Pith. sign in

REVIEW 3 major objections 5 minor 2 cited by

Selective excitation of collective modes in multiband superconductor MgB2

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read By switching between multi-cycle and single-cycle terahertz pump pulses, this paper shows that the π-band Higgs mode and the Leggett mode in the two-band superconductor MgB2 can be selectively excited and separately identified.

desk verdict Solid comparative THz study with a plausible but incomplete case for selective Higgs vs Leggett excitation; the missing single-cycle control is the main gap. read the letter →

arxiv 2412.13830 v1 pith:TXIQ5VNQ submitted 2024-12-18 cond-mat.supr-con

Jiayu Yuan , Liyu Shi , Tiequan Xu , Yue Wang , Zizhao Gan , Hao Wang , Tianyi Wu , Dong Wu
show 2 more authors
Tao Dong Nanlin Wang
This is my paper · ORCID
classification cond-mat.supr-con
keywords MgB2multibandsuperconductivityHiggsmodeLeggettterahertzpump-probespectroscopynonlinearthird-orderresponsenonadiabaticexcitationcollectiveselection
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using terahertz pump–probe spectroscopy on thin-film MgB2, this paper claims that the collective mode dominating the nonlinear response is selected by the pump pulse's duration and spectrum. Multi-cycle narrowband pulses produce nonlinear signals at the pump frequency and its second harmonic that resonate when 2Δπ(T) matches 2ωp or ωp, identifying the π-band Higgs mode as the dominant response under periodic driving. Switching to a single-cycle pulse satisfying non-adiabatic excitation produces an overdamped ~1.8 THz oscillation, assigned by frequency matching to the Leggett mode. The two excitation protocols would thereby resolve a controversy between earlier experiments on MgB2 and give a route to distinguish Higgs modes from BCS single-particle fluctuations in multiband superconductors.

What carries the argument

The central objects are two excitation protocols: periodic driving by a narrowband multi-cycle THz pump, and non-adiabatic excitation by a single-cycle pump with τpΔ<1. The argument runs through the third-order nonlinear channels χ(3)(ωp,ωp,ωprobe), seen as a 2ω oscillation, and χ(3)(ωp,ωprobe,−ωprobe), seen as an ω oscillation, with temperature-scanned resonances matched to 2Δπ(T). The Leggett-mode assignment uses the two-band oscillator formula $ω_L^{2}$ = (Nσ+Nπ)/(NσNπ) · 4Vσπ Δσ(T)Δπ(T)/detV, fed with Δσ≈3Δπ and literature pairing potentials to get ωL=1.81±0.27 THz. The piece of the argument that distinguishes Higgs from BCS fluctuations is the 2D THz spectroscopy separation of rephasing and two-quantum processes at ω in the multi-cycle experiment.

What would settle it

Measure the single-cycle pump-probe response in MgB2 films with independently determined σ-band gaps, or with strain or doping that changes Δσ/Δπ, and check whether the observed overdamped oscillation frequency tracks the Leggett-mode formula's predicted ωL; alternatively, suppress pump spectral weight near 1.8 THz with a notch filter while keeping τpΔπ<1 and observe whether the oscillation disappears and a π-Higgs free oscillation emerges.

Watch

Extended reading notes

Core claim

The paper establishes that the dominant THz nonlinear response of MgB2 changes identity with pump waveform. Under narrowband periodic driving, the χ(3)(ωp,ωp,ωprobe) and χ(3)(ωp,ωprobe,−ωprobe) signals resonate with 2Δπ(T), not with the σ-band gap or the Leggett frequency, so the π-band Higgs mode is the main contributor; the ω channel in particular is argued to select the amplitude (Higgs) mode over BCS charge fluctuations. Under single-cycle, non-adiabatic driving with τpΔπ≈0.44 and τpωL/2≈0.88, the response is an overdamped 1.8±0.8 THz oscillation that matches the computed Leggett eigenfrequency ωL=1.81±0.27 THz, and the expected π-Higgs free oscillation is absent. The conclusion is that interband coupling makes the Leggett mode the dominant non-adiabatic response, and that pulse spectrum and duration can be tuned to excite either mode.

