tinkham, Metallic to tunneling transition in Cu-Nb point contacts, Phys. Rev. B 27, 112 (1983).
  14. R. J. Soulen, J. M. Byers, M. S. Osofsky, B. Nadgorny, T. Ambrose, S. F. Cheng, P. R. Broussard, C. T. Tanaka, J. Nowak, J. S. Moodera, A. Barry, and J. M. D. Coey, Measuring the spin polarization of a metal with a superconducting point contact, Science 282, 85 (1998).
  15. S. K. Upadhyay, A. Palanisami, R. N. Louie, and R. A. Buhrman, Probing ferromagnets with Andreev reflection, Phys. Rev. Lett. 81, 3247 (1998).
  16. A. Nitzan, Chemical Dynamics in Condensed Phases: Relaxation, Transfer,and Reactions in Condensed Molecular Systems (Oxford University Press, New York, 2006).
  17. P. Chalsani, S. K. Upadhyay, O. Ozatay, and R. A. Buhrman, Andreev reflection measurements of spin polarization, Phys. Rev. B 75, 094417 (2007).
  18. N. Agraït, J. G. Rodrigo, and S. Vieira, Transition from the tunneling regime to point contact and proximity-induced Josephson effect in lead-normal-metal nanojunctions, Phys. Rev. B 46, 5814 (1992).
  19. J. Y. T. Wei, N.-C. Yeh, D. F. Garrigus, and M. Strasik, Directional tunneling and Andreev reflection on YBa2Cu3O7−δ single crystals: Predominance of d-wave pairing symmetry verified with the generalized Blonder, Tinkham, and Klapwijk theory, Phys. Rev. Lett. 81, 2542 (1998).
  20. N. Hauptmann, M. Becker, J. Kröger, and R. Berndt, Surface reconstruction and energy gap of superconducting V3Si(001), Phys. Rev. B 79, 144522 (2009).
  21. J. Brand, P. Ribeiro, N. Néel, S. Kirchner, and J. Kröger, Impact of atomic-scale contact geometry on Andreev reflection, Phys. Rev. Lett. 118, 107001 (2017).
  22. L. Meyer, M. Kögler, A. Das, J. L. Lado, N. Néel, and J. Kröger, Charge transport across single molecules at the metal–superconductor interface, Small, 2412706 (2025).
  23. W. Ko, J. L. Lado, and P. Maksymovych, Noncontact Andreev reflection as a direct probe of superconductivity on the atomic scale, Nano Lett. 22, 4042 (2022).
  24. W. Ko, S. Y. Song, J. Yan, J. L. Lado, and P. Maksymovych, Atomic-scale Andreev probe of unconventional superconductivity, Nano Lett. 23, 8310 (2023).
  25. L. Meyer, J. L. Lado, N. Néel, and J. Kröger, Control of Andreev reflection via a single-molecule orbital, Phys. Rev. Lett. 134, 146201 (2025).
  26. N. Néel, J. Kröger, and R. Berndt, Two-level conductance fluctuations of a single-molecule junction, Nano Lett. 11, 3593 (2011).
  27. N. Néel, L. Limot, J. Kröger, and R. Berndt, Rotation of C60 in a single-molecule contact, Phys. Rev. B 77, 125431 (2008).
  28. G. Schulze, K. J. Franke, A. Gagliardi, G. Romano, C. S. Lin, A. L. Rosa, T. A. Niehaus, T. Frauenheim, A. Di Carlo, A. Pecchia, and J. I. Pascual, Resonant electron heating and molecular phonon cooling in single C60 junctions, Phys. Rev. Lett. 100, 136801 (2008).
  29. J. Kondo, Resistance minimum in dilute magnetic alloys, Prog. Theor. Phys. 32, 37 (1964).
  30. A. A. Abrikosov, Electron scattering on magnetic impurities in metals and anomalous resistivity effects, Phys. Phys. Fiz. 2, 5 (1965).
  31. A. A. Abrikosov, Influence of impurity ferromagnetism and of the external magnetic field on the resistance of a metal with magnetic impurities, Phys. Phys. Fiz. 2, 61 (1965).
