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  • Letter
  • Open Access

Theory for anomalous terahertz emission in striped cuprate superconductors

Pavel E. Dolgirev1,*,†, Marios H. Michael1,3,*,‡, Jonathan B. Curtis1,2, Daniele Nicoletti3, Michele Buzzi3, Michael Fechner3, Andrea Cavalleri3,4, and Eugene Demler5

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
  • 3Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
  • 4Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
  • 5Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

  • *These authors contributed equally to this work.
  • †p_dolgirev@g.harvard.edu
  • ‡marios.michael@mpsd.mpg.de

Phys. Rev. B 108, L180508 – Published 20 November, 2023

DOI: https://doi.org/10.1103/PhysRevB.108.L180508

Abstract

Recent experiments in the doped cuprates La2−xBaxCuO4 have revealed the emission of anomalous terahertz radiation after impulsive optical excitation. Here, we theoretically investigate the nonlinear electrodynamics of such striped superconductors and explore the origin of the observed radiation. We argue that photoexcitation is converted into a photocurrent by a second-order optical nonlinearity, which is activated by the breaking of inversion symmetry in certain stripe configurations. We point out the importance of including umklapp photocurrents modulated at the stripe periodicity itself, which impulsively drive surface Josephson plasmons and lead to a resonant structure of outgoing radiation, consistent with the experiments. We speculate on the utility of the proposed mechanism in the context of generating tunable terahertz radiation.

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References (61)

