Skip to main content
Log in

Spatial modulation of unitary impurity-induced resonances in superconducting CeCoIn5

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Motivated by recent experimental progress in high-resolution scanning tunneling microscopy (STM) techniques, we investigate the local quasiparticle density of states around a unitary impurity in the heavy-fermion superconductor CeCoIn5. Based on the T-matrix approach we obtain a sharp nearly zero-energy resonance state in the strong impurity potential scattering localized around the impurity and find qualitative differences in the spatial pattern of the tunneling conductance modulated by the nodal structure of the superconducting gap. These unique features may be used as a probe of the superconducting gap symmetry and, in combination with further STM measurements, may help to confirm the \({d_{{x^2} - {y^2}}}\) pairing in CeCoIn5 at ambient pressure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D. J. Scalapino, A common thread: The pairing interaction for unconventional superconductors, Rev. Mod. Phys. 84(4), 1383 (2012)

    Article  ADS  Google Scholar 

  2. Ø. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, and C. Renner, Scanning tunneling spectroscopy of hightemperature superconductors, Rev. Mod. Phys. 79(1), 353 (2007)

    Article  ADS  Google Scholar 

  3. B. D. White, J. D. Thompson, and M. B. Maple, Unconventional superconductivity in heavy-fermion compounds, Physica C 514, 246 (2015)

    Article  ADS  Google Scholar 

  4. G. Knebel, D. Aoki, and J. Flouquet, Antiferromagnetism and superconductivity in cerium based heavy-fermion compounds, C. R. Phys. 12(5–6), 542 (2011)

    Article  ADS  Google Scholar 

  5. G. Stewart, Non-Fermi-liquid behavior in d- and f-electron metals, Rev. Mod. Phys. 73(4), 797 (2001)

    Article  ADS  Google Scholar 

  6. G. Stewart, Heavy-fermion systems, Rev. Mod. Phys. 56(4), 755 (1984)

    Article  ADS  Google Scholar 

  7. F. Steglich, J. Aarts, C. D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schafer, Superconductivity in the presence of strong Pauli paramagnetism: CeCu2Si2, Phys. Rev. Lett. 43(25), 1892 (1979)

    Article  ADS  Google Scholar 

  8. S. Kittaka, Y. Aoki, Y. Shimura, T. Sakakibara, S. Seiro, C. Geibel, F. Steglich, H. Ikeda, and K. Machida, Multiband superconductivity with unexpected deficiency of nodal quasiparticles in CeCu2Si2, Phys. Rev. Lett. 112(6), 067002 (2014)

    Article  ADS  Google Scholar 

  9. H. Ikeda, M. Suzuki, and R. Arita, Emergent loop-nodal s±-wave superconductivity in CeCu2Si2: Similarities to the iron-based superconductors, Phys. Rev. Lett. 114(14), 147003 (2015)

    Article  ADS  Google Scholar 

  10. H. Hegger, C. Petrovic, E. G. Moshopoulou, M. F. Hundley, J. L. Sarrao, Z. Fisk, and J. D. Thompson, Pressureinduced superconductivity in quasi-2D CeRhIn5, Phys. Rev. Lett. 84(21), 4986 (2000)

    Article  ADS  Google Scholar 

  11. C. Petrovic, P. G. Pagliuso, M. F. Hundley, R. Movshovich, J. L. Sarrao, J. D. Thompson, Z. Fisk, and P. Monthoux, Heavy-fermion superconductivity in CeCoIn5 at 2.3 K, J. Phys.: Condens. Matter 13(17), L337 (2001)

    Article  ADS  Google Scholar 

  12. C. Petrovic, R. Movshovich, M. Jaime, P. G. Pagliuso, M. F. Hundley, J. L. Sarrao, Z. Fisk, and J. D. Thompson, A new heavy-fermion superconductor CeIrIn5: Relative of the cuprates? Europhys. Lett. 53(3), 354 (2001)

    Article  ADS  Google Scholar 

  13. A. McCollam, S. R. Julian, P. M. C. Rourke, D. Aoki, and J. Flouquet, Anomalous de Haas–van Alphen Oscillations in CeCoIn5, Phys. Rev. Lett. 94(18), 186401 (2005)