  32. H. Suhl, Theory of Magnetism in Transition Metals (Academic, London, 1967), pp. 116–205.
  33. I. Horcas, R. Fernández, J. M. Gómez-Rodríguez, J. Colchero, J. Gómez-Herrero, and A. M. Baro, WSXM: A software for scanning probe microscopy and a tool for nanotechnology, Rev. Sci. Instrum. 78, 013705 (2007).
  34. M. Müller, N. Néel, S. Crampin, and J. Kröger, Lateral electron confinement with open boundaries: Quantum well states above nanocavities at Pb(111), Phys. Rev. Lett. 117, 136803 (2016).
  35. M. Müller, N. Néel, S. Crampin, and J. Kröger, Open-boundary reflection of quantum well states at Pb(111), Phys. Rev. B 96, 205426 (2017).
  36. M. Schmid, W. Hebenstreit, P. Varga, and S. Crampin, Quantum well and electron interference phenomena in Al due to subsurface noble gas bubbles, Phys. Rev. Lett. 76, 2298 (1996).
  37. O. Kurnosikov, O. A. O. Adam, H. J. M. Swagten, W. J. M. de Jonge, and B. Koopmans, Probing quantum wells induced above a subsurface nanocavity in copper, Phys. Rev. B 77, 125429 (2008).
  38. O. Kurnosikov, J. H. Nietsch, M. Sicot, H. J. M. Swagten, and B. Koopmans, Long-range electron interferences at a metal surface induced by buried nanocavities, Phys. Rev. Lett. 102, 066101 (2009).
  39. O. Kurnosikov, D. V. Kulikov, V. S. Kharlamov, H. J. M. Swagten, and Y. V. Trushin, Temperature-induced evolution of subsurface nanocavities in argon-implanted copper, Phys. Rev. B 84, 054109 (2011).
  40. O. Kurnosikov, H. J. M. Swagten, and B. Koopmans, Internal electron diffraction from atomically ordered subsurface nanostructures in metals, Phys. Rev. Lett. 106, 196803 (2011).
  41. C. Sprodowski and K. Morgenstern, Three types of bulk impurity induced interference patterns on the (100) and (111) faces of Ne- and Ar-doped silver, Phys. Rev. B 82, 165444 (2010).
  42. J. Schaffert, M. C. Cottin, A. Sonntag, H. Karacuban, C. A. Bobisch, N. Lorente, J.-P. Gauyacq, and R. Möller, Imaging the dynamics of individually adsorbed molecules, Nat. Mater. 12, 223 (2013).
  43. J. Schaffert, M. C. Cottin, A. Sonntag, C. A. Bobisch, R. Möller, J.-P. Gauyacq, and N. Lorente, Tunneling electron induced rotation of a copper phthalocyanine molecule on Cu(111), Phys. Rev. B 88, 075410 (2013).
  44. S. Fremy-Koch, A. Sadeghi, R. Pawlak, S. Kawai, A. Baratoff, S. Goedecker, E. Meyer, and T. Glatzel, Controlled switching of a single CuPc molecule on Cu(111) at low temperature, Phys. Rev. B 100, 155427 (2019).
  45. N. Néel and J. Kröger, Orbital and skeletal structure of a single molecule on a metal surface unveiled by scanning tunneling microscopy, J. Phys. Chem. Lett. 14, 3946 (2023).
  46. Q. Zhou, Z.-F. Liu, T. J. Marks, and P. Darancet, Electronic structure of metallophthalocyanines, MPc (M = Fe, Co, Ni, Cu, Zn, Mg) and fluorinated MPc, J. Phys. Chem. A 125, 4055 (2021).
  47. P. Townsend and J. Sutton, Investigation by electron tunneling of the superconducting energy gaps in Nb, Ta, Sn, and Pb, Phys. Rev. 128, 591 (1962).
  48. J. Kröger, N. Néel, and L. Limot, Contact to single atoms and molecules with the tip of a scanning tunneling microscope, J. Phys.: Condens. Matter 20, 223001 (2008).