  1. D. J. Scalapino, S. R. White, and S. Zhang, Insulator, metal, or superconductor: The criteria, Phys. Rev. B 47, 7995 (1993).
  2. W. Kohn, Theory of this insulating state, Phys. Rev. 133, A171 (1964).
  3. C. Yang, Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors, Rev. Mod. Phys. 34, 694 (1962).
  4. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
  5. X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Topological field theory of time-reversal invariant insulators, Phys. Rev. B 78, 195424 (2008).
  6. A. Kapitulnik, J. Xia, E. Schemm, and A. Palevski, Polar Kerr effect as probe for time-reversal symmetry breaking in unconventional superconductors, New J. Phys. 11, 055060 (2009).
  7. M. Imada, A. Fujimori, and Y. Tokura, Metal-insulator transitions, Rev. Mod. Phys. 70, 1039 (1998).
  8. J. Orenstein, J. Moore, T. Morimoto, D. Torchinsky, J. Harter, and D. Hsieh, Topology and symmetry of quantum materials via nonlinear optical responses, Annu. Rev. Condens. Matter Phys. 12, 247 (2021).
  9. K. Tamasaku, Y. Nakamura, and S. Uchida, Charge dynamics across the CuO2 planes in La2−xSrxCuO4, Phys. Rev. Lett. 69, 1455 (1992).
  10. S. Uchida, K. Tamasaku, and S. Tajima, c-axis optical spectra and charge dynamics in La2−xSrxCuO4, Phys. Rev. B 53, 14558 (1996).
  11. T. Motohashi, K. M. Kojima, J. Shimoyama, S. Tajima, K. Kitazawa, S. Uchida, and K. Kishio, Observation of the Josephson plasma reflectivity edge in the infrared region in Bi-based superconducting cuprates, Phys. Rev. B 61, R9269 (2000).
  12. A. Dienst, E. Casandruc, D. Fausti, L. Zhang, M. Eckstein, M. Hoffmann, V. Khanna, N. Dean, M. Gensch, S. Winnerl, W. Seidel, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Optical excitation of Josephson plasma solitons in a cuprate superconductor, Nat. Mater. 12, 535 (2013).
  13. P. Lee, T. Rice, and P. Anderson, Fluctuation effects at a Peierls transition, Phys. Rev. Lett. 31, 462 (1973).
  14. P. A. Lee and T. M. Rice, Electric field depinning of charge density waves, Phys. Rev. B 19, 3970 (1979).
  15. P. Lee, T. Rice, and P. Anderson, Conductivity from charge or spin density waves, Solid State Commun. 88, 1001 (1993).
  16. D. Nicoletti, M. Buzzi, M. Fechner, P. E. Dolgirev, M. H. Michael, J. B. Curtis, E. Demler, G. D. Gu, and A. Cavalleri, Coherent emission from surface Josephson plasmons in striped cuprates, Proc. Natl. Acad. Sci. USA 119, e2211670119 (2022).
  17. E. Berg, E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Striped superconductors: how spin, charge and superconducting orders intertwine in the cuprates, New J. Phys. 11, 115004 (2009).
  18. E. Berg, E. Fradkin, and S. A. Kivelson, Theory of the striped superconductor, Phys. Rev. B 79, 064515 (2009).
  19. E. Berg, E. Fradkin, and S. Kivelson, Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors, Nat. Phys. 5, 830 (2009).
  20. K. Cremin, J. Zhang, C. Homes, G. Gu, Z. Sun, M. Fogler, A. Millis, D. Basov, and R. Averitt, Photoenhanced metastable c-axis electrodynamics in stripe-ordered cuprate La1.885Ba0.115CuO4, Proc. Natl. Acad. Sci. USA 116, 19875 (2019).
  21. W. Lee, K.-J. Zhou, M. Hepting, J. Li, A. Nag, A. C. Walters, M. Garcia-Fernandez, H. C. Robarts, M. Hashimoto, H. Lu, B. Nosarzewski, D. Song, H. Eisaki, Z. X. Shen, B. Moritz, J. Zaanen, and T. P. Devereaux, Spectroscopic fingerprint of charge order melting driven by quantum fluctuations in a cuprate, Nat. Phys. 17, 53 (2021).
  22. R. Comin and A. Damascelli, Resonant x-ray scattering studies of charge order in cuprates, Annu. Rev. Condens. Matter Phys. 7, 369 (2016).
  23. R. Comin, R. Sutaro, F. He, E. da Silva Neto, L. Chauviere, A. Fraño, R. Liang, W. Hardy, D. Bonn, Y. Yoshida, H. Eisaki, A. Achkar, D. Hawthorn, B. Keimer, G. Sawatzky, and A. Damascelli, Symmetry of charge order in cuprates, Nat. Mater. 14, 796 (2015).
  24. P. E. Dolgirev et al. (unpublished).
  25. T. Kaneko, Z. Sun, Y. Murakami, D. Golež, and A. J. Millis, Bulk photovoltaic effect driven by collective excitations in a correlated insulator, Phys. Rev. Lett. 127, 127402 (2021).
  26. A. de la Torre, K. Seyler, L. Zhao, S. Di Matteo, M. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. Norman, and D. Hsieh, Mirror symmetry breaking in a model insulating cuprate, Nat. Phys. 17, 777 (2021).
  27. L. Zhao, C. Bevin, D. Bonn, W. Hardy, N. Armitage, and D. Hsieh, A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy, Nat. Phys. 13, 250 (2017).
  28. J. Pettine, P. Padmanabhan, N. Sirica, R. P. Prasankumar, A. J. Taylor, and H.-T. Chen, Ultrafast terahertz emission from emerging symmetry-broken materials, Light: Sci. Appl. 12, 133 (2023).
  29. Said differently, nonlinear terms quadratic in the optical field and linear in plasmon fields are forbidden in materials with inversion symmetry.
  30. S. J. Smith and E. Purcell, Visible light from localized surface charges moving across a grating, Phys. Rev. 92, 1069 (1953).
  31. S. A. Mikhailov, Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems, Phys. Rev. B 58, 1517 (1998).
  32. V. Y. Kachorovskii and M. Shur, Current-induced terahertz oscillations in plasmonic crystal, Appl. Phys. Lett. 100, 232108 (2012).
  33. A. S. Petrov, D. Svintsov, M. Rudenko, V. Ryzhii, and M. Shur, Plasma instability of 2D electrons in a field effect transistor with a partly gated channel, Int. J. High Speed Electron. Syst. 25, 1640015 (2016).
