A distinct bosonic mode in an electron-doped high-transition-temperature superconductor

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.

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.

Evidence for unconventional superconductivity in twisted trilayer graphene

Magic-angle twisted trilayer graphene (MATTG) has emerged as a moiré material that exhibits strong electronic correlations and unconventional superconductivity^1,2. However, local spectroscopic studies of this system are still lacking. Here we perform high-resolution scanning tunnelling microscopy and spectroscopy of MATTG that reveal extensive regions of atomic reconstruction favouring mirror-symmetric stacking. In these regions, we observe symmetry-breaking electronic transitions and doping-dependent band-structure deformations similar to those in magic-angle bilayers, as expected theoretically given the commonality of flat bands^3,4. Most notably in a density window spanning two to three holes per moiré unit cell, the spectroscopic signatures of superconductivity are manifest as pronounced dips in the tunnelling conductance at the Fermi level accompanied by coherence peaks that become gradually suppressed at elevated temperatures and magnetic fields. The observed evolution of the conductance with doping is consistent with a gate-tunable transition from a gapped superconductor to a nodal superconductor, which is theoretically compatible with a sharp transition from a Bardeen-Cooper-Schrieffer superconductor to a Bose-Einstein-condensation superconductor with a nodal order parameter. Within this doping window, we also detect peak-dip-hump structures that suggest that superconductivity is driven by strong coupling to bosonic modes of MATTG. Our results will enable further understanding of superconductivity and correlated states in graphene-based moiré structures beyond twisted bilayers⁵.

Direct observation of nodeless superconductivity and phonon modes in electron-doped copper oxide Sr1-xNdxCuO2

The microscopic understanding of high-temperature superconductivity in cuprates has been hindered by the apparent complexity of crystal structures in these materials. We used scanning tunneling microscopy and spectroscopy to study the electron-doped copper oxide compound Sr_1−xNd_xCuO₂, which has only bare cations separating the CuO₂ planes and thus the simplest infinite-layer structure of all cuprate superconductors. Tunneling conductance spectra of the major CuO₂ planes in the superconducting state revealed direct evidence for a nodeless pairing gap, regardless of variation of its magnitude with the local doping of trivalent neodymium. Furthermore, three distinct bosonic modes are observed as multiple peak-dip-hump features outside the superconducting gaps and their respective energies depend little on the spatially varying gaps. As well as the bosonic modes, with energies identical to those of the external, bending and stretching phonons of copper oxides, our findings reveal the origin of the bosonic modes in lattice vibrations rather than spin excitations.

Signatures of two-dimensional superconductivity emerging within a three-dimensional host superconductor

Spatial disorder has been shown to drive two-dimensional (2D) superconductors to an insulating phase through a superconductor-insulator transition (SIT). Numerical calculations predict that with increasing disorder, emergent electronic granularity is expected in these materials-a phenomenon where superconducting (SC) domains on the scale of the material's coherence length are embedded in an insulating matrix and coherently coupled by Josephson tunneling. Here, we present spatially resolved scanning tunneling spectroscopy (STS) measurements of the three-dimensional (3D) superconductor BaPb_1-x Bi _x O₃ (BPBO), which surprisingly demonstrate three key signatures of emergent electronic granularity, having only been previously conjectured and observed in 2D thin-film systems. These signatures include the observation of emergent SC domains on the scale of the coherence length, finite energy gap over all space, and strong enhancement of spatial anticorrelation between pairing amplitude and gap magnitude as the SIT is approached. These observations are suggestive of 2D SC behavior embedded within a conventional 3D s-wave host, an intriguing but still unexplained interdimensional phenomenon, which has been hinted at by previous experiments in which critical scaling exponents in the vicinity of a putative 3D quantum phase transition are consistent only with dimensionality d = 2.

Superconductivity enhancement in FeSe/SrTiO3: a review from the perspective of electron-phonon coupling

Single-layer FeSe films grown on SrTiO3, with the highest superconducting transition temperature (TC) among all the iron-based superconductors, serves as an ideal platform for studying the microscopic mechanisms of high-TCsuperconductivity. The significant role of interfacial coupling has been widely recognized, while the precise nature of theTCenhancement remains open. In this review, we focus on the investigations of the interfacial coupling in FeSe/SrTiO3from the perspective of electron-phonon coupling (EPC). The main content will include an overview of the experimental measurements associated with different theoretical models and arguments about the EPC. Especially, besides the discussions of EPC based on the measurements of electronic states, we will emphasize the analyses based on phonon measurements. A uniform picture about the nature of the EPC and its relation to theTCenhancement in FeSe/SrTiO3has still not achieved, which should be the key for further studies aiming to the in-depth understanding of high-TCsuperconductivity and the discovery of new superconductors with even enhancedTC.