  49. R. Berndt, J. Kröger, N. Néel, and G. Schull, Controlled single atom and single molecule contacts, Phys. Chem. Chem. Phys. 12, 1022 (2010).
  50. J. Eisenstein, Superconducting elements, Rev. Mod. Phys. 26, 277 (1954).
  51. B. T. Matthias, T. H. Geballe, and V. B. Compton, Superconductivity, Rev. Mod. Phys. 35, 1 (1963).
  52. A. Mugarza, R. Robles, C. Krull, R. Korytár, N. Lorente, and P. Gambardella, Electronic and magnetic properties of molecule-metal interfaces: Transition-metal phthalocyanines adsorbed on Ag(100), Phys. Rev. B 85, 155437 (2012).
  53. N. Néel, C. Dreßler, and J. Kröger, Effect of orbital symmetry on probing the single-molecule Kondo effect, Phys. Rev. B 109, L241401 (2024).
  54. J. Homberg, A. Weismann, R. Berndt, and M. Gruber, Inducing and controlling molecular magnetism through supramolecular manipulation, ACS Nano 14, 17387 (2020).
  55. A. Mugarza, C. Krull, R. Robles, S. Stepanow, G. Ceballos, and P. Gambardella, Spin coupling and relaxation inside molecule–metal contacts, Nat. Commun. 2, 490 (2011).
  56. M. R. Buitelaar, T. Nussbaumer, and C. Schönenberger, Quantum dot in the Kondo regime coupled to superconductors, Phys. Rev. Lett. 89, 256801 (2002).
  57. J. Tersoff and D. R. Hamann, Theory and application for the scanning tunneling microscope, Phys. Rev. Lett. 50, 1998 (1983).
  58. J. Tersoff and D. R. Hamann, Theory of the scanning tunneling microscope, Phys. Rev. B 31, 805 (1985).
  59. T. Ida, M. Ando, and H. Toraya, Extended pseudo-Voigt function for approximating the Voigt profile, J. Appl. Crystallogr. 33, 1311 (2000).
  60. M. Schmid, H.-P. Steinrück, and J. M. Gottfried, A new asymmetric pseudo-Voigt function for more efficient fitting of XPS lines, Surf. Interface Anal. 46, 505 (2014).
  61. H. O. Frota, Shape of the Kondo resonance, Phys. Rev. B 45, 1096 (1992).
  62. M. Gruber, A. Weismann, and R. Berndt, The Kondo resonance line shape in scanning tunneling spectroscopy: Instrumental aspects, J. Phys.: Condens. Matter 30, 424001 (2018).
  63. J. Li, W.-D. Schneider, R. Berndt, and B. Delley, Kondo scattering observed at a single magnetic impurity, Phys. Rev. Lett. 80, 2893 (1998).
  64. V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, Tunneling into a single magnetic atom: Spectroscopic evidence of the Kondo resonance, Science 280, 567 (1998).
  65. A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, UK, 1993).
  66. K. Nagaoka, T. Jamneala, M. Grobis, and M. F. Crommie, Temperature dependence of a single Kondo impurity, Phys. Rev. Lett. 88, 077205 (2002).
  67. K. J. Franke, G. Schulze, and J. I. Pascual, Competition of superconducting phenomena and Kondo screening at the nanoscale, Science 332, 940 (2011).
  68. H. Shiba, Classical spins in superconductors, Prog. Theor. Phys. 40, 435 (1968).
  69. A. I. Rusinov, On the theory of gapless superconductivity in alloys containing paramagnetic impurities, Sov. Phys. JETP 29, 1101 (1969).
  70. R. S. Deacon, Y. Tanaka, A. Oiwa, R. Sakano, K. Yoshida, K. Shibata, K. Hirakawa, and S. Tarucha, Kondo-enhanced Andreev transport in single self-assembled InAs quantum dots contacted with normal and superconducting leads, Phys. Rev. B 81, 121308(R) (2010).
