Observation of Leggett's collective mode in a multiband MgB2 superconductor

Superconductivity in ordered Li-Al-B compounds

Using first principles calculations, we show that [Formula: see text] materials have strong electron-phonon coupling, with many having a superconducting critical temperature ([Formula: see text]) that exceeds that of the more familiar [Formula: see text] at ambient pressure. In particular, we find that [Formula: see text] is the most stable member of the family, with [Formula: see text] whilst the peak [Formula: see text] is with [Formula: see text] which has [Formula: see text]. Our results reveal that these materials are both thermodynamically and dynamically stable, with strong electron-phonon coupling, indicating significant potential for practical superconducting applications.

Raman Spectroscopy Investigation of Phonon Behavior in ZnO-Buffered MgB2 Tapes: Exploring Lattice Dynamics and Anharmonicity

We investigated the phonon behavior of ZnO-buffered MgB2 tapes with varying ZnO buffer layer thicknesses using polarized Raman spectroscopy at room and cryogenic temperatures. Polar plots from integrated angle-resolved polarized Raman spectroscopy (ARPRS) at room temperature revealed substantial distortion in the boron plane geometry due to lattice mismatch among the MgB2 film, ZnO buffer layer, and Hastelloy substrate. This distortion significantly affects the electron-phonon coupling (EPC) constant, λ, which we calculated using the modified McMillan equation by Allen-Dynes in relation to the superconducting transition temperature (Tc) of the sample. At cryogenic temperatures, our investigation of the E2g mode exhibited a notable phonon hardening effect of up to ∼4.1%, correlated with the ZnO buffer layer thickness. Furthermore, analysis of the anharmonic E2g phonon mechanism through line width (full width at half maximum) revealed damping behavior, indicating an additional coupling mechanism within the sample that varies with the temperature. This unique Raman scattering behavior potentially elucidates the high Tc mechanism of MgB2, which is underestimated by traditional EPC calculations. Additionally, increasing the thickness of the ZnO layer is predicted to alleviate the distortion in the boron plane geometry, thereby promoting MgB2 toward its inherent electron-phonon superconducting nature by mitigating the additional coupling mechanisms. Understanding how the ZnO buffer layer influences the phonon dynamics and EPC in MgB2 will provide critical insights into optimizing its superconducting properties and advancing its practical applications in high-performance superconducting devices.

Evidence of a distinct collective mode in Kagome superconductors

The collective modes of the superconducting order parameter fluctuation can provide key insights into the nature of the superconductor. Recently, a family of superconductors has emerged in non-magnetic kagome materials AV3Sb5 (A = K, Rb, Cs), exhibiting fertile emergent phenomenology. However, the collective behaviors of Cooper pairs have not been studied. Here, we report a distinct collective mode in CsV3-xTaxSb5 using scanning tunneling microscope/spectroscopy. The spectral line-shape is well-described by one isotropic and one anisotropic superconducting gap, and a bosonic mode due to electron-mode coupling. With increasing x, the two gaps move closer in energy, merge into two isotropic gaps of equal amplitude, and then increase synchronously. The mode energy decreases monotonically to well below 2 Δ and survives even after the charge density wave order is suppressed. We propose the interpretation of this collective mode as Leggett mode between different superconducting components or the Bardasis-Schrieffer mode due to a subleading superconducting component.

Revealing Novel Aspects of Light-Matter Coupling by Terahertz Two-Dimensional Coherent Spectroscopy: The Case of the Amplitude Mode in Superconductors

Recently developed terahertz (THz) two-dimensional coherent spectroscopy (2DCS) is a powerful technique to obtain materials information in a fashion qualitatively different from other spectroscopies. Here, we utilized THz 2DCS to investigate the THz nonlinear response of conventional superconductor NbN. Using broadband THz pulses as light sources, we observed a third-order nonlinear signal whose spectral components are peaked at twice the superconducting gap energy 2Δ. With narrow-band THz pulses, a THz nonlinear signal was identified at the driving frequency Ω and exhibited a resonant enhancement at temperature when Ω=2Δ. General theoretical considerations show that such a resonance can arise only from a disorder-activated paramagnetic coupling between the light and the electronic current. This proves that the nonlinear THz response can access processes distinct from the diamagnetic Raman-like density fluctuations, which are believed to dominate the nonlinear response at optical frequencies in metals. Our numerical simulations reveal that, even for a small amount of disorder, the Ω=2Δ resonance is dominated by the superconducting amplitude mode over the entire investigated disorder range. This is in contrast to other resonances, whose amplitude-mode contribution depends on disorder. Our findings demonstrate the unique ability of THz 2DCS to explore collective excitations inaccessible in other spectroscopies.

Possible Eliashberg-Type Superconductivity Enhancement Effects in a Two-Band Superconductor MgB_{2} Driven by Narrow-Band THz Pulses

We study THz-driven condensate dynamics in epitaxial thin films of MgB_{2}, a prototype two-band superconductor (SC) with weak interband coupling. The temperature and excitation density dependent dynamics follow the behavior predicted by the phenomenological bottleneck model for the single-gap SC, implying adiabatic coupling between the two condensates on the ps timescale. The amplitude of the THz-driven suppression of condensate density reveals an unexpected decrease in pair-breaking efficiency with increasing temperature-unlike in the case of optical excitation. The reduced pair-breaking efficiency of narrow-band THz pulses, displaying minimum near ≈0.7  T_{c}, is attributed to THz-driven, long-lived, nonthermal quasiparticle distribution, resulting in Eliashberg-type enhancement of superconductivity, competing with pair breaking.

Observation of Superconducting Collective Modes from Competing Pairing Instabilities in Single-Layer NbSe2

In certain unconventional superconductors with sizable electronic correlations, the availability of closely competing pairing channels leads to characteristic soft collective fluctuations of the order parameters, which leave fingerprints in many observables and allow the phase competition to be scrutinized. Superconducting layered materials, where electron-electron interactions are enhanced with decreasing thickness, are promising candidates to display these correlation effects. In this work, the existence of a soft collective mode in single-layer NbSe₂ , observed as a characteristic resonance excitation in high-resolution tunneling spectra is reported. This resonance is observed along with higher harmonics, its frequency Ω/2Δ is anticorrelated with the local superconducting gap Δ, and its amplitude gradually vanishes by increasing the temperature and upon applying a magnetic field up to the critical values (T_C and H_C2 ), which sets an unambiguous link to the superconducting state. Aided by a microscopic model that captures the main experimental observations, this resonance is interpreted as a collective Leggett mode that represents the fluctuation toward a proximate f-wave triplet state, due to subleading attraction in the triplet channel. These findings demonstrate the fundamental role of correlations in superconducting 2D transition metal dichalcogenides, opening a path toward unconventional superconductivity in simple, scalable, and transferable 2D superconductors.

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.

Superfluid density and collective modes of fermion superfluid in dice lattice

The superfluid properties of attractive Hubbard model in dice lattice are investigated. It is found that three superfluid order parameters increase as the interaction increases. When the filling factor falls into the flat band, due to the infinite large density of states, the resultant superfluid order parameters are proportional to interaction strength, which is in striking contrast with the exponentially small counterparts in usual superfluid (or superconductor). When the interaction is weak, and the filling factor is near the bottom of the lowest band (or the top of highest band), the superfluid density is determined by the effective mass of the lowest (or highest) single-particle band. When the interaction is strong and filling factor is small, the superfluid density is inversely proportional to interaction strength, which is related to effective mass of tightly bound pairs. In the strong interaction limit and finite filling, the asymptotic behaviors of superfluid density can be captured by a parabolic function of filling factor. Furthermore, when the filling is in flat band, the superfluid density shows a logarithmic singularity as the interaction approaches zero. In addition, there exist three undamped collective modes for strong interactions. The lowest excitation is gapless phonon, which is characterized by the total density oscillations. The two others are gapped Leggett modes, which correspond relative density fluctuations between sublattices. The collective modes are also reflected in the two-particle spectral functions by sharp peaks. Furthermore, it is found that the two-particle spectral functions satisfy an exact sum-rule, which is directly related to the filling factor (or density of particle). The sum-rule of the spectral functions may be useful to distinguish between the hole-doped and particle-doped superfluid (superconductor) in experiments.

Raman Study of Cooper Pairing Instabilities in (Li_{1-x}Fe_{x})OHFeSe

We studied the electronic Raman spectra of (Li_{1-x}Fe_{x})OHFeSe as a function of light polarization and temperature. In the B_{1g} spectra alone we observe the redistribution of spectral weight expected for a superconductor and two well-resolved peaks below T_{c}. The nearly resolution-limited peak at 110  cm^{-1} (13.6 meV) is identified as a collective mode. The peak at 190  cm^{-1} (23.6 meV) is presumably another collective mode since the line is symmetric and its energy is significantly below the gap energy observed by single-particle spectroscopies. Given the experimental band structure of (Li_{1-x}Fe_{x})OHFeSe, the most plausible explanations include conventional spin-fluctuation pairing between the electron bands and the incipient hole band and pairing between the hybridized electron bands. The absence of gap features in A_{1g} and B_{2g} symmetry favors the second case. Thus, in spite of various differences between the pnictides and chalcogenides, this Letter demonstrates the proximity of pairing states and the importance of band structure effects in the Fe-based compounds.

Fluctuations and pairing in Fe-based superconductors: light scattering experiments

Inelastic scattering of visible light (Raman effect) offers a window into properties of correlated metals such as spin, electron and lattice dynamics as well as their mutual interactions. In this review we focus on electronic and spin excitations in Fe-based pnictides and chalcogenides, in particular but not exclusively superconductors. After a general introduction to the basic theory including the selection rules for the various scattering processes we provide an overview over the major experimental results. In the superconducting state below the transition temperatureTcthe pair-breaking effect can be observed, and the gap energies may be derived and associated with the gaps on the electron and hole bands. In spite of the similarities of the overall band structures the results are strongly dependent on the family and may even change qualitatively within one family. In some of the compounds strong collective modes appear belowTc. In Ba1-xKxFe2As2, which has the most isotropic gap of all Fe-based superconductors, there are indications that these modes are exciton-like states appearing in the presence of a hierarchy of pairing tendencies. The strong in-gap modes observed in Co-doped NaFeAs are interpreted in terms of quadrupolar orbital excitations which become undamped in the superconducting state. The doping dependence of the scattering intensity in Ba(Fe1-xCox)2As2is associated with a nematic resonance above a quantum critical point and interpreted in terms of a critical enhancement at the maximalTc. In the normal state the response from particle-hole excitations reflects the resistivity. In addition, there are strongly temperature-dependent contributions from presumably critical fluctuations in the energy range ofkBTwhich can be compared to the elastic properties. Currently it is not settled whether the fluctuations observed by light scattering are related to spin or charge. Another controversy relates to putative two-magnon excitations, typically in the energy range below 0.5 eV. Whereas this response presumably originates from charge excitations in most of the Fe-based compounds theory and experiment suggest that the excitations in the 60 meV range in FeSe stem from localized spins in a nearly frustrated system.

Coupling of Higgs and Leggett modes in non-equilibrium superconductors

In equilibrium systems amplitude and phase collective modes are decoupled, as they are mutually orthogonal excitations. The direct detection of these Higgs and Leggett collective modes by linear-response measurements is not possible, because they do not couple directly to the electromagnetic field. In this work, using numerical exact simulations we show for the case of two-gap superconductors, that optical pump–probe experiments excite both Higgs and Leggett modes out of equilibrium. We find that this non-adiabatic excitation process introduces a strong interaction between the collective modes, which is absent in equilibrium. Moreover, we propose a type of pump–probe experiment, which allows to probe and coherently control the Higgs and Leggett modes, and thus the order parameter directly. These findings go beyond two-band superconductors and apply to general collective modes in quantum materials.

Collective modes of amplitude and phase are decoupled in equilibrium systems, limiting the understanding of competing orders in correlated material. Here, Krull et al. report that a non-adiabatic pump pulse can induce an intricate coupling between Leggett and Higgs modes, providing a way to couple collective modes in non-equilibrium condition.

Leggett Modes and the Anderson-Higgs Mechanism in Superconductors without Inversion Symmetry

We develop a microscopic and gauge-invariant theory for collective modes resulting from the phase of the superconducting order parameter in noncentrosymmetric superconductors. Considering various crystal symmetries, we derive the corresponding gauge mode ω_{G}(q) and find, in particular, new Leggett modes ω_{L}(q) with characteristic properties that are unique to noncentrosymmetric superconductors. We calculate their mass and dispersion that reflect the underlying spin-orbit coupling and thus the balance between triplet and singlet superconductivity occurring simultaneously. Finally, we demonstrate the role of the Anderson-Higgs mechanism: while the long-range Coulomb interaction shifts ω_{G}(q) to the condensate plasma mode ω_{P}(q), it leaves the mass Λ_{0} of the new Leggett mode unaffected and only slightly modifies its dispersion.

Ground state, collective mode, phase soliton and vortex in multiband superconductors

This article reviews theoretical and experimental work on the novel physics in multiband superconductors. Multiband superconductors are characterized by multiple superconducting energy gaps in different bands with interaction between Cooper pairs in these bands. The discovery of prominent multiband superconductors MgB2 and later iron-based superconductors, has triggered enormous interest in multiband superconductors. The most recently discovered superconductors exhibit multiband features. The multiband superconductors possess novel properties that are not shared with their single-band counterpart. Examples include: the time-reversal symmetry broken state in multiband superconductors with frustrated interband couplings; the collective oscillation of number of Cooper pairs between different bands, known as the Leggett mode; and the phase soliton and fractional vortex, which are the main focus of this review. This review presents a survey of a wide range of theoretical exploratory and experimental investigations of novel physics in multiband superconductors. A vast amount of information derived from these studies is shown to highlight unusual and unique properties of multiband superconductors and to reveal the challenges and opportunities in the research on the multiband superconductivity.

Tetrahedral and orbital pairing: a fully gapped pairing scenario for the iron-based superconductors

Motivated by the fully gapped superconductivity in iron-based superconductors with uncompensated electron pockets, we propose a spin singlet, but orbital triplet analogue of the superfluid phase of ^{3}He-B. We show that orbital triplets with a nominal d-wave symmetry at the iron sites can transform as s-wave pairs under rotations about the selenium sites. Linear combinations of such d(xy) and d(x2-y(2)) triplets form a fully gapped, topological superconductor. Raman-active excitations are predicted to develop below the superconducting transition temperature.

Time-reversal-symmetry-broken state in the BCS formalism for a multi-band superconductor

In three-band BCS superconductors with repulsive inter-band interactions, frustration between the bands can lead to an inherently complex gap function, arising out of a phase difference between the bands in the range 0 and π. Since the complex conjugate of this state is also a solution, the ground state is degenerate, and there appears a time-reversal-symmetry-broken state. In this paper we investigate the existence of this state as a function of inter-band coupling strength and show how a new phase transition appears between the TRSB and conventional BCS states.

Dissociation transition of a composite lattice of magnetic vortices in the flux-flow regime of two-band superconductors

In multiband superconductors, each superconducting condensate supports vortices with fractional quantum flux. In the ground state, vortices in different bands are spatially bounded together to form a composite vortex, carrying one quantum flux Φ(0). Here we predict dissociation of the composite vortices lattice in the flux flow state due to the disparity of the vortex viscosity and flux of the vortex in different bands. For a small driving current, composite vortices start to deform, but the constituting vortices in different bands move with the same velocity. For a large current, composite vortices dissociate and vortices in different bands move with different velocities. The dissociation transition shows up as an increase of flux flow resistivity. In the dissociated phase, Shapiro steps are developed when an ac current is superimposed with a dc current.