Bosonic Mode and Impurity-Scattering in Monolayer Fe(Te,Se) High-Temperature Superconductors

The electron pairing mechanism has always been one of the most challenging problems in high-temperature superconductors. Fe(Te,Se), as the superconductor with intrinsic topological property, may host Majorana bound states and has attracted tremendous interest. While in bulk Fe(Te,Se) the pairing mechanism has been experimentally investigated, it remains little understood in its two-dimensional limit counterpart. Here, by in situ scanning tunneling spectroscopy, we show clear evidence of the bosonic mode Ω beyond the superconducting gap Δ in monolayer FeTe_0.5Se_0.5/SrTiO₃(001) high-temperature superconductor. Statistically, Ω shows an obvious anticorrelation with Δ and appears below 2Δ, consistent with the spin-excitation nature. Furthermore, the in-gap bound states induced by two types of magnetically different impurities support the sign-reversing pairing scenario. Our results not only suggest that the spin-excitation-like bosonic mode within a sign-reversing pairing plays an essential role in monolayer FeTe_0.5Se_0.5/SrTiO₃(001) but also offer the crucial information for investigating the high-temperature superconductivity in interfacial iron selenides.

Why the anti-nodal quasiparticle dispersion is so flat in the superconducting cuprates?

The emergence of the coherent quasiparticle peak and the development of the peak-dip-hump structure in the anti-nodal region below T _c is the most prominent non-BCS signature of the under-doped high-T _c cuprates, in which no coherent quasiparticle can be defined in the anti-nodal region above T _c. The peak-dip-hump structure has been commonly interpreted as the result of the coupling of the electron to some Bosonic mode. However, such an electron-Boson coupling picture does not answer the question of why the quasiparticle dispersion is so flat in the anti-nodal region, a behavior totally unexpected for Bogoliubov quasiparticle in a d-wave BCS superconductor. Here we show that the sharp quasiparticle peak in the anti-nodal region should be understood as a new pole in the electron Green's function generated by the strong coupling of the electron to diffusive spin fluctuation around the antiferromagnetic wave vector Q = (π, π), rather than a nearly free Bogoliubov quasiparticle in a d-wave BCS superconductor. More specifically, we find that the normal self-energy of the electron from the scattering with the diffusive spin fluctuation manifests itself mainly as a level repulsion effect and is responsible for the reduction of both the quasiparticle dispersion and the quasiparticle dissipation rate in the anti-nodal region. We argue that the peak-dip separation in the anti-nodal spectrum should not be interpreted as the energy of the pairing glue.

Detection of Bosonic Mode as a Signature of Magnetic Excitation in One-Unit-Cell FeSe on SrTiO3

A "fingerprint" of Cooper pairing mediated by collective bosonic excitation mode is the reconstruction of the quasiparticle-density-of-states (DOS) spectrum with an additional "dip-hump" structure located outside the superconducting coherence peak. Here, we report an in situ scanning tunneling spectroscopy study of one-unit-cell (1-UC) FeSe film on a SrTiO₃(001) substrate. In the quasiparticle-DOS spectrum, the bosonic excitation mode characterized by the dip-hump structure is detected outside the larger superconducting gap. Statistically, the excitation mode shows an anticorrelation with pairing strength in magnitude and yields an energy scale upper-bounded by twice the superconducting gap. The observation coincides with the characteristics of magnetic resonance in cuprates and iron-based superconductors. Furthermore, the local response of superconducting spectra to magnetically distinct Se defects all exhibits the induced in-gap quasiparticle bound states, indicating an unconventional sign-reversing pairing over the Fermi surface in 1-UC FeSe. These results clarify the magnetic nature of the bosonic excitation mode and reveal a signature of electron-magnetic-excitation coupling in 1-UC FeSe/SrTiO₃(001) besides the previously established pairing channel of electron-phonon interaction.

Imaging the real space structure of the spin fluctuations in an iron-based superconductor

Spin fluctuations are a leading candidate for the pairing mechanism in high temperature superconductors, supported by the common appearance of a distinct resonance in the spin susceptibility across the cuprates, iron-based superconductors and many heavy fermion materials. The information we have about the spin resonance comes almost exclusively from neutron scattering. Here we demonstrate that by using low-temperature scanning tunnelling microscopy and spectroscopy we can characterize the spin resonance in real space. We show that inelastic tunnelling leads to the characteristic dip-hump feature seen in tunnelling spectra in high temperature superconductors and that this feature arises from excitations of the spin fluctuations. Spatial mapping of this feature near defects allows us to probe non-local properties of the spin susceptibility and to image its real space structure.

The knowledge of how spin fluctuations affect high-Tc superconductivity comes exclusively from neutron scattering. Here, Chi et al. establish characteristic excitation features of the spin fluctuations in real space from the scanning tunnelling spectra in an iron-based superconductor.

Tracing the Electronic Pairing Glue in Unconventional Superconductors via Inelastic Scanning Tunneling Spectroscopy

Scanning tunneling microscopy has been shown to be a powerful experimental probe to detect electronic excitations and further allows us to deduce fingerprints of bosonic collective modes in superconductors. Here, we demonstrate that the inclusion of inelastic tunnel events is crucial for the interpretation of tunneling spectra of unconventional superconductors and allows us to directly probe electronic and bosonic excitations via scanning tunneling microscopy. We apply the formalism to the iron based superconductor LiFeAs. With the inclusion of inelastic contributions, we find strong evidence for a nonconventional pairing mechanism, likely via magnetic excitations.

Nanoscale determination of the mass enhancement factor in the lightly doped bulk insulator lead selenide

Bismuth chalcogenides and lead telluride/selenide alloys exhibit exceptional thermoelectric properties that could be harnessed for power generation and device applications. Since phonons play a significant role in achieving these desired properties, quantifying the interaction between phonons and electrons, which is encoded in the Eliashberg function of a material, is of immense importance. However, its precise extraction has in part been limited due to the lack of local experimental probes. Here we construct a method to directly extract the Eliashberg function using Landau level spectroscopy, and demonstrate its applicability to lightly doped thermoelectric bulk insulator PbSe. In addition to its high energy resolution only limited by thermal broadening, this novel experimental method could be used to detect variations in mass enhancement factor at the nanoscale level. This opens up a new pathway for investigating the local effects of doping and strain on the mass enhancement factor.

Electron–phonon coupling influences the thermal and electronic properties of many solid materials. Zeljkovic et al. now combine Landau level spectroscopy and scanning tunnelling microscopy to extract quantitative information on electron–phonon coupling in the insulator lead selenide.

Imaging the electron-boson coupling in superconducting FeSe films using a scanning tunneling microscope

Scanning tunneling spectroscopy has been used to reveal signatures of a bosonic mode in the local quasiparticle density of states of superconducting FeSe films. The mode appears below Tc as a "dip-hump" feature at energy Ω∼4.7kBTc beyond the superconducting gap Δ. Spectra on strained regions of the FeSe films reveal simultaneous decreases in Δ and Ω. This contrasts with all previous reports on other high-Tc superconductors, where Δ locally anticorrelates with Ω. A local strong coupling model is found to reconcile the discrepancy well, and to provide a unified picture of the electron-boson coupling in unconventional superconductors.

Signatures of the electronic nature of pairing in high-T(c) superconductors obtained by non-equilibrium boson spectroscopy

Understanding the pairing mechanism that gives rise to high-temperature superconductivity is one of the longest-standing problems of condensed-matter physics. Almost three decades after its discovery, even the question of whether or not phonons are involved remains a point of contention to some. Here we describe a technique for determining the spectra of bosons generated during the formation of Cooper pairs on recombination of hot electrons as they tunnel between the layers of a cuprate superconductor. The results obtained indicate that the bosons that mediate pairing decay over micrometre-scale distances and picosecond timescales, implying that they propagate at a speed of around 10⁶ m s⁻¹. This value is more than two orders of magnitude greater than the phonon propagation speed but close to Fermi velocity for electrons, suggesting that the pairing mechanism is mediated by unconventional repulsive electron–electron, rather than attractive electron–phonon, interactions.

The mechanism of high-temperature superconductivity remains a subject of debate. Krasnov et al. describe a technique for measuring the spectra of bosons generated during the formation of Cooper pairs in a cuprate, the results of which suggest that the process is governed by electron–electron interactions.

Evidence of a spin resonance mode in the iron-based superconductor Ba(0.6)K(0.4)Fe2As2 from scanning tunneling spectroscopy

We used high-resolution scanning tunneling spectroscopy to study the hole-doped iron pnictide superconductor Ba(0.6)K(0.4)Fe(2)As(2) (T(c)=38 K). Features of a bosonic excitation (mode) are observed in the measured quasiparticle density of states. The bosonic features are intimately associated with the superconducting order parameter and have a mode energy of ~14 meV, similar to the spin resonance measured by inelastic neutron scattering. These results indicate a strong electron-spin excitation coupling in iron pnictide superconductors, similar to that in high-T(c) copper oxide superconductors.

A tunneling spectroscopy study of the pairing symmetry in the electron-doped Pr(1-x)LaCe(x)CuO(4-y)

We have performed scanning tunneling spectroscopy and point contact spectroscopy measurements on the electron-doped superconductor Pr(1-x)LaCe(x)CuO(4-y) (x = 0.12, T(c) is approximately equal 25 K). We address the question of the symmetry of the order parameter and of the amplitude of the energy gap. We compare three possible scenarios, i.e. isotropic s-wave, 'anisotropic' s-wave, and d-wave. Evidence for a d-wave symmetry of the order parameter is given. From the temperature evolution of the dI/dV versus V characteristics we extract a BCS-like temperature dependence of the superconducting energy gap Δ. Despite the variety of measured spectra we give a consistent explanation for the whole set of data, indicating Δ = (3.6 ± 0.2) meV and a ratio 2Δ/K(B)T(C) is approximately equal 3.5 ±0.2. In particular, point contact characteristics showing gap-like features at higher voltages have been interpreted by considering the formation of an intergrain Josephson junction in series with the point contact junction. Further confirmation of the correctness of the model is given by the behavior of the critical current of the intergrain Josephson junction versus temperature which follows the Ambegaokar-Baratoff behavior.

Fine structure in the tunneling spectra of electron-doped cuprates: no coupling to the magnetic resonance mode

We reanalyze high-resolution scanning tunneling spectra of the electron-doped cuprate Pr(0.88)LaCe(0.12)CuO(4) (T(c) = 24 K). We find that the spectral fine structure below 35 meV is consistent with strong coupling to a bosonic mode at about 16 meV, in quantitative agreement with early tunneling spectra of Nd(1.85)Ce(0.15)CuO(4). Since the energy of the bosonic mode is significantly higher than that (9.5-11 meV) of the magnetic resonancelike mode observed by inelastic neutron scattering, the coupling feature at about 16 meV cannot arise from strong coupling to the magnetic mode. The present work thus demonstrates that the magnetic resonancelike mode cannot be the origin of high-temperature superconductivity in electron-doped cuprates.

Coexistence of competing orders with two energy gaps in real and momentum space in the high temperature superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}

Through a combined scanning tunneling microscopy and angle-resolved photoemission spectroscopy study, we report the observation of two distinct gaps (a small and a large gap) that coexist both in real space and in the antinodal region of momentum space, below the superconducting transition temperature (T_{c}) of Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}. We show that the small gap is associated with superconductivity. The large-gap persists above T_{c}, and seems linked to observed charge ordering. We find a strong correlation between the large and small gaps suggesting that they are affected by similar physical processes.

Angle-resolved photoemission spectroscopy of electron-doped cuprate superconductors: isotropic electron-phonon coupling

We have performed high resolution angle-resolved photoemission (ARPES) studies on electron-doped cuprate superconductors Sm2-xCexCuO4 (x=0.10, 0.15, 0.18), Nd2-xCexCuO4 (x=0.15), and Eu2-xCexCuO4 (x=0.15). Imaginary parts of the electron removal self energy show steplike features due to an electron-bosonic mode coupling. The steplike feature is seen along both nodal and antinodal directions but at energies of 50 and 70 meV, respectively, independent of the doping and rare earth element. Such energy scales can be understood as being due to preferential coupling to half- and full-breathing mode phonons, revealing the phononic origin of the kink structures. Estimated electron-phonon coupling constant lambda from the self energy is roughly independent of the doping and momentum. The isotropic nature of lambda is discussed in comparison with the hole-doped case where a strong anisotropy exists.

Low-energy spin fluctuations in the ground states of electron-doped Pr1-x LaCexCuO4+delta cuprate superconductors

Low-energy spin fluctuations have been investigated in the electron-doped Pr{1-x}LaCe{x}CuO{4+delta} over a wide concentration range of 0.07<or=x<or=0.18, spanning from the antiferromagnetic phase to the heavily overdoped superconducting (SC) phase. The low-energy excitations exhibit commensurate peaks centered at the (pi, pi) position for all x. Our data show that the characteristics of the excitations, such as the relaxation rate and the spin stiffness, decrease with increasing x in the SC phase and disappear with the disappearance of superconductivity.