    Article  ADS  Google Scholar 

  14. T. Shang, R. E. Baumbach, K. Gofryk, F. Ronning, Z. F. Weng, J. L. Zhang, X. Lu, E. D. Bauer, J. D. Thompson, and H. Q. Yuan, CeIrIn5: Superconductivity on a magnetic instability, Phys. Rev. B 89(4), 041101 (2014)

    Article  ADS  Google Scholar 

  15. J. S. van Dyke, F. Massee, M. P. Allan, J. C. S. Davisb, C. Petrovic, and D. K. Morr, Direct evidence for a magnetic f-electron-mediated pairing mechanism of heavy-fermion superconductivity in CeCoIn5, Proc. Natl. Acad. Sci. USA 111(32), 11663 (2014)

    Article  ADS  Google Scholar 

  16. M. P. Allan, F. Massee, D. K. Morr, J. van Dyke, A. W. Rost, A. P. Mackenzie, C. Petrovic, and J. C. Davis, Imaging Cooper pairing of heavy fermions in CeCoIn5, Nat. Phys. 9(8), 468 (2013)

    Article  Google Scholar 

  17. B. B. Zhou, S. Misra, E. H. da Silva Neto, P. Aynajian, R. E. Baumbach, J. D. Thompson, E. D. Bauer, and A. Yazdani, Visualizing nodal heavy fermion superconductivity in CeCoIn5, Nat. Phys. 9(8), 474 (2013)

    Article  Google Scholar 

  18. T. Hu, H. Xiao, T. A. Sayles, M. Dzero, M. B. Maple, and C. C. Almasan, Strong magnetic fluctuations in a superconducting state of CeCoIn5, Phys. Rev. Lett. 108(5), 056401 (2012)

    Article  ADS  Google Scholar 

  19. M. Kenzelmann, S. Gerber, N. Egetenmeyer, J. L. Gavilano, Th. Strässle, A. D. Bianchi, E. Ressouche, R. Movshovich, E. D. Bauer, J. L. Sarrao, and J. D. Thompson, Evidence for a magnetically driven superconducting Q phase of CeCoIn5, Phys. Rev. Lett. 104(12), 127001 (2010)

    Article  ADS  Google Scholar 

  20. X. Lu, H. Lee, T. Park, F. Ronning, E. D. Bauer, and J. D. Thompson, Heat-capacity measurements of energy-gap nodes of the heavy-fermion superconductor CeIrIn5 deep inside the pressure-dependent dome structure of its superconducting phase diagram, Phys. Rev. Lett. 108(2), 027001 (2012)

    Article  ADS  Google Scholar 

  21. T. Park, H. Lee, I.Martin, X. Lu, V. A. Sidorov, K. Gofryk, F. Ronning, E. D. Bauer, and J. D. Thompson, Textured superconducting phase in the heavy fermion CeRhIn5, Phys. Rev. Lett. 108(7), 077003 (2012)

    Article  ADS  Google Scholar 

  22. Y. Kohori, Y. Yamato, Y. Iwamoto, T. Kohara, E. D. Bauer, M. B. Maple, and J. L. Sarrao, NMR and NQR studies of the heavy fermion superconductors CeTIn5 (T = Co and Ir), Phys. Rev. B 64(13), 134526 (2001)

    Article  ADS  Google Scholar 

  23. Y. Matsuda and K. Izawa, Determination of the directions of gap nodes in exotic superconductors, Physica C 388–389, 487 (2003)

    Article  Google Scholar 

  24. Matsuda and K. Izawa, Nodal structure of unconventional superconductors determined by thermal conductivity, J. Low Temp. Phys. 131, 429 (2003)

  25. K. Izawa, H. Yamaguchi, Y. Matsuda, H. Shishido, R. Settai, and Y. Onuki, Angular position of nodes in the superconducting gap of quasi-2D heavy-fermion superconductor CeCoIn5, Phys. Rev. Lett. 87(5), 057002 (2001)

    Article  ADS  Google Scholar 

  26. H. Aoki, T. Sakakibara, H. Shishido, R. Settai, Y. Nuki, P. Miranovi, and K. Machida, Field-angle dependence of the zero-energy density of states in the unconventional heavyfermion superconductor CeCoIn5, J. Phys.: Condens. Matter 16(3), L13 (2004)

    ADS  Google Scholar 

  27. K. An, T. Sakakibara, R. Settai, Y. Onuki, M. Hiragi, M. Ichioka, and K. Machida, Sign reversal of field-angle resolved heat capacity oscillations in a heavy fermion superconductor CeCoIn5 and \({d_{{x^2} - {y^2}}}\) pairing symmetry, Phys. Rev. Lett. 104(3), 037002 (2010)