Massless Leggett mode in three-band superconductors with time-reversal-symmetry breaking

The Leggett mode associated with out-of-phase oscillations of the superconducting phase in multiband superconductors usually is heavy due to interband coupling, which makes its excitation and detection difficult. We report on the existence of a massless Leggett mode in three-band superconductors with time-reversal-symmetry breaking. The mass of this Leggett mode is small close to the time-reversal-symmetry-breaking transition and vanishes at the transition point, and thus locates within the smallest superconducting energy gap, which makes it stable and detectable, e.g., by means of the Raman spectroscopy. The thermodynamic consequences of this massless mode and possible realization in iron-based superconductors are also discussed.

Theory of multiband superconductivity in spin-density-wave metals

We study the emergence of multiband superconductivity with s- and d-wave symmetry on the background of a spin density wave (SDW). We show that the SDW coherence factors renormalize the momentum dependence of the superconducting (SC) gap, yielding a SC state with an unconventional s-wave symmetry. Interband Cooper pair scattering stabilizes superconductivity in both symmetries. With increasing SDW order, the s-wave state is more strongly suppressed than the d-wave state. Our results are universally applicable to two-dimensional systems with a commensurate SDW.

Electronic Raman scattering of two-band superconductors: a time-dependent Landau-Ginzburg theory approach

Electronic Raman scattering of two-band superconductors is studied based on the time-dependent Landau-Ginzburg theory. The focus is on the possible features of the π phase shift between the two superconducting order parameters which may be realized in the Fe-pnictides. The Raman response was computed up to the Gaussian fluctuations in the functional integral formalism including the long range Coulomb interaction with the four channels of symmetric and antisymmetric combinations of the phases and amplitudes of the two order parameters. The Raman spectra is found to be composed of the quasiparticle and the phase collective mode contributions without mixing between them. The contributions from the quasiparticle and the symmetric phase collective mode (the Anderson-Bogolyubov mode) are similar to the two-band superconductors without the π phase shift. The antisymmetric phase mode (the Leggett mode) originates from the fluctuations of the relative phase of the two order parameters. It lies between twice the smaller gap and twice the larger gap and is damped by the quasiparticles. However, this mode is eliminated by the long range Coulomb interaction in the zero-wavenumber limit.

Theory of heterotic superconductor-insulator-superconductor Josephson junctions between single- and multiple-gap superconductors

Using the functional integral method, we construct a theory of heterotic superconductor-insulator-superconductor Josephson junctions between one- and two-gap superconductors. The theory predicts the presence of in-phase and out-of-phase collective oscillation modes of superconducting phases. The former corresponds to the Josephson plasma mode whose frequency is drastically reduced for +/- s-wave symmetry, and the latter is a counterpart of Leggett's mode in Josephson junctions. We also reveal that the critical current and the Fraunhofer pattern strongly depend on the symmetry type of the two-gap superconductor.

Type-1.5 superconductivity

We demonstrate the existence of a novel superconducting state in high quality two-component MgB2 single crystalline superconductors where a unique combination of both type-1 (lambda{1}/xi{1}<1/sqrt[2]) and type-2 (lambda{2}/xi{2}>1/sqrt[2]) superconductor conditions is realized for the two components of the order parameter. This condition leads to a vortex-vortex interaction attractive at long distances and repulsive at short distances, which stabilizes unconventional stripe- and gossamerlike vortex patterns that we have visualized in this type-1.5 superconductor using Bitter decoration and also reproduced in numerical simulations.

Even parity, orbital singlet, and spin triplet pairing for superconducting LaFeAsO1-xFx

We examine the spin-triplet superconducting state of even parity mediated by ferromagnetic Hund's coupling between electrons in two almost degenerate orbital bands. This state may be realized in the recently discovered LaFeAsO(1-x)F(x). It is robust against orbital-independent disorder. The splitting of the orbital degeneracy suppresses superconductivity and leads to an anisotropic spectrum in the Bogoliubov quasiparticle. The former predicts a strong pressure dependence of T(c) and the latter predicts Fermi pockets, which may be tested in angle resolved photoemission spectra.