  34. A. S. Petrov, D. Svintsov, V. Ryzhii, and M. S. Shur, Amplified-reflection plasmon instabilities in grating-gate plasmonic crystals, Phys. Rev. B 95, 045405 (2017).
  35. C. Aversa and J. E. Sipe, Nonlinear optical susceptibilities of semiconductors: Results with a length-gauge analysis, Phys. Rev. B 52, 14636 (1995).
  36. J. E. Sipe and A. I. Shkrebtii, Second-order optical response in semiconductors, Phys. Rev. B 61, 5337 (2000).
  37. A. M. Cook, B. M. Fregoso, F. De Juan, S. Coh, and J. E. Moore, Design principles for shift current photovoltaics, Nat. Commun. 8, 1 (2017).
  38. D. E. Parker, T. Morimoto, J. Orenstein, and J. E. Moore, Diagrammatic approach to nonlinear optical response with application to Weyl semimetals, Phys. Rev. B 99, 045121 (2019).
  39. T. Xu, T. Morimoto, and J. E. Moore, Nonlinear optical effects in inversion-symmetry-breaking superconductors, Phys. Rev. B 100, 220501(R) (2019).
  40. S. Patankar, L. Wu, Baozhu Lu, M. Rai, J. D. Tran, T. Morimoto, D. E. Parker, A. G. Grushin, N. L. Nair, J. G. Analytis, J. E. Moore, J. Orenstein, and D. H. Torchinsky, Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs, Phys. Rev. B 98, 165113 (2018).
  41. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.108.L180508 for additional theoretical details. The discussion there includes five sections: (i) plane waves in the medium with stripes; (ii) bulk polariton scenario; (iii) surface Josephson plasmons at large momenta; (iv) bulk vs surface contributions to the spectrum of outgoing radiation; and (v) reflection from a medium with Bragg mixing. The Supplemental Material includes Refs. [16, 46, 57, 59, 60, 61].
  42. C. Gadermaier, A. S. Alexandrov, V. V. Kabanov, P. Kusar, T. Mertelj, X. Yao, C. Manzoni, D. Brida, G. Cerullo, and D. Mihailovic, Electron-phonon coupling in high-temperature cuprate superconductors determined from electron relaxation rates, Phys. Rev. Lett. 105, 257001 (2010).
  43. L. Stojchevska, P. Kusar, T. Mertelj, V. V. Kabanov, Y. Toda, X. Yao, and D. Mihailovic, Mechanisms of nonthermal destruction of the superconducting state and melting of the charge-density-wave state by femtosecond laser pulses, Phys. Rev. B 84, 180507(R) (2011).
  44. D. van der Marel, H.-U. Habermaier, D. Heitmann, W. Konig, and A. Wittlin, Infrared study of the superconducting transition in YBa2Cu3O7−x, Phys. C (Amsterdam, Neth.) 176, 1 (1991).
  45. L. N. Bulaevskii, M. Zamora, D. Baeriswyl, H. Beck, and J. R. Clem, Time-dependent equations for phase differences and a collective mode in Josephson-coupled layered superconductors, Phys. Rev. B 50, 12831 (1994).
  46. Q. Lu, A. T. Bollinger, X. He, R. Sundling, I. Bozovic, and A. Gozar, Surface Josephson plasma waves in a high-temperature superconductor, npj Quantum Mater. 5, 69 (2020).
  47. P. E. Dolgirev, A. Zong, M. H. Michael, J. B. Curtis, D. Podolsky, A. Cavalleri, and E. Demler, Periodic dynamics in superconductors induced by an impulsive optical quench, Commun. Phys. 5, 234 (2022).
  48. D. N. Basov and T. Timusk, Electrodynamics of high-Tc superconductors, Rev. Mod. Phys. 77, 721 (2005).
  49. S. Savel'ev, V. Yampolskii, and F. Nori, Surface Josephson plasma waves in layered superconductors, Phys. Rev. Lett. 95, 187002 (2005).
  50. S. Savel'ev, V. Yampol'skii, A. Rakhmanov, and F. Nori, Terahertz Josephson plasma waves in layered superconductors: spectrum, generation, nonlinear and quantum phenomena, Rep. Prog. Phys. 73, 026501 (2010).
  51. S. Chatterjee, P. E. Dolgirev, I. Esterlis, A. Zibrov, M. D. Lukin, N. Y. Yao, and E. Demler, Single-spin qubit magnetic spectroscopy of two dimensional superconductivity, Phys. Rev. Res. 4, L012001 (2022).
  52. P. E. Dolgirev, S. Chatterjee, I. Esterlis, A. A. Zibrov, M. D. Lukin, N. Y. Yao, and E. Demler, Characterizing two-dimensional superconductivity via nanoscale noise magnetometry with single-spin qubits, Phys. Rev. B 105, 024507 (2022).
  53. F. J. Dunmore, D. Z. Liu, H. D. Drew, S. Das Sarma, Q. Li, and D. B. Fenner, Observation of below-gap plasmon excitations in superconducting YBa2Cu3O7 films, Phys. Rev. B 52, R731 (1995).
  54. D. Schumacher, C. Rea, D. Heitmann, and K. Scharnberg, Surface plasmons and Sommerfeld–Zenneck waves on corrugated surfaces: Application to high-Tc superconductors, Surf. Sci. 408, 203 (1998).
  55. A. Tsiatmas, A. Buckingham, V. Fedotov, S. Wang, Y. Chen, P. De Groot, and N. Zheludev, Superconducting plasmonics and extraordinary transmission, Appl. Phys. Lett. 97, 111106 (2010).
  56. A. Tsiatmas, V. A. Fedotov, F. J. G. de Abajo, and N. I. Zheludev, Low-loss terahertz superconducting plasmonics, New J. Phys. 14, 115006 (2012).
  57. S. Rajasekaran, J.-i. Okamoto, L. Mathey, M. Fechner, V. Thampy, G. Gu, and A. Cavalleri, Probing optically silent superfluid stripes in cuprates, Science 359, 575 (2018).
  58. S. Chaudhary, C. Lewandowski, and G. Refael, Shift-current response as a probe of quantum geometry and electron-electron interactions in twisted bilayer graphene, arXiv:2107.09090.
  59. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Theory of surface plasmons and surface-plasmon polaritons, Rep. Prog. Phys. 70, 1 (2007).
  60. F. Alpeggiani and L. C. Andreani, Josephson surface plasmons in spatially confined cuprate superconductors, Phys. Rev. B 88, 174513 (2013).
  61. M. Tinkham, Introduction to Superconductivity (Courier Corporation, Chelmsford, MA, 2004).

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