Load-bearing premise

The load-bearing premise is that the 1.8 THz overdamped oscillation is the Leggett mode because its measured frequency matches an eigenfrequency computed with Δσ≈3Δπ and literature pairing potentials, so if the actual gap ratio or interband couplings differ, the identification reduces to a frequency coincidence.

Editorial extensions

If this is right

  • Under periodic driving, resonances appear only when 2ωp or ωp crosses 2Δπ(T), not at σ-gap or Leggett conditions, so the multicycle protocol isolates the π-band Higgs response.
  • The ω-channel resonance at ωp=2Δπ(T) offers a practical discriminator between the Higgs amplitude mode and BCS single-particle fluctuations.
  • Under non-adiabatic single-cycle excitation with enough spectral weight near ωL, the Leggett mode dominates and the π-Higgs free oscillation is overdamped or invisible.
  • The Leggett mode sets an upper frequency boundary for the pump spectrum if one wants to observe π-Higgs free oscillations in a two-band superconductor.
  • A single-cycle pump shaped to avoid spectral overlap with the Leggett mode should reveal the expected π-Higgs free oscillation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If waveform-selective excitation is generic, the same pulse-shaping logic could be applied to iron-pnictide and nickelate multiband superconductors, where Higgs and Leggett assignments are also contested.
  • The paper's Leggett identification is essentially an eigenfrequency match; a cleaner test would vary the σ/π gap ratio through strain, doping, or different films and check that the observed overdamped frequency tracks the predicted ωL rather than staying fixed.
  • The authors' proposed two-pulse experiment—one non-adiabatic pulse to excite the Leggett mode and one periodic driving to probe the π Higgs—could directly measure Higgs–Leggett coupling, and is a natural next step they only outline.
  • The ω (rephasing/two-quantum) channel may serve as a generic Higgs-selective diagnostic beyond MgB2, since it is argued to suppress BCS-fluctuation backgrounds.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reports THz pump–probe experiments on a 10 nm MgB2 film and uses two pulse protocols to address the controversy over which collective mode dominates the nonlinear response. Under multi-cycle narrowband driving, the authors resolve nonlinear signals at the pump frequency ω and at 2ω, with temperature-dependent spectral weight showing resonances at 2ωp = 2Δπ(T) and ωp = 2Δπ(T); they attribute these to the π-band Higgs mode, supported by a two-dimensional THz spectroscopy analysis that separates the contributing nonlinear processes. Under single-cycle non-adiabatic excitation, they observe an overdamped oscillation at 1.8 ± 0.8 THz, which they assign to the Leggett mode on the basis of a computed eigenfrequency ωL ≈ 1.81 ± 0.27 THz. The central claim is that the Higgs and Leggett modes can be selectively excited by tuning the spectrum and duration of the THz pump.

Significance. If the mode assignments hold, the paper would resolve a genuine conflict between previous MgB2 experiments: Giorgianni et al. reported Leggett-mode dominance under single-cycle driving, while Kovalev et al. reported π-band Higgs dominance under narrowband driving. The present work attempts a unified picture within a single sample. The experimental effort is substantial: the authors carefully calibrate screening effects through measured transmission coefficients, check fluence dependence to stay in the perturbative regime, and include an NbN comparison as a positive control for the observation of a Higgs-mode free oscillation. The 2D THz spectroscopy analysis is a strength because it assigns the ω and 2ω features to specific nonlinear kernels. The paper is also explicit about a key limitation: the Summary states that observing the π-band Higgs free oscillation with a single-cycle pulse lacking Leggett-mode overlap is 'highly desirable', thereby conceding that a necessary control is missing. This transparency is commendable, but the missing control is load-bearing for the selective-excitation claim.

major comments (3)
  1. [Leggett mode response within non-adiabatic excitation (Fig. 3B)] The assertion that the single-cycle pump has 'sufficient spectral overlap' with the Leggett mode is not quantified. The pump spectrum shown in Fig. 3B peaks near 0.8 THz and the text notes its tail extends to higher frequencies, but no measure is given of the spectral weight at ωL ≈ 1.8 THz relative to that at 2Δπ ≈ 0.88 THz. Since τpωL/2 ≈ 0.88 is only marginally in the non-adiabatic regime, a quantitative overlap estimate is needed to support the claim that the observed overdamped response is specifically due to Leggett-mode activation rather than a weak tail effect.
  2. [Summary] The selective-excitation conclusion rests on an incomplete comparison. The manuscript itself states that a single-cycle pulse without sufficient overlap with the Leggett mode is 'highly desirable' to observe the π-band Higgs free oscillation, but no such control is reported. Without that control, the absence of a 0.88 THz free oscillation in Fig. 3F/G constitutes negative evidence: it could reflect overdamping of the π-Higgs mode in this 10 nm film or detection sensitivity limitations rather than dominance of the Leggett mode. Demonstrating selectivity requires showing both that the Leggett mode appears when the pump overlaps it and that the π-Higgs mode appears when the pump does not.
  3. [Supplementary Eq. S11 and Fig. 3G] The identification of the 1.8 THz overdamped oscillation as the Leggett mode is based on a frequency match between the measured feature (1.8 ± 0.8 THz) and a calculation using Δσ ≈ 3Δπ and literature pairing potentials (ωL = 1.81 ± 0.27 THz). Given the large uncertainty in the observed frequency and the sensitivity of Eq. S11 to the assumed gap ratio and pairing potentials, this is not a mode-specific fingerprint. Although the text states that the oscillation softens with temperature, a quantitative comparison with the calculated ωL(T) shown in Fig. S14 is not provided; such a comparison would substantially strengthen the assignment.
minor comments (5)
  1. [Figure 2 caption and main text] The main text refers to 'Fig. 2B and C' for the time-domain and frequency-domain waveforms, but the figure caption labels the time-domain and frequency-domain waveforms as C and D; the χ(3) plot is B. The cross-reference should be corrected.
  2. [Supplementary Eq. S11] The determinant detV in Eq. S11 is not explicitly defined. Specify that it is the determinant of the 2×2 pairing-potential matrix, so that the formula is self-contained.
  3. [Page 10, first paragraph] There is a typo: 'Figuree 3D' should read 'Figure 3D'.
  4. [Supplementary Table S2] The table note says the parameters correspond to 'the flux and temperature conditions used for plotting Fig. 3B in the main text', but the table concerns the multi-cycle 2ω signals and appears to refer to Fig. 2B. The cross-reference should be corrected.
  5. [Page 9, final paragraph] There is a typo: 'Legget mode' should read 'Leggett mode'.

Circularity Check

0 steps flagged · score 1.0 of 10

No load-bearing circularity: the Leggett-mode assignment is an external frequency benchmark, and the π-Higgs assignment rests on the paper's own resonance data; only a minor non-load-bearing self-citation is present.

full rationale

The central derivations are benchmark tests rather than fitted predictions. In the multicycle experiments, the 2ω and ω resonances are located by their temperature dependence and checked against independently measured 2Δπ(T) from the same film's THz conductivity; this is a resonance-condition test, not a fit. The single-cycle experiment's 1.8±0.8 THz oscillation is compared with ωL=1.81±0.27 THz computed from Eq. S11 using the measured Δπ=0.44 THz, the empirical relation Δσ≈3Δπ, and three literature pairing-potential sets; the calculation does not use the observed 1.8 THz peak as an input, so the agreement is an external consistency check rather than a self-fulfilling fit. The citation of the authors' prior THG work [26] for the π-Higgs interpretation is a self-citation, but the present paper's own 2ωp=2Δπ and ωp=2Δπ resonances carry the assignment; [26] is corroborative only. The paper itself concedes that a single-cycle pulse without sufficient overlap with the Leggett mode would be needed to observe the expected π-Higgs free oscillation ('A fine-tuning of wavelengths and durations of the excitation THz pulse in a single-cycle waveform without sufficient overlap with Leggett mode is highly desirable to observe the expectant π band Higgs mode free oscillation'), so the selective-excitation claim lacks a control condition; this is an empirical completeness limitation, not circularity, because no step of the argument is equivalent to its inputs by construction. No eq-to-eq identity or fitted-parameter-renamed-as-prediction was found. Score 1 reflects one minor self-citation that is not load-bearing.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the measured gap Delta_pi, the assumed gap ratio Delta_sigma≈3Delta_pi, literature pairing parameters used to predict the Leggett frequency, and theoretical attributions of the omega and 2omega channels to the Higgs mode. No new physical entities are introduced.

free parameters (3)
  • Delta_sigma / Delta_pi ratio = 3 (dimensionless)
    Empirical relation used to set 2Delta_sigma≈2.64 THz. This enters the Leggett mode frequency calculation (Eq. S11). The paper does not measure Delta_sigma on this film.
  • Pairing potentials V_sigma_sigma, V_pi_pi, V_sigma_pi = Three literature sets (Table S4): Liu et al. 0.47/0.1/0.08 Ry; Choi et al. 0.38/0.076/0.054 Ry; Golubov et al.
    Inputs to Eq. S11 for omega_L. The spread across sets gives the ±0.27 THz uncertainty quoted.
  • Densities of states N_sigma, N_pi = N_sigma=2.04, N_pi=2.78 Ry^-1 spin^-1 cell^-1
    Taken from Ref [24] and used in Eq. S11.
assumptions (4)
  • domain assumption The collective amplitude (Higgs) mode of a BCS superconductor sits at energy 2Delta in the long-wavelength limit and couples nonlinearly to THz fields, either as 2omega_p=2Delta resonances under periodic driving or as free oscillations after a quench satisfying tau_p*Delta<1.
    Invoked in the Introduction and Results to assign the 2omega and omega resonances to the pi-band Higgs mode and to interpret the single-cycle experiment.
  • domain assumption The Leggett mode frequency in a two-band superconductor is given by omega_L^2 = (N_sigma+N_pi)/(N_sigma*N_pi) * 4*V_sigma_pi*Delta_sigma*Delta_pi / det(V) (Eq. S11), with N's and V's from band-structure literature.
    Used to predict omega_L≈1.8 THz for comparison with the observed oscillation. The formula is taken from Ref [24] without re-derivation.
  • domain assumption A THz pulse satisfies the non-adiabatic condition for a mode at energy Delta when tau_p*Delta<1, where tau_p is the pulse duration.
    Used to argue that the single-cycle pulse (tau_p≈1 ps) non-adiabatically excites both the pi-Higgs (tau_p*Delta_pi≈0.44) and the Leggett mode (tau_p*omega_L/2≈0.88). References [8,40].
  • domain assumption In the (omega_p,omega_probe,-omega_probe) nonlinear channel, the response at omega_p=2Delta is dominated by the amplitude (Higgs) mode rather than by BCS quasiparticle fluctuations.
    This underpins the central assignment of the omega resonance to the pi-band Higgs mode. The paper relies on Refs [31,32] for this attribution.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Selective excitation of collective modes in multiband superconductor MgB2." pith.science (2026). https://pith.science/paper/TXIQ5VNQ

@misc{pith2026241213830,
  author       = {Pith},
  title        = {Pith review of: Selective excitation of collective modes in multiband superconductor MgB2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TXIQ5VNQ}},
  note         = {Machine review of arXiv:2412.13830}
}
abstract

Recent developments in nonequilibrium and nonlinear terahertz (THz) spectroscopies have significantly advanced our understanding of collective excitations in superconductors. However, there is still debate surrounding the identification of Higgs or Leggett modes, as well as BCS charge fluctuations, in the well-known two-band superconductor MgB$_2$. Here, we utilized both multi-cycle and single-cycle THz pump-broadband THz probe techniques to investigate the THz nonlinear response of MgB$_2$. Through multicycle THz pump-THz probe experiments on MgB$_2$, we observed distinct nonlinear signals at both the fundamental frequency ($\omega$) and the second harmonic frequency (2$\omega$) of the pump pulses, which exhibited resonant enhancement at temperatures where their frequencies respectively match 2$\Delta_{\pi}(T)$. They are mainly attributed to the $\pi$-band Higgs mode. By adjusting the THz pump pulse to a single-cycle waveform that satisfies non-adiabatic excitation criteria, we observed an over-damped oscillation corresponding to the Leggett mode. Our findings contribute to solving the ongoing debates and demonstrate the selective excitation of collective modes in multiband superconductors, offering new insights into the interaction between Higgs and Leggett modes.

Figures

Figures reproduced from arXiv: 2412.13830 by the authors.

Figure 1
Figure 1. 0.35 THz multi-cycle pump-probe experiment results at 6 K. A: Definition of t [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. The nonlinear signal from multi-cycle pump-probe measurements at di [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. THz single-cycle pump-probe experiment set-up and results. (A) Schematic of the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Two-dimensional THz spectroscopy in electronic systems: a many-body diagrammatic approach

    cond-mat.supr-con 2025-09 conditional novelty 7.0 of 10

    A many-body diagrammatic theory computes 2D THz spectroscopy maps from third-order nonlinear kernels, separates paramagnetic and diamagnetic processes, and shows propagation through the sample can dominate and mask th...

  2. Amplitude mode in a multi-gap superconductor MgB$_2$ investigated by terahertz two-dimensional coherent spectroscopy

    cond-mat.supr-con 2024-11 conditional novelty 6.0 of 10

    The normalized first-harmonic THz nonlinear response of MgB2 rises monotonically as temperature falls, fitting an overdamped π-band amplitude mode with damping rate 0.55 THz, about four times larger than in NbN.

Reference graph

Works this paper leans on

45 extracted references · 43 canonical work pages · cited by 2 Pith papers

  1. [1]

    P. W. Anderson, Random-phase approximation in the theory of superconductivity, Physical Review 112, 1900 (1958)

    work page 1958

  2. [2]

    P. W. Anderson, Plasmons, gauge invariance, and mass, Physical Review 130, 439 (1963)

    work page 1963

  3. [3]

    P. B. Littlewood and C. M. Varma, Amplitude collective modes in superconductors and their coupling to charge-density waves, Physical Review B 26, 4883 (1982)

    work page 1982

  4. [4]

    Pekker and C

    D. Pekker and C. Varma, Amplitude /higgs modes in condensed matter physics, Annual Review of Condensed Matter Physics 6, 269 (2015)

    work page 2015

  5. [5]

    J. C. Tsang, J. E. Smith, and M. W. Shafer, Raman Spectroscopy of Soft Modes at the Charge-Density- Wave Phase Transition in 2 H - Nb Se 2, Physical Review Letters37, 1407 (1976)

    work page 1976

  6. [6]

    Sooryakumar and M

    R. Sooryakumar and M. V . Klein, Raman Scattering by Superconducting-Gap Excitations and Their Coupling to Charge-Density Waves, Physical Review Letters45, 660 (1980)

    work page 1980

  7. [7]

    M ´easson, Y

    M.-A. M ´easson, Y . Gallais, M. Cazayous, B. Clair, P. Rodi `ere, L. Cario, and A. Sacuto, Amplitude Higgs mode in the 2 H - NbSe 2 superconductor, Physical Review B 89, 060503 (2014)

    work page 2014

  8. [8]

    Matsunaga, Y

    R. Matsunaga, Y . I. Hamada, K. Makise, Y . Uzawa, H. Terai, Z. Wang, and R. Shimano, Higgs am- plitude mode in the bcs superconductors nb1-xtixn induced by terahertz pulse excitation, Physical Review Letters 111, 057002 (2013)

    work page 2013

Show all 45 references
  1. [9]

    Matsunaga, N

    R. Matsunaga, N. Tsuji, H. Fujita, A. Sugioka, K. Makise, Y . Uzawa, H. Terai, Z. Wang, H. Aoki, and R. Shimano, Light-induced collective pseudospin precession resonating with higgs mode in a superconductor, Science 345, 1145 (2014)

    2014

  2. [10]

    Krull, D

    H. Krull, D. Manske, G. S. Uhrig, and A. P. Schnyder, Signatures of nonadiabatic bcs state dynamics in pump-probe conductivity, Phys. Rev. B90, 014515 (2014)

    2014

  3. [11]

    Tsuji and H

    N. Tsuji and H. Aoki, Theory of anderson pseudospin resonance with higgs mode in superconductors, Phys. Rev. B 92, 064508 (2015)

    2015

  4. [12]

    Shimano and N

    R. Shimano and N. Tsuji, Higgs mode in superconductors, Annual Review of Condensed Matter Physics 11, 103 (2020)

    2020

  5. [13]

    Chu, M.-J

    H. Chu, M.-J. Kim, K. Katsumi, S. Kovalev, R. D. Dawson, L. Schwarz, N. Yoshikawa, G. Kim, D. Putzky, Z. Z. Li, H. Raffy, S. Germanskiy, J.-C. Deinert, N. Awari, I. Ilyakov, B. Green, M. Chen, M. Bawatna, G. Cristiani, G. Logvenov, Y . Gallais, A. V . Boris, B. Keimer, A. P. S...

    2020

  6. [14]

    Wang, J.-R

    Z.-X. Wang, J.-R. Xue, H.-K. Shi, X.-Q. Jia, T. Lin, L.-Y . Shi, T. Dong, F. Wang, and N.-L. Wang, Transient higgs oscillations and high-order nonlinear light-higgs coupling in a terahertz wave driven nbn superconductor, Physical Review B 105, L100508 (2022)

    2022

  7. [15]

    Dong, S.-J

    T. Dong, S.-J. Zhang, and N.-L. Wang, Recent Development of Ultrafast Optical Characterizations for Quantum Materials, Advanced Materials 35, 2110068 (2023)

    2023

  8. [16]

    T. Cea, C. Castellani, and L. Benfatto, Nonlinear optical e ffects and third-harmonic generation in superconductors: Cooper pairs versus higgs mode contribution, Physical Review B93, 180507 (2016)

    2016

  9. [17]

    Silaev, Nonlinear electromagnetic response and Higgs-mode excitation in BCS superconductors with impurities, Physical Review B 99, 224511 (2019)

    M. Silaev, Nonlinear electromagnetic response and Higgs-mode excitation in BCS superconductors with impurities, Physical Review B 99, 224511 (2019)

    2019

  10. [18]

    Tsuji and Y

    N. Tsuji and Y . Nomura, Higgs-mode resonance in third harmonic generation in NbN superconduc- tors: Multiband electron-phonon coupling, impurity scattering, and polarization-angle dependence, Physical Review Research 2, 043029 (2020)

    2020

  11. [19]

    Seibold, M

    G. Seibold, M. Udina, C. Castellani, and L. Benfatto, Third harmonic generation from collective modes in disordered superconductors, Physical Review B 103, 014512 (2021)

    2021

  12. [20]

    A. J. Leggett, Number-phase fluctuations in two-band superconductors, Progress of Theoretical Physics 36, 901 (1966)

    1966

  13. [21]

    Krull, N

    H. Krull, N. Bittner, G. S. Uhrig, D. Manske, and A. P. Schnyder, Coupling of higgs and leggett modes in non-equilibrium superconductors, Nature Communications 7, 11921 (2016)

    2016

  14. [22]