  71. L. Li, Z. Cao, T.-F. Fang, H.-G. Luo, and W.-Q. Chen, Kondo screening of Andreev bound states in a normal metal–quantum dot–superconductor system, Phys. Rev. B 94, 165144 (2016).
  72. D. Goldhaber-Gordon, J. Göres, M. A. Kastner, H. Shtrikman, D. Mahalu, and U. Meirav, From the Kondo regime to the mixed-valence regime in a single-electron transistor, Phys. Rev. Lett. 81, 5225 (1998).
  73. P. W. Anderson, Localized magnetic states in metals, Phys. Rev. 124, 41 (1961).
  74. T. A. Costi, A. C. Hewson, and V. Zlatic, Transport coefficients of the Anderson model via the numerical renormalization group, J. Phys.: Condens. Matter 6, 2519 (1994).
  75. J. C. Cuevas, A. Levy Yeyati, and A. Martín-Rodero, Kondo effect in normal-superconductor quantum dots, Phys. Rev. B 63, 094515 (2001).
  76. U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124, 1866 (1961).
  77. M. Ternes, A. J. Heinrich, and W.-D. Schneider, Spectroscopic manifestations of the Kondo effect on single adatoms, J. Phys.: Condens. Matter 21, 053001 (2009).
  78. M. Ternes, Probing magnetic excitations and correlations in single and coupled spin systems with scanning tunneling spectroscopy, Prog. Surf. Sci. 92, 83 (2017).
  79. H. O. Frota and L. N. Oliveira, Photoemission spectroscopy for the spin-degenerate Anderson model, Phys. Rev. B 33, 7871 (1986).
  80. A. Rosch, T. A. Costi, J. Paaske, and P. Wölfle, Spectral function of the Kondo model in high magnetic fields, Phys. Rev. B 68, 014430 (2003).
  81. H. Prüser, M. Wenderoth, P. E. Dargel, A. Weismann, R. Peters, T. Pruschke, and R. G. Ulbrich, Long-range Kondo signature of a single magnetic impurity, Nat. Phys. 7, 203 (2011).
  82. H. Prüser, M. Wenderoth, A. Weismann, and R. G. Ulbrich, Mapping itinerant electrons around Kondo impurities, Phys. Rev. Lett. 108, 166604 (2012).
  83. A. F. Otte, M. Ternes, K. von Bergmann, S. Loth, H. Brune, C. P. Lutz, C. F. Hirjibehedin, and A. J. Heinrich, The role of magnetic anisotropy in the Kondo effect, Nat. Phys. 4, 847 (2008).
  84. R. Žitko, Kondo resonance lineshape of magnetic adatoms on decoupling layers, Phys. Rev. B 84, 195116 (2011).
  85. S. Karan and R. Berndt, Generation of spin in single cholesterol molecules on gold, Phys. Chem. Chem. Phys. 18, 9334 (2016).
  86. S. Karan, N. Li, Y. Zhang, Y. He, I.-P. Hong, H. Song, J.-T. Lü, Y. Wang, L. Peng, K. Wu, G. S. Michelitsch, R. J. Maurer, K. Diller, K. Reuter, A. Weismann, and R. Berndt, Spin manipulation by creation of single-molecule radical cations, Phys. Rev. Lett. 116, 027201 (2016).
  87. X. Zhang, N. Li, Y. Zhang, R. Berndt, and Y. Wang, 13-cis-retinoic acid on coinage metals: Hierarchical self-assembly and spin generation, Phys. Chem. Chem. Phys. 19, 14919 (2017).
  88. M. Gruber and R. Berndt, Manipulation of cyclohexene-based organic molecules on various metallic substrates, J. Phys. Chem. C 120, 18642 (2016).
  89. R. C. Dynes, V. Narayanamurti, and J. P. Garno, Direct measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor, Phys. Rev. Lett. 41, 1509 (1978).

Outline

Information

Phys. Rev. B 113, 085427– Published 19 February, 2026
  • Received 17 October 2025
  • Revised 17 December 2025
  • Accepted 28 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation