Following the Higgs mode across the BCS-BEC crossover in two dimensions

Phan, Dan; Chubukov, Andrey V.

doi:10.1103/physrevb.107.134519

Title: Following the Higgs mode across the BCS-BEC crossover in two dimensions

Journal Article · 27 April 2023 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.107.134519 · OSTI ID:2007067

^[1];

^[1]

University of Minnesota, Minneapolis, MN (United States)

Although substantial effort has been dedicated to analyzing the Higgs (amplitude) mode in superconducting systems, there are relatively few studies of the Higgs peak's dispersion and width, quantities which are observable in spectroscopic measurements. These properties can be obtained from the location of the pole of the amplitude (Higgs) susceptibility in the lower half plane of complex frequency. We analyze the behavior of the Higgs mode in a two-dimensional neutral fermionic superfluid at T = 0 throughout the crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) behavior. Here, this occurs when the dressed chemical potential μ changes sign from positive to negative. For μ > 0, we find a pole in the Higgs susceptibility in the lower half plane of frequency and demonstrate that it leads to a well-defined peak in spectroscopic probes. For μ < 0, the pole still exists but is “hidden,” not giving rise to a peak in spectroscopic probes. Extending this analysis to a charged superconductor, we find that the Higgs mode is unaffected by the long-range Coulomb interaction.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0014402

OSTI ID:: 2007067

Journal Information:: Physical Review. B, Vol. 107, Issue 13; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (68)

