Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The Higgs mode in disordered superconductors close to a quantum phase transition

Abstract

The concept of mass generation by means of the Higgs mechanism was strongly inspired by earlier works on the Meissner–Ochsenfeld effect in superconductors. In quantum field theory, the excitations of longitudinal components of the Higgs field manifest as massive Higgs bosons. The analogous Higgs mode in superconductors has not yet been observed owing to its rapid decay into particle–hole pairs. According to recent theories, however, the Higgs mode should decrease below the superconducting pairing gap 2Δ and become visible in two-dimensional systems close to the superconductor–insulator transition. For experimental verification, we measured the complex terahertz transmission and tunnelling density of states of various thin films of superconducting NbN and InO close to criticality. Comparing both techniques reveals a growing discrepancy between the finite 2Δ and the threshold energy for electromagnetic absorption, which vanishes critically towards the superconductor–insulator transition. We identify the excess absorption below 2Δ as strong evidence of the Higgs mode in two-dimensional quantum critical superconductors.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Broken U(1)-symmetry phase and quantum Monte Carlo calculation of the Higgs conductivity.
Figure 2: Tunnelling versus optical spectroscopy.
Figure 3: Higgs conductivity and spectral weight.

References

  1. Álvarez-Gaumé, L. & Ellis, J. Eyes on a prize particle. Nature Phys. 7, 2–3 (2011).

    ADS  Article  Google Scholar 

  2. Anderson, P. W. Plasmons, gauge invariance and mass. Phys. Rev. 130, 439–442 (1963).

    ADS  MathSciNet  Article  Google Scholar 

  3. ATLAS Collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B 716, 1–29 (2012).

    ADS  Article  Google Scholar 

  4. Sooryakumar, R. & Klein, M. V. Raman scattering by superconducting-gap excitations and their coupling to charge-density waves. Phys. Rev. Lett. 45, 660–662 (1980).

    ADS  Article  Google Scholar 

  5. Rüegg, Ch. et al. Quantum magnets under pressure: Controlling elementary excitations in TlCuCl3 . Phys. Rev. Lett. 100, 205701 (2008).

    ADS  Article  Google Scholar 

  6. Endres, M. et al. The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition. Nature 487, 454–458 (2012).

    ADS  Article  Google Scholar 

  7. Littlewood, P. B. & Varma, C. M. Amplitude collective modes in superconductors and their coupling to charge density waves. Phys. Rev. B. 26, 4883–4893 (1982).

    ADS  Article  Google Scholar 

  8. Matsunaga, R. et al. Higgs amplitude mode in the BCS superconductors Nb1−xTixN induced by terahertz pulse excitation. Phys. Rev. Lett. 111, 057002 (2013).

    ADS  Article  Google Scholar 

  9. Sachdev, S. Universal relaxational dynamics near two-dimensional quantum critical points. Phys. Rev. B 59, 14054–14073 (1999).

    ADS  Article  Google Scholar 

  10. Zwerger, W. Anomalous fluctuations in phases with a broken continuous symmetry. Phys. Rev. Lett. 92, 027203 (2004).

    ADS  Article  Google Scholar 

  11. Cea, T. et al. Optical excitation of phase modes in strongly disordered superconductors. Phys. Rev. B 89, 174506 (2014).

    ADS  Article  Google Scholar 

  12. Podolsky, D., Auerbach, A. & Arovas, D. P. Visibility of the amplitude (Higgs) mode in condensed matter. Phys. Rev. B 84, 174522 (2011).

    ADS  Article  Google Scholar 

  13. Gazit, S., Podolsky, D., Auerbach, A. & Arovas, D. P. Dynamics and conductivity near quantum criticality. Phys. Rev. B 88, 235108 (2013).

    ADS  Article  Google Scholar 

  14. Gazit, S., Podolsky, D. & Auerbach, A. Fate of the Higgs mode near quantum criticality. Phys. Rev. Lett. 110, 140401 (2013).

    ADS  Article  Google Scholar 

  15. Kowal, D. & Ovadyahu, Z. Disorder induced granularity in an amorphous superconductor. Solid State Commun. 90, 783–786 (1994).

    ADS  Article  Google Scholar 

  16. Sacepe, B. et al. Disorder-induced inhomogeneities of the superconducting state close to the superconductor–insulator transition. Phys. Rev. Lett. 101, 157006 (2008).

    ADS  Article  Google Scholar 

  17. Kamlapure, A. et al. Emergence of nanoscale inhomogeneity in the superconducting state of a homogeneously disordered conventional superconductor. Sci. Rep. 3, 2979 (2013).