    Szab ´o, P

    P. Szab ´o, P. Samuely, J. Kaˇcmarˇc´ık, T. Klein, J. Marcus, D. Fruchart, S. Miraglia, C. Marcenat, and A. G. M. Jansen, Evidence for two superconducting energy gaps in mgb 2 by point-contact spec- troscopy, Physical Review Letters 87, 137005 (2001)

    2001

  15. [23]

    Y . Xu, M. Khafizov, L. Satrapinsky, P. K´uˇs, A. Plecenik, and R. Sobolewski, Time-resolved photoex- citation of the superconducting two-gap state in mgb 2 thin films, Physical Review Letters91, 197004 (2003)

    2003

  16. [24]

    Blumberg, A

    G. Blumberg, A. Mialitsin, B. S. Dennis, M. V . Klein, N. D. Zhigadlo, and J. Karpinski, Observation of leggett’s collective mode in a multiband mgb2 superconductor, Physical Review Letters99, 227002 (2007)

    2007

  17. [25]

    Giorgianni, T

    F. Giorgianni, T. Cea, C. Vicario, C. P. Hauri, W. K. Withanage, X. Xi, and L. Benfatto, Leggett mode controlled by light pulses, Nature Physics 15, 341 (2019). 31

    2019

  18. [26]

    Kovalev, T

    S. Kovalev, T. Dong, L.-Y . Shi, C. Reinhoffer, T.-Q. Xu, H.-Z. Wang, Y . Wang, Z.-Z. Gan, S. German- skiy, J.-C. Deinert, I. Ilyakov, P. H. M. Van Loosdrecht, D. Wu, N.-L. Wang, J. Demsar, and Z. Wang, Band-selective third-harmonic generation in superconducting mgb2: Possible...

    2021

  19. [27]

    Haenel, P

    R. Haenel, P. Froese, D. Manske, and L. Schwarz, Time-resolved optical conductivity and Higgs oscillations in two-band dirty superconductors, Physical Review B 104, 134504 (2021)

    2021

  20. [28]

    Fiore, M

    J. Fiore, M. Udina, M. Marciani, G. Seibold, and L. Benfatto, Contribution of collective excitations to third harmonic generation in two-band superconductors: The case of mgb2, Physical Review B 106, 094515 (2022)

    2022

  21. [29]

    Reinho ffer, P

    C. Reinho ffer, P. Pilch, A. Reinold, P. Derendorf, S. Kovalev, J.-C. Deinert, I. Ilyakov, A. Ponomaryov, M. Chen, T.-Q. Xu, Y . Wang, Z.-Z. Gan, D.-S. Wu, J.-L. Luo, S. Germanskiy, E. A. Mashkovich, P. H. M. Van Loosdrecht, I. M. Eremin, and Z. Wang, High-order nonlinear tera...

    2022

  22. [30]

    Matsunaga, N

    R. Matsunaga, N. Tsuji, K. Makise, H. Terai, H. Aoki, and R. Shimano, Polarization-resolved tera- hertz third-harmonic generation in a single-crystal superconductor nbn: Dominance of the higgs mode beyond the bcs approximation, Physical Review B 96, 020505 (2017)

    2017

  23. [31]

    Katsumi, J

    K. Katsumi, J. Fiore, M. Udina, R. Romero, D. Barbalas, J. Jesudasan, P. Raychaudhuri, G. Seibold, L. Benfatto, and N. P. Armitage, Revealing Novel Aspects of Light-Matter Coupling by Terahertz Two-Dimensional Coherent Spectroscopy: The Case of the Amplitude Mode in Supercondu...