Conservation laws, vertex corrections, and screening in Raman spectroscopy Maiti, Saurabh; Chubukov, Andrey V.; Hirschfeld, P. J. Physical Review B, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevB.96.014503	journal	July 2017
Plasmons, Gauge Invariance, and Mass Anderson, P. W. Physical Review, Vol. 130, Issue 1 https://doi.org/10.1103/PhysRev.130.439	journal	April 1963
Large cation ethylammonium incorporated perovskite for efficient and spectra stable blue light-emitting diodes Chu, Zema; Zhao, Yang; Ma, Fei Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-17943-6	journal	August 2020
Polarization-resolved terahertz third-harmonic generation in a single-crystal superconductor NbN: Dominance of the Higgs mode beyond the BCS approximation Matsunaga, Ryusuke; Tsuji, Naoto; Makise, Kazumasa Physical Review B, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevB.96.020505	journal	July 2017
Amplitude Higgs mode in the 2 H − NbSe 2 superconductor Méasson, M. -A.; Gallais, Y.; Cazayous, M. Physical Review B, Vol. 89, Issue 6 https://doi.org/10.1103/PhysRevB.89.060503	journal	February 2014
BCS to Bose crossover: Broken-symmetry state Engelbrecht, Jan R.; Randeria, Mohit; Sáde Melo, C. A. R. Physical Review B, Vol. 55, Issue 22 https://doi.org/10.1103/PhysRevB.55.15153	journal	June 1997
Branche d’excitation collective du continuum dans les gaz de fermions condensés par paires : étude analytique et lois d’échelle Castin, Yvan; Kurkjian, Hadrien Comptes Rendus. Physique, Vol. 21, Issue 3 https://doi.org/10.5802/crphys.1	journal	November 2020
Observing the Influence of Reduced Dimensionality on Fermionic Superfluids Sobirey, Lennart; Biss, Hauke; Luick, Niclas Physical Review Letters, Vol. 129, Issue 8 https://doi.org/10.1103/PhysRevLett.129.083601	journal	August 2022
Quantum phase transition in a clean superconductor with repulsive dynamical interaction Pimenov, Dimitri; Chubukov, Andrey V. npj Quantum Materials, Vol. 7, Issue 1 https://doi.org/10.1038/s41535-022-00457-3	journal	April 2022
Hydrodynamic action and Bose spectrum of superfluid Fermi systems Andrianov, V. A.; Popov, V. N. Theoretical and Mathematical Physics, Vol. 28, Issue 3 https://doi.org/10.1007/BF01029175	journal	September 1976
Gauge-Invariant Theory of the Dynamical Interaction of Charge Density Waves and Superconductivity Littlewood, P. B.; Varma, C. M. Physical Review Letters, Vol. 47, Issue 11 https://doi.org/10.1103/PhysRevLett.47.811	journal	September 1981
Amplitude Higgs Mode and Admittance in Superconductors with a Moving Condensate Moor, Andreas; Volkov, Anatoly F.; Efetov, Konstantin B. Physical Review Letters, Vol. 118, Issue 4 https://doi.org/10.1103/PhysRevLett.118.047001	journal	January 2017
Nature and Raman signatures of the Higgs amplitude mode in the coexisting superconducting and charge-density-wave state Cea, T.; Benfatto, L. Physical Review B, Vol. 90, Issue 22 https://doi.org/10.1103/PhysRevB.90.224515	journal	December 2014
Plasmons in three-dimensional superconductors Repplinger, T.; Klimin, S.; Gélédan, M. Physical Review B, Vol. 107, Issue 1 https://doi.org/10.1103/PhysRevB.107.014504	journal	January 2023
Spectral function of the Higgs mode in 4 − ε dimensions Katan, Yaniv Tenenbaum; Podolsky, Daniel Physical Review B, Vol. 91, Issue 7 https://doi.org/10.1103/PhysRevB.91.075132	journal	February 2015
Coherent Excited States in the Theory of Superconductivity: Gauge Invariance and the Meissner Effect Anderson, P. W. Physical Review, Vol. 110, Issue 4 https://doi.org/10.1103/PhysRev.110.827	journal	May 1958
Higgs Mode in Superconductors Shimano, Ryo; Tsuji, Naoto Annual Review of Condensed Matter Physics, Vol. 11, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031119-050813	journal	September 2019
