Leggett mode controlled by light pulses

ABSTRACT The discovery of symmetry-broken phases that host multiple order parameters, such as multiband superconductors1,2, has triggered an enormous interest in condensed matter physics.

However, many challenges continue to hinder the fundamental understanding of how to control the collective modes corresponding to these multiple order parameters3,4. Here we demonstrate

that, in full analogy with phonons, Raman-active electronic collective modes can be manipulated by intense light pulses. By tuning a sum-frequency excitation process, we selectively trigger

collective excitations that can be ascribed to the relative phase fluctuations between two superconducting order parameters—the so-called Leggett mode—in the multiband superconductor MgB2.

The excellent comparison between experiments and theory establishes a general protocol for the advanced control of Raman-active electronic modes in symmetry-broken quantum phases of matter.

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OTHERS TERAHERTZ DISPLACIVE EXCITATION OF A COHERENT RAMAN-ACTIVE PHONON IN V2O3 Article Open access 28 April 2022 QUANTUM COHERENCE TOMOGRAPHY OF LIGHT-CONTROLLED SUPERCONDUCTIVITY Article

Open access 05 December 2022 OBSERVATION OF LIGHT-DRIVEN BAND STRUCTURE VIA MULTIBAND HIGH-HARMONIC SPECTROSCOPY Article Open access 02 June 2022 DATA AVAILABILITY The data that support the

plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. REFERENCES * Xi, X. X. Two-band superconductor magnesium

diboride. _Rep. Prog. Phys._ 71, 116501 (2008). Article  ADS  Google Scholar  * Johnston, D. C. The puzzle of high temperature superconductivity in layered iron pnictides and chalcogenides.

_Adv. Phys._ 59, 803–1061 (2010). Article  ADS  Google Scholar  * Nicoletti, D. & Cavalleri, A. Nonlinear light–matter interaction at terahertz frequencies. _Adv. Opt. Photon._ 8,

401–464 (2016). Article  Google Scholar  * Giannetti, C. et al. Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium

approach. _Adv. Phys._ 65, 58–238 (2016). Article  ADS  Google Scholar  * Zhang, X. C., Alexander Shkurinov & Zhang, Y. Extreme terahertz science. _Nat. Photon._ 11, 16–18 (2017).

Article  ADS  Google Scholar  * Kampfrath, T., Tanaka, K. & Nelson, K. A. Resonant and nonresonant control over matter and light by intense terahertz transients. _Nat. Photon._ 7,

680–690 (2013). Article  ADS  Google Scholar  * Landau, L. D. & Lifshitz, E. M. _Statistical Physics_ 3rd edn (Elsevier, Moscow, 2013). * Bardeen, J., Cooper, L. N. & Schrieffer, J.

R. Microscopic theory of superconductivity. _Phys. Rev._ 106, 162–164 (1957). Article  ADS  MathSciNet  Google Scholar  * Volkov, F. & Kogan, S. M. Collisionless relaxation of the energy

gap in a superconductor. _Zh. Eksp. Teor. Fiz._ 65, 2038–2046 (1973). Google Scholar  * Pekker, D. & Varma, C. M. Amplitude/Higgs modes in condensed matter. _Annu. Rev. Condens. Matter

Phys._ 6, 269–297 (2015). Article  ADS  Google Scholar  * Sooryakumar, R. & Klein, M. V. Raman scattering by superconducting-gap excitations and their coupling to charge-density waves.

_Phys. Rev. Lett._ 45, 660 (1980). Article  ADS  Google Scholar  * Méasson, M. A. et al. Amplitude Higgs mode in the 2H−NbSe2 superconductor. _Phys. Rev. B_ 89, 060503(R) (2014). Article 

ADS  Google Scholar  * Grasset, R. et al. Higgs-mode radiance and charge-density-wave order in 2H-NbSe2. _Phys. Rev. B_ 97, 094502 (2018). Article  ADS  Google Scholar  * Littlewood, P. B.

& Varma, C. M. Amplitude collective modes in superconductors and their coupling to charge-density waves. _Phys. Rev. B_ 26, 4883 (1982). Article  ADS  Google Scholar  * Matsunaga, R. et

al. Higgs amplitude mode in the BCS superconductors Nb1−_x_Ti_x_N induced by terahertz pulse excitation. _Phys. Rev. Lett._ 111, 057002 (2013). Article  ADS  Google Scholar  * Matsunaga, R.

et al. Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor. _Science_ 345, 1145–1149 (2014). Article  ADS  MathSciNet  Google Scholar  * Matsunaga,

R. et al. Polarization-resolved terahertz third-harmonic generation in a single-crystal superconductor NbN: dominance of the Higgs mode beyond the BCS approximation. _Phys. Rev. B_ 96,

020505 (2017). Article  ADS  Google Scholar  * Cea, T., Castellani, C. & Benfatto, L. Nonlinear optical effects and third-harmonic generation in superconductors: Cooper pairs versus

Higgs mode contribution. _Phys. Rev. B_ 93, 180507 (2016). Article  ADS  Google Scholar  * Cea, T., Barone, P., Castellani, C. & Benfatto, L. Polarization dependence of the

third-harmonic generation in multiband superconductors. _Phys. Rev. B_ 97, 094516 (2018). Article  ADS  Google Scholar  * Leggett, A. J. Number-phase fluctuations in two-band

superconductors. _Progr. Theoret. Phys._ 36, 901–930 (1966). Article  ADS  Google Scholar  * Blumberg, G. et al. Observation of Leggett’s collective mode in a multiband MgB2 superconductor.