    2024

  24. [32]

    Katsumi, J

    K. Katsumi, J. Liang, R. R. III, K. Chen, X. Xi, and N. P. Armitage, Amplitude mode in a multi-gap superconductor MgB$ 2$ investigated by terahertz two-dimensional coherent spectroscopy (2024), arXiv:2411.10852 [cond-mat]

    2024 arXiv

  25. [33]

    Udina, T

    M. Udina, T. Cea, and L. Benfatto, Theory of coherent-oscillations generation in terahertz pump-probe spectroscopy: From phonons to electronic collective modes, Physical Review B 100, 165131 (2019)

    2019

  26. [34]

    Matsunaga and R

    R. Matsunaga and R. Shimano, Nonequilibrium bcs state dynamics induced by intense terahertz pulses in a superconducting nbn film, Physical Review Letters 109, 187002 (2012)

    2012

  27. [35]

    X. Yang, C. Vaswani, C. Sundahl, M. Mootz, L. Luo, J. H. Kang, I. E. Perakis, C. B. Eom, and J. Wang, Lightwave-driven gapless superconductivity and forbidden quantum beats by terahertz sym- metry breaking, Nature Photonics 13, 707 (2019). 32

    2019

  28. [36]

    Nakamura, K

    S. Nakamura, K. Katsumi, H. Terai, and R. Shimano, Nonreciprocal Terahertz Second-Harmonic Gen- eration in Superconducting NbN under Supercurrent Injection, Physical Review Letters 125, 097004 (2020)

    2020

  29. [37]

    Vaswani, M

    C. Vaswani, M. Mootz, C. Sundahl, D. H. Mudiyanselage, J. H. Kang, X. Yang, D. Cheng, C. Huang, R. H. J. Kim, Z. Liu, L. Luo, I. E. Perakis, C. B. Eom, and J. Wang, Terahertz Second-Harmonic Generation from Lightwave Acceleration of Symmetry-Breaking Nonlinear Supercurrents, P...

    2020

  30. [38]

    Nakamura, H

    S. Nakamura, H. Matsumoto, H. Ogawa, T. Kobayashi, F. Nabeshima, A. Maeda, and R. Shimano, Picosecond Trajectory of Two-Dimensional V ortex Motion in FeSe 0.5 Te 0.5 Visualized by Terahertz Second Harmonic Generation, Physical Review Letters 133, 036004 (2024)

    2024

  31. [39]

    Mootz, L

    M. Mootz, L. Luo, J. Wang, and L. E. Perakis, Visualization and quantum control of light-accelerated condensates by terahertz multi-dimensional coherent spectroscopy, Communications Physics 5, 47 (2022)

    2022

  32. [40]

    Papenkort, V

    T. Papenkort, V . M. Axt, and T. Kuhn, Coherent dynamics and pump-probe spectra of bcs supercon- ductors, Physical Review B 76, 224522 (2007)

    2007

  33. [41]

    K.-L. Yeh, M. C. Ho ffmann, J. Hebling, and K. A. Nelson, Generation of 10 µJ ultrashort terahertz pulses by optical rectification, Applied Physics Letters 90, 171121 (2007)

    2007

  34. [42]

    Casalbuoni, H

    S. Casalbuoni, H. Schlarb, B. Schmidt, P. Schm ¨user, B. Ste ffen, and A. Winter, Numerical studies on the electro-optic detection of femtosecond electron bunches, Physical Review Special Topics - Accelerators and Beams 11, 072802 (2008)

    2008

  35. [43]

    A. Y . Liu, I. I. Mazin, and J. Kortus, Beyond Eliashberg Superconductivity in MgB 2 : Anharmonicity, Two-Phonon Scattering, and Multiple Gaps, Physical Review Letters 87, 087005 (2001)

    2001

  36. [44]

    H. J. Choi, D. Roundy, H. Sun, M. L. Cohen, and S. G. Louie, The origin of the anomalous supercon- ducting properties of MgB(2), Nature 418, 758 (2002)

    2002

  37. [45]

    A. A. Golubov, J. Kortus, O. V . Dolgov, O. Jepsen, Y . Kong, O. K. Andersen, B. J. Gibson, K. Ahn, and R. K. Kremer, Specific heat of MgB2 in a one- and a two-band model from first-principles calculations, Journal of Physics: Condensed Matter 14, 1353 (2002). 33

    2002

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.