Bound states, Cooper pairing, and Bose condensation in two dimensions Randeria, Mohit; Duan, Ji-Min; Shieh, Lih-Yir Physical Review Letters, Vol. 62, Issue 9 https://doi.org/10.1103/PhysRevLett.62.981	journal	February 1989
Raman Scattering by Superconducting-Gap Excitations and Their Coupling to Charge-Density Waves Sooryakumar, R.; Klein, M. V. Physical Review Letters, Vol. 45, Issue 8 https://doi.org/10.1103/PhysRevLett.45.660	journal	August 1980
On the Plasma Oscillation in Superconductivity Ohashi, Yoji; Takada, Satoshi Journal of the Physical Society of Japan, Vol. 67, Issue 2 https://doi.org/10.1143/JPSJ.67.551	journal	February 1998
Visibility of the amplitude (Higgs) mode in condensed matter Podolsky, Daniel; Auerbach, Assa; Arovas, Daniel P. Physical Review B, Vol. 84, Issue 17 https://doi.org/10.1103/PhysRevB.84.174522	journal	November 2011
Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor Matsunaga, R.; Tsuji, N.; Fujita, H. Science, Vol. 345, Issue 6201 https://doi.org/10.1126/science.1254697	journal	July 2014
Universal Properties of the Higgs Resonance in (2+1)-Dimensional U(1) Critical Systems Chen, Kun; Liu, Longxiang; Deng, Youjin Physical Review Letters, Vol. 110, Issue 17 https://doi.org/10.1103/PhysRevLett.110.170403	journal	April 2013
Fractal Basins of Attraction Associated with a Damped Newton's Method Epureanu, Bogdan I.; Greenside, Henry S. SIAM Review, Vol. 40, Issue 1 https://doi.org/10.1137/S0036144596310033	journal	January 1998
Nonreciprocal Terahertz Second-Harmonic Generation in Superconducting NbN under Supercurrent Injection Nakamura, Sachiko; Katsumi, Kota; Terai, Hirotaka Physical Review Letters, Vol. 125, Issue 9 https://doi.org/10.1103/PhysRevLett.125.097004	journal	August 2020
Higgs amplitude mode in the vicinity of a ( 2 + 1 ) -dimensional quantum critical point Rançon, A.; Dupuis, N. Physical Review B, Vol. 89, Issue 18 https://doi.org/10.1103/PhysRevB.89.180501	journal	May 2014
Higgs-mode radiance and charge-density-wave order in 2 H − NbSe 2 Grasset, Romain; Cea, Tommaso; Gallais, Yann Physical Review B, Vol. 97, Issue 9 https://doi.org/10.1103/PhysRevB.97.094502	journal	March 2018
Lightwave-driven gapless superconductivity and forbidden quantum beats by terahertz symmetry breaking Yang, X.; Vaswani, C.; Sundahl, C. Nature Photonics, Vol. 13, Issue 10 https://doi.org/10.1038/s41566-019-0470-y	journal	July 2019
Superconducting fluctuations probed by the Higgs mode in Bi 2 Sr 2 Ca Cu 2 O 8 + x thin films Katsumi, Kota; Li, Zhi Zhong; Raffy, Hélène Physical Review B, Vol. 102, Issue 5 https://doi.org/10.1103/PhysRevB.102.054510	journal	August 2020
Amplitude/Higgs Modes in Condensed Matter Physics Pekker, David; Varma, C. M. Annual Review of Condensed Matter Physics, Vol. 6, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031214-014350	journal	March 2015
Collective excitations of superfluid Fermi gases near the transition temperature Klimin, S. N.; Tempere, J.; Kurkjian, H. Physical Review A, Vol. 103, Issue 4 https://doi.org/10.1103/PhysRevA.103.043336	journal	April 2021
Higgs amplitude mode in a two-dimensional quantum antiferromagnet near the quantum critical point Hong, Tao; Matsumoto, Masashige; Qiu, Yiming Nature Physics, Vol. 13, Issue 7 https://doi.org/10.1038/nphys4182	journal	July 2017
Quantum fluctuations in the superfluid state of the BCS-BEC crossover Diener, Roberto B.; Sensarma, Rajdeep; Randeria, Mohit Physical Review A, Vol. 77, Issue 2 https://doi.org/10.1103/PhysRevA.77.023626	journal	February 2008
Higgs Mode in a Two-Dimensional Superfluid Pollet, L.; Prokof’ev, N. Physical Review Letters, Vol. 109, Issue 1 https://doi.org/10.1103/PhysRevLett.109.010401	journal	July 2012
Calculation of the Superconducting State Parameters with Retarded Electron-Phonon Interaction Morel, P.; Anderson, P. W. Physical Review, Vol. 125, Issue 4 https://doi.org/10.1103/PhysRev.125.1263	journal	February 1962
Hidden and mirage collective modes in two dimensional Fermi liquids Klein, Avraham; Maslov, Dmitrii L.; Chubukov, Andrey V. npj Quantum Materials, Vol. 5, Issue 1 https://doi.org/10.1038/s41535-020-0250-4	journal	August 2020
Terahertz pulse-driven collective mode in the nematic superconducting state of Ba1−xKxFe2As2 Grasset, Romain; Katsumi, Kota; Massat, Pierre npj Quantum Materials, Vol. 7, Issue 1 https://doi.org/10.1038/s41535-021-00411-9	journal	January 2022
Higgs mode in a strongly interacting fermionic superfluid Behrle, A.; Harrison, T.; Kombe, J. Nature Physics, Vol. 14, Issue 8 https://doi.org/10.1038/s41567-018-0128-6	journal	May 2018
Higgs Mode in the d -Wave Superconductor Bi 2 Sr 2 CaCu 2 O 8 + x Driven by an Intense Terahertz Pulse Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I. Physical Review Letters, Vol. 120, Issue 11 https://doi.org/10.1103/PhysRevLett.120.117001	journal	March 2018
Higgs Boson in Superconductors Varma, C. M. Journal of Low Temperature Physics, Vol. 126, Issue 3/4, p. 901-909 https://doi.org/10.1023/A:1013890507658	journal	January 2002
Amplitude collective modes in superconductors and their coupling to charge-density waves Littlewood, P. B.; Varma, C. M. Physical Review B, Vol. 26, Issue 9 https://doi.org/10.1103/PhysRevB.26.4883	journal	November 1982
Dynamic properties of superconductors: Anderson-Bogoliubov mode and Berry phase in the BCS and BEC regimes Mozyrsky, Dmitry; Chubukov, Andrey V. Physical Review B, Vol. 99, Issue 17 https://doi.org/10.1103/PhysRevB.99.174510	journal	May 2019
Leggett collective excitations in a two-band Fermi superfluid at finite temperatures Klimin, S. N.; Kurkjian, H.; Tempere, J. New Journal of Physics, Vol. 21, Issue 11 https://doi.org/10.1088/1367-2630/ab54b0	journal	November 2019
New Mechanism for Superconductivity Kohn, W.; Luttinger, J. M. Physical Review Letters, Vol. 15, Issue 12 https://doi.org/10.1103/PhysRevLett.15.524	journal	September 1965
Pressure-Induced Collapse of the Charge Density Wave and Higgs Mode Visibility in 2 H − TaS 2 Grasset, Romain; Gallais, Yann; Sacuto, Alain Physical Review Letters, Vol. 122, Issue 12 https://doi.org/10.1103/PhysRevLett.122.127001	journal	March 2019
Coherence length in superconductors from weak to strong coupling Benfatto, L.; Toschi, A.; Caprara, S. Physical Review B, Vol. 66, Issue 5 https://doi.org/10.1103/PhysRevB.66.054515	journal	August 2002
Fate of the Higgs Mode Near Quantum Criticality Gazit, Snir; Podolsky, Daniel; Auerbach, Assa Physical Review Letters, Vol. 110, Issue 14 https://doi.org/10.1103/PhysRevLett.110.140401	journal	April 2013
Superconductivity versus bound-state formation in a two-band superconductor with small Fermi energy: Applications to Fe pnictides/chalcogenides and doped SrTiO 3 Chubukov, Andrey V.; Eremin, Ilya; Efremov, Dmitri V. Physical Review B, Vol. 93, Issue 17 https://doi.org/10.1103/PhysRevB.93.174516	journal	May 2016
Phononic collective excitations in superfluid Fermi gases at nonzero temperatures Klimin, S. N.; Tempere, J.; Kurkjian, H. Physical Review A, Vol. 100, Issue 6 https://doi.org/10.1103/PhysRevA.100.063634	journal	December 2019
Nonlinear optical effects and third-harmonic generation in superconductors: Cooper pairs versus Higgs mode contribution Cea, T.; Castellani, C.; Benfatto, L. Physical Review B, Vol. 93, Issue 18 https://doi.org/10.1103/PhysRevB.93.180507	journal	May 2016
Effect of repulsion on superconductivity at low density Phan, Dan; Chubukov, Andrey V. Physical Review B, Vol. 105, Issue 6 https://doi.org/10.1103/PhysRevB.105.064518	journal	February 2022