_Phys. Rev. Lett._ 99, 227002 (2007). Article  ADS  Google Scholar  * Klein, M. V. Theory of Raman scattering from Leggett’s collective mode in a multiband superconductor: application to

MgB2. _Phys. Rev. B_ 82, 014507 (2010). Article  ADS  Google Scholar  * Cea, T. & Benfatto, L. Signature of the Leggett mode in the A1g Raman response: from MgB2 to iron-based

superconductors. _Phys. Rev. B_ 94, 064512 (2016). Article  ADS  Google Scholar  * Canfield, P. C. & Crabtree, G. W. Magnesium diboride: better late than never. _Phys. Today_ 56, 34–40

(March, 2003). * Maehrlein, S., Paarmann, A., Wolf, M. & Kampfrath, T. Terahertz sum-frequency excitation of a Raman-active phonon. _Phys. Rev. Lett._ 119, 127402 (2017). Article  ADS 

Google Scholar  * Merlin, R. Generating coherent THz phonons with light pulses. _Solid State Commun._ 102, 207–220 (1997). Article  ADS  Google Scholar  * Rajasekaran, S. et al. Parametric

amplification of a superconducting plasma wave. _Nat. Phys._ 12, 1012–1016 (2016). Article  Google Scholar  * Murotani, Y., Tsuji, N. & Aoki, H. Theory of light-induced resonances with

collective Higgs and Leggett modes in multiband superconductors. _Phys. Rev. B_ 95, 104503 (2017). Article  ADS  Google Scholar  * Krull, H., Bittner, N., Uhrig, G. S., Manske, D. &

Schnyder, A. P. Coupling of Higgs and Leggett modes in non-equilibrium superconductors. _Nat. Commun._ 7, 11921 (2016). Article  ADS  Google Scholar  * Blumberg, G. et al. Multi-gap

superconductivity in MgB2: Magneto-Raman spectroscopy. _Physica C_ 456, 75–82 (2007). Article  ADS  Google Scholar  * Orenstein, J. & Millis, A. J. Advances in the physics of

high-temperature superconductivity. _Science_ 288, 468–474 (2000). Article  ADS  Google Scholar  * Srivats, S. Rajasekaran et al. Probing optically silent superfluid stripes in cuprates.

_Science_ 359, 575–579 (2018). Article  MathSciNet  Google Scholar  * Kindt, J. T. & Schmuttenmaer, C. A. Theory for determination of the low-frequency time-dependent response function

in liquids using time-resolved terahertz pulse spectroscopy. _J. Chem. Phys._ 110, 8589 (1999). Article  ADS  Google Scholar  * Orenstein, J. & Dodge, J. S. Terahertz time-domain

spectroscopy of transient metallic and superconducting states. _Phys. Rev. B_ 92, 134507 (2015). Article  ADS  Google Scholar  Download references ACKNOWLEDGEMENTS This work was supported by

Swiss National Science Foundation, project nos. IZLRZ2_164051 and 200021_146769. C.P.H. acknowledges association with NCCR-MUST. The work at Temple University was supported in part by the

US Department of Energy, Office of Science, under grant no. DE-SC0011616. T.C. acknowledges financial support by the Graphene Flagship, project CNECTICT-604391. L.B. acknowledges financial

support from Italian Maeci under the Italia–India collaborative project SUPERTOP-PGR04879. AUTHOR INFORMATION Author notes * These authors contributed equally: Flavio Giorgianni, Tommaso

Cea. AUTHORS AND AFFILIATIONS * Paul Scherrer Institute, Laboratory for Non-linear Optics (LNO), Villigen-PSI, Switzerland Flavio Giorgianni, Carlo Vicario & Christoph P. Hauri * IMDEA

Nanoscience, Madrid, Spain Tommaso Cea * ISC-CNR and Department of Physics, Sapienza University of Rome, Rome, Italy Tommaso Cea & Lara Benfatto * Department of Physics, Temple

University, Philadelphia, PA, USA Wenura K. Withanage & Xiaoxing Xi Authors * Flavio Giorgianni View author publications You can also search for this author inPubMed Google Scholar *

Tommaso Cea View author publications You can also search for this author inPubMed Google Scholar * Carlo Vicario View author publications You can also search for this author inPubMed Google

Scholar * Christoph P. Hauri View author publications You can also search for this author inPubMed Google Scholar * Wenura K. Withanage View author publications You can also search for this

author inPubMed Google Scholar * Xiaoxing Xi View author publications You can also search for this author inPubMed Google Scholar * Lara Benfatto View author publications You can also search

for this author inPubMed Google Scholar CONTRIBUTIONS F.G., T.C. and L.B. initiated the research. W.K.W. and X.X. provided the samples. F.G., C.V. and C.P.H. designed the experimental

set-up and carried out the experiment. T.C. and L.B. performed the theoretical calculations. F.G., T.C. and L.B. wrote the manuscript with the input from all co-authors. CORRESPONDING AUTHOR

Correspondence to Lara Benfatto. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE: Springer Nature remains neutral

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https://doi.org/10.1038/s41567-018-0385-4 Download citation * Received: 07 March 2018 * Accepted: 21 November 2018 * Published: 21 January 2019 * Issue Date: April 2019 * DOI:

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