    Article  ADS  Google Scholar 

  28. R. Ikeda and H. Adachi, Modulated vortex lattice in high fields and gap nodes, Phys. Rev. B 69(21), 212506 (2004)

    Article  ADS  Google Scholar 

  29. C. Stock, C. Broholm, J. Hudis, H. J. Kang, and C. Petrovic, Spin resonance in the d-wave superconductor CeCoIn5, Phys. Rev. Lett. 100(8), 087001 (2008)

    Article  ADS  Google Scholar 

  30. I. Eremin, G. Zwicknagl, P. Thalmeier, and P. Fulde, Feedback spin resonance in superconducting CeCu2Si2 and CeCoIn5, Phys. Rev. Lett. 101(18), 187001 (2008)

    Article  ADS  Google Scholar 

  31. N. Hiasa and R. Ikeda, Instability of square vortex lattice in d-wave superconductors is due to paramagnetic depairing, Phys. Rev. Lett. 101(2), 027001 (2008)

    Article  ADS  Google Scholar 

  32. W. K. Park, J. L. Sarrao, J. D. Thompson, and L. H. Greene, Andreev reflection in heavy-fermion superconductors and order parameter symmetry in CeCoIn5, Phys. Rev. Lett. 100(17), 177001 (2008)

    Article  ADS  Google Scholar 

  33. A. Vorontsov and I. Vekhter, Nodal structure of quasi-twodimensional superconductors probed by a magnetic field, Phys. Rev. Lett. 96(23), 237001 (2006)

    Article  ADS  Google Scholar 

  34. A. Vorontsov and I. Vekhter, Unconventional superconductors under a rotating magnetic field (I): Density of states and specific heat, Phys. Rev. B 75(22), 224501 (2007)

    Article  ADS  Google Scholar 

  35. F. Ronning, J. X. Zhu, T. Das, M. J. Graf, R. C. Albers, H. B. Rhee, and W. E. Pickett, Superconducting gap structure of the 115s revisited, J. Phys.: Condens. Matter 24(29), 294206 (2012)

    Google Scholar 

  36. T. Das, A. B. Vorontsov, I. Vekhter, and M. J. Graf, Fieldangle-resolved anisotropy in superconducting CeCoIn5 using realistic Fermi surfaces, Phys. Rev. B 87(17), 174514 (2013)

    Article  ADS  Google Scholar 

  37. B. Liu, Nonmagnetic impurity resonance states as a test of superconducting pairing symmetry in CeCoIn5, Phys. Rev. B 88(24), 245127 (2013)

    Article  ADS  Google Scholar 

  38. A. Koitzsch, I. Opahle, S. Elgazzar, S. V. Borisenko, J. Geck, V. B. Zabolotnyy, D. Inosov, H. Shiozawa, M. Richter, M. Knupfer, J. Fink, B. Büchner, E. D. Bauer, J. L. Sarrao, and R. Follath, Electronic structure of CeCoIn5 from angleresolved photoemission spectroscopy, Phys. Rev. B 79(7), 075104 (2009)

    Article  ADS  Google Scholar 

  39. P. Aynajian, E. H. da Silva Neto, A. Gyenis, R. E. Baumbach, J. D. Thompson, Z. Fisk, E. D. Bauer, and A. Yazdani, Visualizing heavy fermions emerging in a quantum critical Kondo lattice, Nature 486(7402), 201 (2012)

    Article  ADS  Google Scholar 

  40. S. Ernst, S. Wirth, F. Steglich, Z. Fisk, J. L. Sarrao, and J. D. Thompson, Scanning tunneling microscopy studies on CeCoIn5 and CeIrIn5, Phys. Status Solidi 247(3), 624 (2010)

    Article  Google Scholar 

  41. A. V. Balatsky, I. Vekhter, and J. X. Zhu, Impurity-induced states in conventional and unconventional superconductors, Rev. Mod. Phys. 78(2), 373 (2006)

    Article  ADS  Google Scholar 

  42. T. Maehira, T. Hotta, K. Ueda, and A. Hasegawa, Relativistic band-structure calculations for CeTIn5 (T = Ir and Co) and analysis of the energy bands by using tight-binding method, J. Phys. Soc. Jpn. 72(4), 854 (2003)

    Article  ADS  Google Scholar 

  43. Y. Öuki, R. Settai, K. Sugiyama, T. Takeuchi, T. C. Kobayashi, Y. Haga, and E. Yamamoto, Recent advances in the magnetism and superconductivity of heavy fermion systems, J. Phys. Soc. Jpn. 73(4), 769 (2004)

    Article  ADS  Google Scholar 

  44. Y. Haga, Y. Inada, H. Harima, K. Oikawa, M. Murakawa, H. Nakawaki, Y. Tokiwa, D. Aoki, H. Shishido, S. Ikeda, N. Watanabe, and Y. Onuki, Quasi-two-dimensional Fermi surfaces of the heavy fermion superconductor CeIrIn5, Phys. Rev. B 63(6), 060503 (2001)

    Article  ADS  Google Scholar 

  45. D. Hall, E. C. Palm, T. P. Murphy, S. W. Tozer, C. Petrovic, E. Miller-Ricci, L. Peabody, C. Li, U. Alver, R. G. Goodrich, J. L. Sarrao, P. G. Pagliuso, J. M. Wills, and Z. Fisk, Electronic structure of CeRhIn5: de Haas–van Alphen and energy band calculations, Phys. Rev. B 64(6), 064506 (2001)

    Article  ADS  Google Scholar 

  46. H. Shishido, T. Ueda, S. Hashimoto, T. Kubo, R. Settai, H. Harima, and Y. Onuki, A de Haas–van Alphen experiment under pressure on CeCoIn5: Deviation from the quantum critical region, J. Phys.: Condens. Matter 15(32), L499 (2003)

  47. L. Dudy, J. D. Denlinger, L. Shu, M. Janoschek, J. W. Allen, and M. B. Maple, Yb valence change in Ce1−x YbxCoIn5 from spectroscopy and bulk properties, Phys. Rev. B 88(16), 165118 (2013)

    Article  ADS  Google Scholar 

  48. K. Tanaka, H. Ikeda, Y. Nisikawa, and K. Yamada, Theory of superconductivity in CeMIn5 (M=Co, Rh, Ir) on the basis of the three dimensional periodic Anderson model, J. Phys. Soc. Jpn. 75(2), 024713 (2006)

    Article  ADS  Google Scholar 

  49. S. H. Pan, E. W. Hudson, K. M. Lang, H. Eisaki, S. Uchida, and J. C. Davis, Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, Nature 403(6769), 746 (2000)

    Article  ADS  Google Scholar 

  50. S. H. Pan, J. P. O’Neal, R. L. Badzey, C. Chamon, H. Ding, J. R. Engelbrecht, Z. Wang, H. Eisaki, S. Uchida, A. K. Gupta, K. W. Ng, E. W. Hudson, K. M. Lang, and J. C. Davis, Microscopic electronic inhomogeneity in the high-T c superconductor Bi2Sr2CaCu2O8+x , Nature 413(6853), 282 (2001)

    Article  ADS  Google Scholar 

  51. E. W. Hudson, K. M. Lang, V. Madhavan, S. H. Pan, H. Eisaki, S. Uchida, and J. C. Davis, Interplay of magnetism and high-T c superconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+d , Nature 411(6840), 920 (2001)

    Article  ADS  Google Scholar 

  52. S. Haas and K. Maki, Quasiparticle bound states around impurities in \({d_{{x^2} - {y^2}}}\)-wave superconductors, Phys. Rev. Lett. 85(10), 2172 (2000)

    Article  ADS  Google Scholar 

  53. A. Yazdani, B. A. Jones, C. P. Lutz, M. F. Crommie, and D. M. Eigler, Probing the local effects of magnetic impurities on superconductivity, Science 275(5307), 1767 (1997)

    Article  Google Scholar 

  54. M. I. Salkola, A. V. Balatsky, and J. R. Schrieffer, Spectral properties of quasiparticle excitations induced by magnetic moments in superconductors, Phys. Rev. B 55(18), 12648 (1997)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bin Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, G., Liu, B., Yang, YF. et al. Spatial modulation of unitary impurity-induced resonances in superconducting CeCoIn5 . Front. Phys. 11, 117402 (2016). https://doi.org/10.1007/s11467-016-0549-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-016-0549-6

Keywords

Navigation