Dynamical structure factors of a two-dimensional Fermi superfluid within random phase approximation Zhao, Huaisong; Gao, Xiaoxu; Liang, Wen New Journal of Physics, Vol. 22, Issue 9 https://doi.org/10.1088/1367-2630/abab3d	journal	September 2020
Spectral functions of the Higgs mode near two-dimensional quantum critical points Podolsky, Daniel; Sachdev, Subir Physical Review B, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevB.86.054508	journal	August 2012
Puviani et al. Reply: Puviani, M.; Baum, A.; Ono, S. Physical Review Letters, Vol. 129, Issue 19 https://doi.org/10.1103/PhysRevLett.129.199702	journal	November 2022
Raman scattering from superconducting gap excitations in the presence of a magnetic field Sooryakumar, R.; Klein, M. V. Physical Review B, Vol. 23, Issue 7 https://doi.org/10.1103/PhysRevB.23.3213	journal	April 1981
Comment on “Calculation of an Enhanced A1g Symmetry Mode Induced by Higgs Oscillations in the Raman Spectrum of High-Temperature Cuprate Superconductors” Benfatto, Lara; Castellani, Claudio; Cea, Tommaso Physical Review Letters, Vol. 129, Issue 19 https://doi.org/10.1103/PhysRevLett.129.199701	journal	November 2022
The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition Endres, Manuel; Fukuhara, Takeshi; Pekker, David Nature, Vol. 487, Issue 7408 https://doi.org/10.1038/nature11255	journal	July 2012
Dispersion and Damping of Phononic Excitations in Fermi Superfluid Gases in 2D Lumbeeck, Lars-Paul; Tempere, Jacques; Klimin, Serghei Condensed Matter, Vol. 5, Issue 1 https://doi.org/10.3390/condmat5010013	journal	February 2020
Nonrelativistic Dynamics of the Amplitude (Higgs) Mode in Superconductors Cea, T.; Castellani, C.; Seibold, G. Physical Review Letters, Vol. 115, Issue 15 https://doi.org/10.1103/PhysRevLett.115.157002	journal	October 2015
Higgs amplitude mode in the vicinity of a ( 2 + 1 ) -dimensional quantum critical point: A nonperturbative renormalization-group approach Rose, F.; Léonard, F.; Dupuis, N. Physical Review B, Vol. 91, Issue 22 https://doi.org/10.1103/PhysRevB.91.224501	journal	June 2015
Calculation of an Enhanced A1g Symmetry Mode Induced by Higgs Oscillations in the Raman Spectrum of High-Temperature Cuprate Superconductors Puviani, M.; Baum, A.; Ono, S. Physical Review Letters, Vol. 127, Issue 19 https://doi.org/10.1103/PhysRevLett.127.197001	journal	November 2021
Collective mode of homogeneous superfluid Fermi gases in the BEC-BCS crossover Combescot, R.; Kagan, M. Yu.; Stringari, S. Physical Review A, Vol. 74, Issue 4 https://doi.org/10.1103/PhysRevA.74.042717	journal	October 2006
Collective density fluctuations of strange metals with critical Fermi surfaces Wang, Xuepeng; Chowdhury, Debanjan Physical Review B, Vol. 107, Issue 12 https://doi.org/10.1103/PhysRevB.107.125157	journal	March 2023
Theory of driven Higgs oscillations and third-harmonic generation in unconventional superconductors Schwarz, Lukas; Manske, Dirk Physical Review B, Vol. 101, Issue 18 https://doi.org/10.1103/PhysRevB.101.184519	journal	May 2020
Superconductivity from nonphonon interactions Grabowski, M.; Sham, L. J. Physical Review B, Vol. 29, Issue 11 https://doi.org/10.1103/PhysRevB.29.6132	journal	June 1984
Linear response of a superfluid Fermi gas inside its pair-breaking continuum Kurkjian, H.; Tempere, J.; Klimin, S. N. Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-020-65371-9	journal	August 2020
Pair-Breaking Collective Branch in BCS Superconductors and Superfluid Fermi Gases Kurkjian, H.; Klimin, S. N.; Tempere, J. Physical Review Letters, Vol. 122, Issue 9 https://doi.org/10.1103/PhysRevLett.122.093403	journal	March 2019
Phase-resolved Higgs response in superconducting cuprates Chu, Hao; Kim, Min-Jae; Katsumi, Kota Rodare https://doi.org/10.14278/rodare.1289	dataset	January 2021