    Article  Google Scholar 

  18. Sherman, D., Kopnov, G., Shahar, D. & Frydman, A. Measurement of a superconducting energy gap in a homogeneously amorphous insulator. Phys. Rev. Lett. 108, 177006 (2012).

    ADS  Article  Google Scholar 

  19. Chand, M. et al. Phase diagram of the strongly disordered s-wave superconductor NbN close to the metal–insulator transition. Phys. Rev. B 85, 014508 (2012).

    ADS  Article  Google Scholar 

  20. Ghosal, A., Randeria, M. & Trivedi, N. Role of spatial amplitude fluctuations in highly disordered s-wave superconductors. Phys. Rev. Lett. 81, 3940–3943 (1998).

    ADS  Article  Google Scholar 

  21. Ghosal, A., Randeria, M. & Trivedi, N. Inhomogeneous pairing in highly disordered s-wave superconductors. Phys. Rev. B 65, 014501 (2001).

    ADS  Article  Google Scholar 

  22. Dubi, Y., Meir, Y. & Avishai, Y. Nature of the superconductor–insulator transition in disordered superconductors. Nature 449, 876–880 (2007).

    ADS  Article  Google Scholar 

  23. Bouadim, K., Loh, Y., Randeria, M. & Trivedi, N. Single and two-particle energy gaps across the disorder-driven superconductor–insulator transition. Nature Phys. 11, 884–889 (2011).

    ADS  Article  Google Scholar 

  24. Mondal, M. et al. Phase fluctuations in a strongly disordered s-wave NbN superconductor close to the metal–insulator transition. Phys. Rev. Lett. 106, 047001 (2011).

    ADS  Article  Google Scholar 

  25. Swanson, M., Loh, Y. L., Randeria, M. & Trivedi, N. Dynamical conductivity across the disorder-tuned superconductor–insulator transition. Phys. Rev. X 4, 021007 (2014).

    Google Scholar 

  26. Dressel, M. & Grüner, G. Electrodynamics of Solids (Cambridge Univ. Press, 2002).

    Book  Google Scholar 

  27. Pracht, U. S. et al. Electrodynamics of the superconducting state in ultra-thin films at THz frequencies. IEEE Trans. THz Sci. Technol. 3, 269–280 (2013).

    Article  Google Scholar 

  28. Dressel, M., Drichko, N., Gorshunov, B. & Pimenov, A. THz spectroscopy of superconductors. IEEE J. Sel. Topics Quantum Electron. 14, 399–406 (2008).

    ADS  Article  Google Scholar 

  29. Pracht, U. S. et al. Direct observation of the superconducting gap in a thin film of titanium nitride using terahertz spectroscopy. Phys. Rev. B 86, 184503 (2012).

    ADS  Article  Google Scholar 

  30. Zimmermann, W., Brandt, E. H., Bauer, M., Seider, E. & Genzel, L. Optical conductivity of BCS superconductors with arbitrary purity. Physica C 183, 99–104 (1991).

    ADS  Article  Google Scholar 

  31. Sherman, D. et al. Effect of Coulomb interactions on the disorder-driven superconductor–insulator transition. Phys. Rev. B 89, 035149 (2014).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We are grateful for useful discussions with D. Arovas, L. Benfatto, S. Gazit, D. Podolsky and E. Shimshoni. We acknowledge support from the the GIF foundation grant I-1250-303.10/2014 and from the Deutsche Forschungsgemeinschaft. U.S.P. acknowledges financial support from the Studienstiftung des deutschen Volkes. B.G. acknowledges support from the Russian Ministry of Education and Science (Program 5 top 100) and A.A. acknowledges support from the ISF and BSF foundations. M.S. acknowledges support from the NSF Graduate Research Fellowship and N.T. acknowledges support from grant DOE DE-FG02-07ER46423 (N.T.) and computational support from the Ohio Supercomputing Center.

Author information

Authors and Affiliations

Authors

Contributions

D.S., J.J., M.C. and P.R. carried out the DC experiments. D.S., U.S.P. and B.G. carried out the THz experiments. D.S., U.S.P. and A.F. analysed the data. D.S., S.P., J.J. and P.R. prepared the samples. N.T., M.S. and A.A. carried out the theoretical analysis and the numerical simulations. U.S.P., D.S., M.D., A.F., M.S., N.T. and A.A. wrote the paper. A.F. and M.D. initiated and supervised the work. All the authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Aviad Frydman.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sherman, D., Pracht, U., Gorshunov, B. et al. The Higgs mode in disordered superconductors close to a quantum phase transition. Nature Phys 11, 188–192 (2015). https://doi.org/10.1038/nphys3227

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys3227

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing