- Letter
- Open Access
Demonstrating Kondo behavior by temperature-dependent scanning tunneling spectroscopy
Phys. Rev. Research 6, L022061 – Published 12 June, 2024
DOI: https://doi.org/10.1103/PhysRevResearch.6.L022061
Abstract
The Kondo effect describes the scattering of conduction electrons by magnetic impurities, manifesting as an electronic resonance at the Fermi energy with a distinctive temperature evolution. In this Letter, we present a critical evaluation of the current methodology employed to demonstrate Kondo behavior in transport measurements, underscoring the limitations of established theoretical frameworks and the influence of extrinsic broadening. We introduce an approach for analyzing spectroscopic indicators of the Kondo effect, employing the Hurwitz-Fano lineshape as a model for the Kondo resonance in the presence of extrinsic broadening. Through precise scanning tunneling spectroscopy measurements on an exemplary spin-1/2 Kondo system, phenalenyl on Au(111), we demonstrate the efficacy of our proposed protocol in extracting accurate intrinsic Kondo linewidths from finite-temperature measurements. The extracted linewidths exhibit a robust fit with a recently derived expression for the temperature-dependent intrinsic Kondo linewidth, providing compelling evidence for the validity of the underlying theory.
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Supplemental Material
References (44)
- J. Kondo, Resistance minimum in dilute magnetic alloys, Prog. Theor. Phys. 32, 37 (1964).
- A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1997).
- P. Fulde, Electron Correlations in Molecules and Solids (Springer, Berlin, 1995).
- P. Fazekas, Lecture Notes on Electron Correlation and Magnetism (World Scientific, Singapore-New Jersey-London-Hong Kong, 1999).
- P. Coleman, Heavy fermions: Electrons at the edge of magnetism, in Handbook of Magnetism and Advanced Magnetic Materials (John Wiley & Sons, Ltd., 2007).
- H. v. Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys. 79, 1015 (2007).
- B. Keimer and J. E. Moore, The physics of quantum materials, Nat. Phys. 13, 1045 (2017).
- W. Zhao, B. Shen, Z. Tao, Z. Han, K. Kang, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Gate-tunable heavy fermions in a moiré Kondo lattice, Nature (London) 616, 61 (2023).
- N. Roch, S. Florens, V. Bouchiat, W. Wernsdorfer, and F. Balestro, Quantum phase transition in a single-molecule quantum dot, Nature (London) 453, 633 (2008).
- 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).
- J. Li, W.-D. Schneider, R. Berndt, and B. Delley, Kondo scattering observed at a single magnetic impurity, Phys. Rev. Lett. 80, 2893 (1998).
- H. C. Manoharan, C. P. Lutz, and D. M. Eigler, Quantum mirages formed by coherent projection of electronic structure, Nature (London) 403, 512 (2000).
- O. Újsághy, J. Kroha, L. Szunyogh, and A. Zawadowski, Theory of the fano resonance in the STM tunneling density of states due to a single Kondo impurity, Phys. Rev. Lett. 85, 2557 (2000).
- A. Schiller and S. Hershfield, Theory of scanning tunneling spectroscopy of a magnetic adatom on a metallic surface, Phys. Rev. B 61, 9036 (2000).
- K. Nagaoka, T. Jamneala, M. Grobis, and M. F. Crommie, Temperature dependence of a single Kondo impurity, Phys. Rev. Lett. 88, 077205 (2002).
- S. Mishra, D. Beyer, K. Eimre, S. Kezilebieke, R. Berger, O. Gröning, C. A. Pignedoli, K. Müllen, P. Liljeroth, P. Ruffieux, X. Feng, and R. Fasel, Topological frustration induces unconventional magnetism in a nanographene, Nat. Nanotechnol. 15, 22 (2020).
- J. Li, S. Sanz, J. Castro-Esteban, M. Vilas-Varela, N. Friedrich, T. Frederiksen, D. Peña, and J. I. Pascual, Uncovering the triplet ground state of triangular graphene nanoflakes engineered with atomic precision on a metal surface, Phys. Rev. Lett. 124, 177201 (2020).
- S. Mishra, G. Catarina, F. Wu, R. Ortiz, D. Jacob, K. Eimre, J. Ma, C. A. Pignedoli, X. Feng, P. Ruffieux, J. Fernández-Rossier, and R. Fasel, Observation of fractional edge excitations in nanographene spin chains, Nature (London) 598, 287 (2021).
- E. Turco, A. Bernhardt, N. Krane, L. Valenta, R. Fasel, M. Jurek, and P. Ruffieux, Observation of the magnetic ground state of the two smallest triangular nanographenes, JACS Au 3, 1358 (2023).
- T. A. Costi, Kondo effect in a magnetic field and the magnetoresistivity of Kondo alloys, Phys. Rev. Lett. 85, 1504 (2000).
- Ž. Osolin and R. Žitko, Padé approximant approach for obtaining finite-temperature spectral functions of quantum impurity models using the numerical renormalization group technique, Phys. Rev. B 87, 245135 (2013).
- C. Chen, I. Sodemann, and P. A. Lee, Competition of spinon Fermi surface and heavy Fermi liquid states from the periodic Anderson to the Hubbard model, Phys. Rev. B 103, 085128 (2021).
- D. Jacob, Temperature evolution of the Kondo peak beyond Fermi liquid theory, Phys. Rev. B 108, L161109 (2023).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022061 for method details, complementary experimental results and simulations.
- Y.-h. Zhang, S. Kahle, T. Herden, C. Stroh, M. Mayor, U. Schlickum, M. Ternes, P. Wahl, and K. Kern, Temperature and magnetic field dependence of a Kondo system in the weak coupling regime, Nat. Commun. 4, 2110 (2013).
- A. A. Khajetoorians, M. Valentyuk, M. Steinbrecher, T. Schlenk, A. Shick, J. Kolorenc, A. I. Lichtenstein, T. O. Wehling, R. Wiesendanger, and J. Wiebe, Tuning emergent magnetism in a Hund's impurity, Nat. Nanotechnol. 10, 958 (2015).
- T. Esat, T. Deilmann, B. Lechtenberg, C. Wagner, P. Krüger, R. Temirov, F. B. Anders, M. Rohlfing, and F. S. Tautz, Transfering spin into an extended orbital of a large molecule, Phys. Rev. B 91, 144415 (2015).
- See Supplemental Note 12 of Ref. [39].
- Here as in Ref. [23] we use Wilson's thermodynamic definition of [40], corrected by Wiegman and Tsvelick [41]. As shown in Ref. [23] is related to the halfwidth of the Kondo peak by .
- M. Gruber, A. Weismann, and R. Berndt, The Kondo resonance line shape in scanning tunnelling spectroscopy: Instrumental aspects, J. Phys.: Condens. Matter 30, 424001 (2018).
- H. O. Frota, Shape of the Kondo resonance, Phys. Rev. B 45, 1096 (1992).
- H. Prüser, M. Wenderoth, A. Weismann, and R. G. Ulbrich, Mapping itinerant electrons around Kondo impurities, Phys. Rev. Lett. 108, 166604 (2012).
- S. Frank and D. Jacob, Orbital signatures of Fano-Kondo lineshapes in STM adatom spectroscopy, Phys. Rev. B 92, 235127 (2015).
- D. Jacob and S. Kurth, Many-body spectral functions from steady state density functional theory, Nano Lett. 18, 2086 (2018).
- For noninteracting electrons, Eq. (2) can be derived from Bardeen tunneling theory, see, e.g., Ch. 21.8 in Ref. [42]. For interacting electrons it can be derived from the Meir-Wingreen equation [43] assuming the ideal STM limit, see Ref. [34].
- Python and Igor programs for fitting Hurwitz and lineshapes are publically available on GitHub at https://github.com/david-jacob/HurwitzFanoFit.
- F. D. M. Haldane, Theory of the atomic limit of the Anderson model: I. Perturbation expansions re-examined, J. Phys. C: Solid State Phys. 11, 5015 (1978).
- An alternative route for determining from STS at , recently proposed in Ref. [44], requires additional control parameters in the experiment such as magnetic field or mechanical gating.
- C. van Efferen, J. Fischer, T. A. Costi, A. Rosch, T. Michely, and W. Jolie, Modulated Kondo screening along magnetic mirror twin boundaries in monolayer , Nat. Phys. 20, 82 (2024).
- K. G. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Rev. Mod. Phys. 47, 773 (1975).
- P. B. Wiegmann and A. M. Tsvelick, Exact solution of the Anderson model: I, J. Phys. C 16, 2281 (1983).
- B. Voigtländer, Scanning Probe Microscopy (Springer, Berlin Heidelberg, 2015).
- Y. Meir and N. S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett. 68, 2512 (1992).
- M. Žonda, O. Stetsovych, R. Korytár, M. Ternes, R. Temirov, A. Raccanelli, F. S. Tautz, P. Jelínek, T. Novotný, and M. Švec, Resolving ambiguity of the Kondo temperature determination in mechanically tunable single-molecule Kondo systems, J. Phys. Chem. Lett. 12, 6320 (2021).