Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors

Charge-transfer dipole low-frequency vibronic excitation at single-molecular scale

Scanning tunneling microscopy (STM) vibronic spectroscopy, which has provided submolecular insights into electron-vibration (vibronic) coupling, faces challenges when probing the pivotal low-frequency vibronic excitations. Because of eigenstate broadening on solid substrates, resolving low-frequency vibronic states demands strong decoupling. This work designs a type II band alignment in STM junction to achieve effective charge-transfer state decoupling. This strategy enables the successful identification of the lowest-frequency Hg(ω1) (Raman-active Hg mode) vibronic excitation within single C60 molecules, which, despite being notably pronounced in electron transport of C60 single-molecule transistors, has remained hidden at submolecular level. Our results show that the observed Hg(ω1) excitation is "anchored" to all molecules, irrespective of local geometry, challenging common understanding of structural definition of vibronic excitation governed by Franck-Condon principle. Density functional theory calculations reveal existence of molecule-substrate interfacial charge-transfer dipole, which, although overlooked previously, drives the dominant Hg(ω1) excitation. This charge-transfer dipole is not specific but must be general at interfaces, influencing vibronic coupling in charge transport.

Evolution from a charge-ordered insulator to a high-temperature superconductor in Bi2Sr2(Ca,Dy)Cu2O8+δ

How Cooper pairs form and condense has been the main challenge in the physics of copper-oxide high-temperature superconductors. Great efforts have been made in the 'underdoped' region of the phase diagram, through doping a Mott insulator or cooling a strange metal. However, there is still no consensus on how superconductivity emerges when electron-electron correlations dominate and the Fermi surface is missing. To address this issue, here we carry out high-resolution resonant inelastic X-ray scattering and scanning tunneling microscopy studies on prototype cuprates Bi2Sr2Ca0.6Dy0.4Cu2O8+δ near the onset of superconductivity, combining bulk and surface, momentum- and real-space information. We show that an incipient charge order exists in the antiferromagnetic regime down to 0.04 holes per CuO2 unit, entangled with a particle-hole asymmetric pseudogap. The charge order induces an intensity anomaly in the bond-buckling phonon branch, which exhibits an abrupt increase once the system enters the superconducting dome. Our results suggest that the Cooper pairs grow out of a charge-ordered insulating state, and then condense accompanied by an enhanced interplay between charge excitations and electron-phonon coupling.

Evidence of strong and mode-selective electron-phonon coupling in the topological superconductor candidate 2M-WS2

The interaction between lattice vibrations and electrons plays a key role in various aspects of condensed matter physics - including electron hydrodynamics, strange metal behavior, and high-temperature superconductivity. In this study, we present systematic investigations using Raman scattering and angle-resolved photoemission spectroscopy (ARPES) to examine the phononic and electronic subsystems of the topological superconductor candidate 2M-WS2. Raman scattering exhibits an anomalous nonmonotonic temperature dependence of phonon linewidths, indicative of strong phonon-electron scattering over phonon-phonon scattering. The ARPES results demonstrate pronounced dispersion anomalies (kinks) at multiple binding energies within both bulk and topological surface states, indicating a robust and mode-selective coupling between the electronic states and various phonon modes. These experimental findings align with previous calculations of the Eliashberg function, providing a deeper understanding of the highest superconducting transition temperature observed in 2M-WS2 (8.8 K) among all transition metal dichalcogenides as induced by electron-phonon coupling. Furthermore, our results may offer valuable insights into other properties of 2M-WS2 and guide the search for high-temperature topological superconductors.

Unconventional Spectral Gaps Induced by Charge Density Waves in the Weyl Semimetal (TaSe4)2I

Coupling Weyl quasiparticles and charge density waves (CDWs) can lead to fascinating band renormalization and many-body effects beyond band folding and Peierls gaps. For the quasi-one-dimensional chiral compound (TaSe4)2I with an incommensurate CDW transition at TC = 263 K, photoemission mappings thus far are intriguing due to suppressed emission near the Fermi level. Models for this unconventional behavior include axion insulator phases, correlation pseudogaps, polaron subbands, bipolaron bound states, etc. Our photoemission measurements show sharp quasiparticle bands crossing the Fermi level at T > TC, but for T < TC, these bands retain their dispersions with no Peierls or axion gaps at the Weyl points. Instead, occupied band edges recede from the Fermi level, opening a spectral gap. Our results confirm localization of quasiparticles (holes created by photoemission) is the key physics, which suppresses spectral weights over an energy window governed by incommensurate modulation and inherent phase defects of CDW.

Quantum acoustics unravels Planckian resistivity

Strange metals exhibit universal linear-in-temperature resistivity described by a Planckian scattering rate, the origin of which remains elusive. By employing an approach inspired by quantum optics, we arrive at the coherent state representation of lattice vibrations: quantum acoustics. Utilizing this nonperturbative framework, we demonstrate that lattice vibrations could serve as active drivers in the Planckian resistivity phenomenon, challenging prevailing theories. By treating charge carriers as quantum wave packets negotiating the dynamic acoustic field, we find that a competition ensues between localization and delocalization giving rise to the previously conjectured universal quantum bound of diffusion, [Formula: see text], independent of temperature or any other material parameters. This leads to the enigmatic T-linear resistivity over hundreds of degrees, except at very low temperatures. Quantum diffusion also explains why strange metals have much higher electrical resistivity than typical metals. Our work elucidates the critical role of phonons in Planckian resistivity from a unique perspective and reconsiders their significance in the transport properties of strange metals.

Magnetic excitations in strained infinite-layer nickelate PrNiO2 films

Strongly correlated materials respond sensitively to external perturbations such as strain, pressure, and doping. In the recently discovered superconducting infinite-layer nickelates, the superconducting transition temperature can be enhanced via only ~ 1% compressive strain-tuning with the root of such enhancement still being elusive. Using resonant inelastic x-ray scattering (RIXS), we investigate the magnetic excitations in infinite-layer PrNiO2 thin films grown on two different substrates, namely SrTiO3 (STO) and (LaAlO3)0.3(Sr2TaAlO6)0.7 (LSAT) enforcing different strain on the nickelates films. The magnon bandwidth of PrNiO2 shows only marginal response to strain-tuning, in sharp contrast to the enhancement of the superconducting transition temperature Tc in the doped superconducting samples. These results suggest the bandwidth of spin excitations of the parent compounds is similar under strain while Tc in the doped ones is not, and thus provide important empirics for the understanding of superconductivity in infinite-layer nickelates.

Spin-Dependent ππ^{*} Gap in Graphene on a Magnetic Substrate

We present a detailed analysis of the electronic properties of graphene/Eu/Ni(111). By using angle- and spin-resolved photoemission spectroscopy and ab initio calculations, we show that the intercalation of Eu in the graphene/Ni(111) interface gives rise to a gapped freestanding dispersion of the ππ^{*} Dirac cones at the K[over ¯] point with an additional lifting of the spin degeneracy due to the mixing of graphene and Eu states. The interaction with the magnetic substrate results in a large spin-dependent gap in the Dirac cones with a topological nature characterized by a large Berry curvature and a spin-polarized Van Hove singularity, whose closeness to the Fermi level gives rise to a polaronic band.

Floquet nonadiabatic mixed quantum-classical dynamics in periodically driven solid systems

In this paper, we introduce the Floquet mean-field dynamics and Floquet surface hopping approaches to study the nonadiabatic dynamics in periodically driven solid systems. We demonstrate that these two approaches can be formulated in both real and reciprocal spaces. Using the two approaches, we are able to simulate the interaction between electronic carriers and phonons under periodic drivings, such as strong light-matter interactions. Employing the Holstein and Peierls models, we show that strong light-matter interactions can effectively modulate the dynamics of electronic population and mobility. Notably, our study demonstrates the feasibility and effectiveness of modeling low-momentum carriers' interactions with phonons using a truncated reciprocal space basis, an approach impractical in real space frameworks. Moreover, we reveal that even with a significant truncation, carrier populations derived from surface hopping maintain greater accuracy compared to those obtained via mean-field dynamics. These results underscore the potential of our proposed methods in advancing the understanding of carrier-phonon interactions in various periodically driven materials.

Quantum-Acoustical Drude Peak Shift

Quantum acoustics-a recently developed framework parallel to quantum optics-establishes a nonperturbative and coherent treatment of the electron-phonon interaction in real space. The quantum-acoustical representation reveals a displaced Drude peak hiding in plain sight within the venerable Fröhlich model: the optical conductivity exhibits a finite frequency maximum in the far-infrared range and the dc conductivity is suppressed. Our results elucidate the origin of the high-temperature absorption peaks in strange or bad metals, revealing that dynamical lattice disorder steers the system towards a non-Drude behavior.

Low temperature Raman spectroscopic study of anharmonic and spin-phonon coupled quasi-two dimensional rare earth based francisites

Mineral francisites Cu3Bi(SeO3)2O2Cl are unique compounds with interesting quasi two-dimensional structure along with fascinating magnetic properties. The magnetic properties can be fine-tuned when non-magnetic Bi is replaced by a suitable rare earth (RE) metal. It is because of the inclusion of additional magnetic sub-centre RE apart from Cu. Temperature dependent Raman spectroscopy measurements in RE based francisites [Cu3RE(SeO3)2O2Cl, shortly RECufr] were performed in the range of 11 K-295 K. Among the three studied RECufr (LaCufr, NdCufr, and DyCufr) compounds, the properties of phonon vibration vary from moderate (in DyCufr) to weak (in LaCufr) spin phonon coupled and the absence of spin phonon coupling (SPC) (i.e. strictly anharmonic in nature) was observed in NdCufr and the reason for this observation has been provided. More specifically, two Raman-active phonons soften below the antiferromagnetic ordering temperature ofTN≈ 39 K in DyCufr compound, indicating the existence of moderate SPC. This trend of phonon vibration is correlated with magnetic properties, particularly field induced metamagnetic transition (MMT). Strong MMT enabled DyCufr develops SPC, while weak MMT enabled NdCufr is unable to develop SPC.

Comparing first-principles density functionals plus corrections for the lattice dynamics of YBa2Cu3O6

The enigmatic mechanism underlying unconventional high-temperature superconductivity, especially the role of lattice dynamics, has remained a subject of debate. Theoretical insights have long been hindered due to the lack of an accurate first-principles description of the lattice dynamics of cuprates. Recently, using the r2SCAN meta-generalized gradient approximation (meta-GGA) functional, we have been able to achieve accurate phonon spectra of an insulating cuprate YBa2Cu3O6 and discover significant magnetoelastic coupling in experimentally interesting Cu-O bond stretching optical modes [Ning et al., Phys. Rev. B 107, 045126 (2023)]. We extend this work by comparing Perdew-Burke-Ernzerhof and r2SCAN performances with corrections from the on-site Hubbard U and the D4 van der Waals (vdW) methods, aiming at further understanding on both the materials science side and the density functional side. We demonstrate the importance of vdW and self-interaction corrections for accurate first-principles YBa2Cu3O6 lattice dynamics. Since r2SCAN by itself partially accounts for these effects, the good performance of r2SCAN is now more fully explained. In addition, the performances of the Tao-Mo series of meta-GGAs, which are constructed in a different way from the strongly constrained and appropriately normed (SCAN) meta-GGA and its revised version r2SCAN, are also compared and discussed.

Superconductivity in Nb: Impact of Temperature, Dimensionality and Cooper-Pairing

The ability to realistically simulate the electronic structure of superconducting materials is important to understand and predict various properties emerging in both the superconducting topological and spintronics realms. We introduce a tight-binding implementation of the Bogoliubov-de Gennes method, parameterized from density functional theory, which we utilize to explore the bulk and thin films of Nb, known to host a significant superconducting gap. The latter is useful for various applications such as the exploration of trivial and topological in-gap states. Here, we focus on the simulation's aspects of superconductivity and study the impact of temperature, Cooper-pair coupling and dimensionality on the value of the superconducting pairing interactions and gaps.

Field control of quasiparticle decay in a quantum antiferromagnet

Dynamics in a quantum material is described by quantized collective motion: a quasiparticle. The single-quasiparticle description is useful for a basic understanding of the system, whereas a phenomenon beyond the simple description such as quasiparticle decay which affects the current carried by the quasiparticle is an intriguing topic. The instability of the quasiparticle is phenomenologically determined by the magnitude of the repulsive interaction between a single quasiparticle and the two-quasiparticle continuum. Although the phenomenon has been studied in several materials, thermodynamic tuning of the quasiparticle decay in a single material has not yet been investigated. Here we show, by using neutron scattering, magnetic field control of the magnon decay in a quantum antiferromagnet RbFeCl3, where the interaction between the magnon and continuum is tuned by the field. At low fields where the interaction is small, the single magnon decay process is observed. In contrast, at high fields where the interaction exceeds a critical magnitude, the magnon is pushed downwards in energy and its lifetime increases. Our study demonstrates that field control of quasiparticle decay is possible in the system where the two-quasiparticle continuum covers wide momentum-energy space, and the phenomenon of the magnon avoiding decay is ubiquitous.

Ubiquitous coexisting electron-mode couplings in high-temperature cuprate superconductors

In conventional superconductors, electron-phonon coupling plays a dominant role in generating superconductivity. In high-temperature cuprate superconductors, the existence of electron coupling with phonons and other boson modes and its role in producing high-temperature superconductivity remain unclear. The evidence of electron-boson coupling mainly comes from angle-resolved photoemission (ARPES) observations of [Formula: see text]70-meV nodal dispersion kink and [Formula: see text]40-meV antinodal kink. However, the reported results are sporadic and the nature of the involved bosons is still under debate. Here we report findings of ubiquitous two coexisting electron-mode couplings in cuprate superconductors. By taking ultrahigh-resolution laser-based ARPES measurements, we found that the electrons are coupled simultaneously with two sharp modes at [Formula: see text]70meV and [Formula: see text]40meV in different superconductors with different dopings, over the entire momentum space and at different temperatures above and below the superconducting transition temperature. These observations favor phonons as the origin of the modes coupled with electrons and the observed electron-mode couplings are unusual because the associated energy scales do not exhibit an obvious energy shift across the superconducting transition. We further find that the well-known "peak-dip-hump" structure, which has long been considered a hallmark of superconductivity, is also omnipresent and consists of "peak-double dip-double hump" finer structures that originate from electron coupling with two sharp modes. These results provide a unified picture for the [Formula: see text]70-meV and [Formula: see text]40-meV energy scales and their evolutions with momentum, doping and temperature. They provide key information to understand the origin of these energy scales and their role in generating anomalous normal state and high-temperature superconductivity.

Cuprate superconducting materials above liquid nitrogen temperature from machine learning

The superconductivity of cuprates remains a challenging topic in condensed matter physics, and the search for materials that superconduct electricity above liquid nitrogen temperature and even at room temperature is of great significance for future applications. Nowadays, with the advent of artificial intelligence, research approaches based on data science have achieved excellent results in material exploration. We investigated machine learning (ML) models by employing separately the element symbolic descriptor atomic feature set 1 (AFS-1) and a prior physics knowledge descriptor atomic feature set 2 (AFS-2). An analysis of the manifold in the hidden layer of the deep neural network (DNN) showed that cuprates still offer the greatest potential as superconducting candidates. By calculating the SHapley Additive exPlanations (SHAP) value, it is evident that the covalent bond length and hole doping concentration emerge as the crucial factors influencing the superconducting critical temperature (T_c). These findings align with our current understanding of the subject, emphasizing the significance of these specific physical quantities. In order to improve the robustness and practicability of our model, two types of descriptors were used to train the DNN. We also proposed the idea of cost-sensitive learning, predicted the sample in another dataset, and designed a virtual high-throughput search workflow.

Traces of electron-phonon coupling in one-dimensional cuprates

The appearance of certain spectral features in one-dimensional (1D) cuprate materials has been attributed to a strong, extended attractive coupling between electrons. Here, using time-dependent density matrix renormalization group methods on a Hubbard-extended Holstein model, we show that extended electron-phonon (e-ph) coupling presents an obvious choice to produce such an attractive interaction that reproduces the observed spectral features and doping dependence seen in angle-resolved photoemission experiments: diminished 3k_F spectral weight, prominent spectral intensity of a holon-folding branch, and the correct holon band width. While extended e-ph coupling does not qualitatively alter the ground state of the 1D system compared to the Hubbard model, it quantitatively enhances the long-range superconducting correlations and suppresses spin correlations. Such an extended e-ph interaction may be an important missing ingredient in describing the physics of the structurally similar two-dimensional high-temperature superconducting layered cuprates, which may tip the balance between intertwined orders in favor of uniform d-wave superconductivity.

Nodeless electron pairing in CsV3Sb5-derived kagome superconductors

The newly discovered kagome superconductors represent a promising platform for investigating the interplay between band topology, electronic order and lattice geometry1-9. Despite extensive research efforts on this system, the nature of the superconducting ground state remains elusive10-17. In particular, consensus on the electron pairing symmetry has not been achieved so far18-20, in part owing to the lack of a momentum-resolved measurement of the superconducting gap structure. Here we report the direct observation of a nodeless, nearly isotropic and orbital-independent superconducting gap in the momentum space of two exemplary CsV3Sb5-derived kagome superconductors-Cs(V0.93Nb0.07)3Sb5 and Cs(V0.86Ta0.14)3Sb5-using ultrahigh-resolution and low-temperature angle-resolved photoemission spectroscopy. Remarkably, such a gap structure is robust to the appearance or absence of charge order in the normal state, tuned by isovalent Nb/Ta substitutions of V. Our comprehensive characterizations of the superconducting gap provide indispensable information on the electron pairing symmetry of kagome superconductors, and advance our understanding of the superconductivity and intertwined electronic orders in quantum materials.

Testing electron-phonon coupling for the superconductivity in kagome metal CsV3Sb5

In crystalline materials, electron-phonon coupling (EPC) is a ubiquitous many-body interaction that drives conventional Bardeen-Cooper-Schrieffer superconductivity. Recently, in a new kagome metal CsV3Sb5, superconductivity that possibly intertwines with time-reversal and spatial symmetry-breaking orders is observed. Density functional theory calculations predicted weak EPC strength, λ, supporting an unconventional pairing mechanism in CsV3Sb5. However, experimental determination of λ is still missing, hindering a microscopic understanding of the intertwined ground state of CsV3Sb5. Here, using 7-eV laser-based angle-resolved photoemission spectroscopy and Eliashberg function analysis, we determine an intermediate λ=0.45-0.6 at T = 6 K for both Sb 5p and V 3d electronic bands, which can support a conventional superconducting transition temperature on the same magnitude of experimental value in CsV3Sb5. Remarkably, the EPC on the V 3d-band enhances to λ~0.75 as the superconducting transition temperature elevated to 4.4 K in Cs(V0.93Nb0.07)3Sb5. Our results provide an important clue to understand the pairing mechanism in the kagome superconductor CsV3Sb5.

Fano interference between collective modes in cuprate high-Tc superconductors

Cuprate high-T_c superconductors are known for their intertwined interactions and the coexistence of competing orders. Uncovering experimental signatures of these interactions is often the first step in understanding their complex relations. A typical spectroscopic signature of the interaction between a discrete mode and a continuum of excitations is the Fano resonance/interference, characterized by the asymmetric light-scattering amplitude of the discrete mode as a function of the electromagnetic driving frequency. In this study, we report a new type of Fano resonance manifested by the nonlinear terahertz response of cuprate high-T_c superconductors, where we resolve both the amplitude and phase signatures of the Fano resonance. Our extensive hole-doping and magnetic field dependent investigation suggests that the Fano resonance may arise from an interplay between the superconducting fluctuations and the charge density wave fluctuations, prompting future studies to look more closely into their dynamical interactions.

Possible enhancement of the superconductingTcdue to sharp Kohn-like soft phonon anomalies

Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constantλ. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperatureTc. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.

Electronic structure and correlations in planar trilayer nickelate Pr4Ni3O8

The discovery of superconductivity in planar nickelates raises the question of how the electronic structure and correlations of Ni¹⁺ compounds compare to those of the Cu²⁺ cuprate superconductors. Here, we present an angle-resolved photoemission spectroscopy (ARPES) study of the trilayer nickelate Pr₄Ni₃O₈, revealing a Fermi surface resembling that of the hole-doped cuprates but with critical differences. Specifically, the main portions of the Fermi surface are extremely similar to that of the bilayer cuprates, with an additional piece that can accommodate additional hole doping. We find that the electronic correlations are about twice as strong in the nickelates and are almost k-independent, indicating that they originate from a local effect, likely the Mott interaction, whereas cuprate interactions are somewhat less local. Nevertheless, the nickelates still demonstrate the strange-metal behavior in the electron scattering rates. Understanding the similarities and differences between these two families of strongly correlated superconductors is an important challenge.

Pressure Evolution of Ultrafast Photocarrier Dynamics and Electron-Phonon Coupling in FeTe0.5Se0.5

Understanding the coupling between electrons and phonons in iron chalcogenides FeTexSe1-x has remained a critical but arduous project in recent decades. The direct observation of the electron-phonon coupling effect through electron dynamics and vibrational properties has been lacking. Here, we report the first pressure-dependent ultrafast photocarrier dynamics and Raman scattering studies on an iron chalcogenide FeTe0.5Se0.5 to explore the interaction between electrons and phonons in this unconventional superconductor. The lifetime of the excited electrons evidently decreases as the pressure increases from 0 to 2.2 GPa, and then increases with further compression. The vibrational properties of the A1g phonon mode exhibit similar behavior, with a pronounced frequency reduction appearing at approximately 2.3 GPa. The dual evidence reveals the enhanced electron-phonon coupling strength with pressure in FeTe0.5Se0.5. Our results give an insight into the role of the electron-phonon coupling effect in iron-based superconductors.

Strong band renormalization and emergent ferromagnetism induced by electron-antiferromagnetic-magnon coupling

The interactions between electrons and antiferromagnetic magnons (AFMMs) are important for a large class of correlated materials. For example, they are the most plausible pairing glues in high-temperature superconductors, such as cuprates and iron-based superconductors. However, unlike electron-phonon interactions (EPIs), clear-cut observations regarding how electron-AFMM interactions (EAIs) affect the band structure are still lacking. Consequently, critical information on the EAIs, such as its strength and doping dependence, remains elusive. Here we directly observe that EAIs induce a kink structure in the band dispersion of Ba_1-xK_xMn₂As₂, and subsequently unveil several key characteristics of EAIs. We found that the coupling constant of EAIs can be as large as 5.4, and it shows strong doping dependence and temperature dependence, all in stark contrast to the behaviors of EPIs. The colossal renormalization of electron bands by EAIs enhances the density of states at Fermi energy, which is likely driving the emergent ferromagnetic state in Ba_1-xK_xMn₂As₂ through a Stoner-like mechanism with mixed itinerant-local character. Our results expand the current knowledge of EAIs, which may facilitate the further understanding of many correlated materials where EAIs play a critical role.

Structural measurement of electron-phonon coupling and electronic thermal transport across a metal-semiconductor interface

Scattering of energetic charge carriers and their coupling to lattice vibrations (phonons) in dielectric materials and semiconductors are crucial processes that determine the functional limits of optoelectronics, photovoltaics, and photocatalysts. The strength of these energy exchanges is often described by the electron-phonon coupling coefficient, which is difficult to measure due to the microscopic time- and length-scales involved. In the present study, we propose an alternate means to quantify the coupling parameter along with thermal boundary resistance and electron conductivity by performing a high angular-resolution time-resolved X-ray diffraction measurement of propagating lattice deformation following laser excitation of a nanoscale, polycrystalline metal film on a semiconductor substrate. Our data present direct experimental evidence for identifying the ballistic and diffusive transport components occurring at the interface, where only the latter participates in thermal diffusion. This approach provides a robust measurement that can be applied to investigate microscopic energy transport in various solid-state materials.

Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization

Ab initio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic Monte Carlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

Multipole polaron in the devil's staircase of CeSb

Rare-earth intermetallic compounds exhibit rich phenomena induced by the interplay between localized f orbitals and conduction electrons. However, since the energy scale of the crystal-electric-field splitting is only a few millielectronvolts, the nature of the mobile electrons accompanied by collective crystal-electric-field excitations has not been unveiled. Here, we examine the low-energy electronic structures of CeSb through the anomalous magnetostructural transitions below the Néel temperature, ~17 K, termed the 'devil's staircase', using laser angle-resolved photoemission, Raman and neutron scattering spectroscopies. We report another type of electron-boson coupling between mobile electrons and quadrupole crystal-electric-field excitations of the 4f orbitals, which renormalizes the Sb 5p band prominently, yielding a kink at a very low energy (~7 meV). This coupling strength is strong and exhibits anomalous step-like enhancement during the devil's staircase transition, unveiling a new type of quasiparticle, named the 'multipole polaron', comprising a mobile electron dressed with a cloud of the quadrupole crystal-electric-field polarization.

Electronic nature of charge density wave and electron-phonon coupling in kagome superconductor KV3Sb5

The Kagome superconductors AV3Sb5 (A = K, Rb, Cs) have received enormous attention due to their nontrivial topological electronic structure, anomalous physical properties and superconductivity. Unconventional charge density wave (CDW) has been detected in AV3Sb5. High-precision electronic structure determination is essential to understand its origin. Here we unveil electronic nature of the CDW phase in our high-resolution angle-resolved photoemission measurements on KV3Sb5. We have observed CDW-induced Fermi surface reconstruction and the associated band folding. The CDW-induced band splitting and the associated gap opening have been revealed at the boundary of the pristine and reconstructed Brillouin zones. The Fermi surface- and momentum-dependent CDW gap is measured and the strongly anisotropic CDW gap is observed for all the V-derived Fermi surface. In particular, we have observed signatures of the electron-phonon coupling in KV3Sb5. These results provide key insights in understanding the nature of the CDW state and its interplay with superconductivity in AV3Sb5 superconductors.

Optical Control of Multistage Phase Transition via Phonon Coupling in MoTe_{2}

The temporal characters of laser-driven phase transition from 2H to 1T^{'} has been investigated in the prototype MoTe_{2} monolayer. This process is found to be induced by fundamental electron-phonon interactions, with an unexpected phonon excitation and coupling pathway closely related to the nonequilibrium relaxation of photoexcited electrons. The order-to-order phase transformation is dissected into three substages, involving energy and momentum scattering processes from optical (A_{1}^{'} and E^{'}) to acoustic phonon modes [LA(M)] in subpicosecond timescale. An intermediate metallic state along the nonadiabatic transition pathway is also identified. These results have profound implications on nonequilibrium phase engineering strategies.

Antiferromagnetism Induced by Bond Su-Schrieffer-Heeger Electron-Phonon Coupling: A Quantum Monte Carlo Study

Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency ω and EPC constant λ can induce AFM ordering for a wide range of phonon frequency ω>ω_{c}. For ω<ω_{c}, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at ω_{c}. The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.

Phonon-Induced Pairing in Quantum Dot Quantum Simulator

Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.

Factors affecting the electron-phonon coupling in FeSe under pressure

Hydrostatic pressure on superconductor FeSe increases the Wyckoff position, z_Se, and decreases lattice constants. However, previously only the increasing of z_Se was emphasized to be important in determining the electron-phonon coupling. We explicitly study each of the two factors individually to understand its influence on the electron-phonon coupling, band structure and Raman frequencies. We find that the increasing of z_Se enhances the states around the Fermi level more, while the decreasing of the lattice constants enhances the phonon frequencies more, which together increase the electron-phonon coupling under pressure. Based on the above facts, we predict and prove that the in-plane biaxial strain on FeSe increases the electron-phonon coupling due to the increasing z_Se value and the decreasing in-plane lattice constant. Our results uncover the factors affecting the increase of the electron-phonon coupling and provide information on how to enhance the electron-phonon coupling in FeSe.

Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates

Establishing a minimal microscopic model for cuprates is a key step towards the elucidation of a high-T_{c} mechanism. By a quantitative comparison with a recent in situ angle-resolved photoemission spectroscopy measurement in doped 1D cuprate chains, our simulation identifies a crucial contribution from long-range electron-phonon coupling beyond standard Hubbard models. Using reasonable ranges of coupling strengths and phonon energies, we obtain a strong attractive interaction between neighboring electrons, whose strength is comparable to experimental observations. Nonlocal couplings play a significant role in the mediation of neighboring interactions. Considering the structural and chemical similarity between 1D and 2D cuprate materials, this minimal model with long-range electron-phonon coupling will provide important new insights on cuprate high-T_{c} superconductivity and related quantum phases.

Anomalously strong near-neighbor attraction in doped 1D cuprate chains

[Figure: see text].

Optical response of laser-driven charge-transfer complex described by Holstein-Hubbard model coupled to heat baths: Hierarchical equations of motion approach

We investigate the optical response of a charge-transfer complex in a condensed phase driven by an external laser field. Our model includes an instantaneous short-range Coulomb interaction and a local optical vibrational mode described by the Holstein-Hubbard (HH) model. Although characterization of the HH model for a bulk system has typically been conducted using a complex phase diagram, this approach is not sufficient for investigations of dynamical behavior at finite temperature, in particular for studies of nonlinear optical properties, where the time irreversibility of the dynamics that arises from the environment becomes significant. We therefore include heat baths with infinite heat capacity in the model to introduce thermal effects characterized by fluctuation and dissipation to the system dynamics. By reducing the number of degrees of freedom of the heat baths, we derive numerically "exact" hierarchical equations of motion for the reduced density matrix of the HH system. As demonstrations, we calculate the optical response of the system in two- and four-site cases under external electric fields. The results indicate that the effective strength of the system-bath coupling becomes large as the number of sites increases. Excitation of electrons promotes the conductivity when the Coulomb repulsion is equivalent to or dominates the electron-phonon coupling, whereas excitation of optical vibrations always suppresses the conductivity.

Electron-Phonon Coupling and Electron-Phonon Scattering in SrVO3

Understanding the physics of strongly correlated electronic systems has been a central issue in condensed matter physics for decades. In transition metal oxides, strong correlations characteristic of narrow d bands are at the origin of remarkable properties such as the opening of Mott gap, enhanced effective mass, and anomalous vibronic coupling, to mention a few. SrVO3 with V4+  in a 3d1  electronic configuration is the simplest example of a 3D correlated metallic electronic system. Here, the authors' focus on the observation of a (roughly) quadratic temperature dependence of the inverse electron mobility of this seemingly simple system, which is an intriguing property shared by other metallic oxides. The systematic analysis of electronic transport in SrVO3  thin films discloses the limitations of the simplest picture of e-e correlations in a Fermi liquid (FL); instead, it is shown show that the quasi-2D topology of the Fermi surface (FS) and a strong electron-phonon coupling, contributing to dress carriers with a phonon cloud, play a pivotal role on the reported electron spectroscopic, optical, thermodynamic, and transport data. The picture that emerges is not restricted to SrVO3  but can be shared with other 3d and 4d metallic oxides.

Machine-Learning-Guided Prediction Models of Critical Temperature of Cuprates

Cuprates have been at the center of long debate regarding their superconducting mechanism; therefore, predicting the critical temperatures of cuprates remains elusive. Herein, using machine learning and first-principles calculations, we predict the maximum superconducting transition temperature (T_c,max) of hole-doped cuprates and suggest the functional form for T_c,max with the root-mean-square-error of 3.705 K and R² of 0.969. We have found that the Bader charge of apical oxygen, the bond strength between apical atoms, and the number of superconducting layers are essential to estimate T_c,max. Furthermore, we predict the T_c,max of hypothetical cuprates generated by replacing apical cations with other elements. Among the hypothetical structures, the cuprates with Ga show the highest predicted T_c,max values, which are 71, 117, and 131 K for one, two, and three CuO₂ layers, respectively. These findings suggest that machine learning could guide the design of new high-T_c superconductors in the future.

Interfacial Electron-Phonon Coupling Constants Extracted from Intrinsic Replica Bands in Monolayer FeSe/SrTiO_{3}

The observation of replica bands by angle-resolved photoemission spectroscopy has ignited interest in the study of electron-phonon coupling at low carrier densities, particularly in monolayer FeSe/SrTiO_{3}, where the appearance of replica bands has motivated theoretical work suggesting that the interfacial coupling of electrons in the FeSe layer to optical phonons in the SrTiO_{3} substrate might contribute to the enhanced superconducting pairing temperature. Alternatively, it has also been recently proposed that such replica bands might instead originate from extrinsic final state losses associated with the photoemission process. Here, we perform a quantitative examination of replica bands in monolayer FeSe/SrTiO_{3}, where we are able to conclusively demonstrate that the replica bands are indeed signatures of intrinsic electron-boson coupling, and not associated with final state effects. A detailed analysis of the energy splittings and relative peak intensities between the higher-order replicas, as well as other self-energy effects, allows us to determine that the interfacial electron-phonon coupling in the system corresponds to a value of λ=0.19±0.02, providing valuable insights into the enhancement of superconductivity in monolayer FeSe/SrTiO_{3}. The methodology employed here can also serve as a new and general approach for making more rigorous and quantitative comparisons to theoretical calculations of electron-phonon interactions and coupling constants.

Plexcitons, electric field gradient and electron-phonon coupling in tip-enhanced Raman spectroscopy (TERS)

Tip-Enhanced Raman Spectroscopy (TERS) provides very high spatial resolution and detection sensitivity, so it has important applications in nano-scale molecular analysis. Plexciton is a polarization mode caused by a strongly coupled interaction between plasma excitons and excitons. It is a hot topic in plasma photonics research. We introduce the characteristics, production methods, observation methods and some applications of TERS. The electric field gradient (EFG) is an important factor affecting TERS resolution. The electron-phonon interaction is a fundamental inelastic interaction and plays an important role in current-carrying single-molecular junctions. This article summarizes the characteristics and applications of these three parts for readers to gain a preliminary understanding.

Fermi blockade of the strong electron-phonon interaction in modelled optimally doped high temperature superconductors

We study how manifestations of strong electron-phonon interaction depend on the carrier concentration by solving the two-dimensional Holstein model for the spin-polarized fermions using an approximation free bold-line diagrammatic Monte Carlo method. We show that the strong electron-phonon interaction, obviously present at very small Fermion concentration, is masked by the Fermi blockade effects and Migdal's theorem to the extent that it manifests itself as moderate one at large carriers densities. Suppression of strong electron-phonon interaction fingerprints is in agreement with experimental observations in doped high temperature superconductors.

Unmasking the Origin of Kinks in the Photoemission Spectra of Cuprate Superconductors

The origin of a ubiquitous bosonic coupling feature in the photoemission spectra of high-T_{c} cuprates, an energy-momentum dispersion "kink" observed at ∼70  meV binding energy, remains a two-decade-old mystery. Understanding this phenomenon requires an accurate description of the coupling between the electron and some collective modes. We report here ab initio calculations based on GW perturbation theory and show that correlation-enhanced electron-phonon interaction in cuprates gives rise to the strong kinks, which not only explains quantitatively the observations but provides new understanding of experiments. Our results reveal it is the electron density of states being the predominant factor in determining the doping dependence of the kink size, manifesting the multiband nature of the cuprates, as opposed to the prevalent belief of it being a measure of the mode-coupling strength.

Electron-plasmon interaction induced plasmonic-polaron band replication in epitaxial perovskite SrIrO3 films

Electron-boson interaction is fundamental to a thorough understanding of various exotic properties emerging in many-body physics. In photoemission spectroscopy, photoelectron emission due to photon absorption would trigger diverse collective excitations in solids, including the emergence of phonons, magnons, electron-hole pairs, and plasmons, which naturally provides a reliable pathway to study electron-boson couplings. While fingerprints of electron-phonon/-magnon interactions in this state-of-the-art technique have been well investigated, much less is known about electron-plasmon coupling, and direct observation of the band renormalization solely due to electron-plasmon interactions is extremely challenging. Here by utilizing integrated oxide molecular-beam epitaxy and angle-resolved photoemission spectroscopy, we discover the long sought-after pure electron-plasmon coupling-induced low-lying plasmonic-polaron replica bands in epitaxial semimetallic SrIrO₃ films, in which the characteristic low carrier concentration and narrow bandwidth combine to provide a unique platform where the electron-plasmon interaction can be investigated kinematically in photoemission spectroscopy. This finding enriches the forms of electron band normalization on collective modes in solids and demonstrates that, to obtain a complete understanding of the quasiparticle dynamics in 5d electron systems, the electron-plasmon interaction should be considered on equal footing with the acknowledged electron-electron interaction and spin-orbit coupling.

Unusual Temperature Evolution of Quasiparticle Band Dispersion in Electron-Doped FeSe Films

The discovery of high-temperature (high-Tc) superconductivity in one-monolayer FeSe on SrTiO3 has attracted tremendous attention. Subsequent studies suggested the importance of cooperation between intra-FeSe-layer and interfacial interactions to enhance Tc. However, the nature of intra-FeSe-layer interactions, which would play a primary role in determining the pairing symmetry, remains unclear. Here we have performed high-resolution angle-resolved photoemission spectroscopy of one-monolayer and alkaline-metal-deposited multilayer FeSe films on SrTiO3, and determined the evolution of quasiparticle band dispersion across Tc. We found that the band dispersion in the superconducting state deviates from the Bogoliubov-quasiparticle dispersion expected from the normal-state band dispersion with a constant gap size. This suggests highly anisotropic pairing originating from small momentum transfer and/or mass renormalization due to electron–boson coupling. This band anomaly is interpreted in terms of the electronic interactions within the FeSe layers that may be related to the high-Tc superconductivity in electron-doped FeSe.

Nonadiabatic coupling of the dynamical structure to the superconductivity in YSr2Cu2.75Mo0.25O7.54 and Sr2CuO3.3

The Cu extended X-ray absorption fine structure of YSr₂Cu_2.75Mo_0.25O_7.54 (with superconducting critical temperature, T_c, = 84 K) and Sr₂CuO_3.3 (T_c = 95 K) through their superconducting transitions demonstrates that the common factor in superconductivity in cuprates, including those prepared by high-pressure oxygenation, is an internal quantum tunneling polaron in its dynamical structure. In addition, Sr₂CuO_3.3 is the first material to show a concomitant transformation in this structure involving atom displacements >1 Å that would be expected to modify its Fermi surface, which would complicate the transition beyond a purely electronic one consisting of the pairing of electrons of opposite momentum across fixed electronic states.

A crucial issue in cuprates is the extent and mechanism of the coupling of the lattice to the electrons and the superconductivity. Here we report Cu K edge extended X-ray absorption fine structure measurements elucidating the internal quantum tunneling polaron (iqtp) component of the dynamical structure in two heavily overdoped superconducting cuprate compounds, tetragonal YSr₂Cu_2.75Mo_0.25O_7.54 with superconducting critical temperature, T_c = 84 K and hole density p = 0.3 to 0.5 per planar Cu, and the tetragonal phase of Sr₂CuO_3.3 with T_c = 95 K and p = 0.6. In YSr₂Cu_2.75Mo_0.25O_7.54 changes in the Cu-apical O two-site distribution reflect a sequential renormalization of the double-well potential of this site beginning at T_c, with the energy difference between the two minima increasing by ∼6 meV between T_c and 52 K. Sr₂CuO_3.3 undergoes a radically larger transformation at T_c, >1-Å displacements of the apical O atoms. The principal feature of the dynamical structure underlying these transformations is the strongly anharmonic oscillation of the apical O atoms in a double-well potential that results in the observation of two distinct O sites whose Cu–O distances indicate different bonding modes and valence-charge distributions. The coupling of the superconductivity to the iqtp that originates in this nonadiabatic coupling between the electrons and lattice demonstrates an important role for the dynamical structure whereby pairing occurs even in a system where displacements of the atoms that are part of the transition are sufficiently large to alter the Fermi surface. The synchronization and dynamic coherence of the iqtps resulting from the strong interactions within a crystal would be expected to influence this process.

Fermi surface and kink structures in [Formula: see text] revealed by synchrotron-based ARPES

The low-energy electronic structure, including the Fermi surface topology, of the itinerant metamagnet [Formula: see text] is investigated for the first time by synchrotron-based angle-resolved photoemission. Well-defined quasiparticle band dispersions with matrix element dependencies on photon energy or photon polarization are presented. Four bands crossing the Fermi-level, giving rise to four Fermi surface sheets are resolved; and their complete topography, effective mass as well as their electron and hole character are determined. These data reveal the presence of kink structures in the near-Fermi-level band dispersion, with energies ranging from 30 to 69 meV. Together with previously reported Raman spectroscopy and lattice dynamic calculation studies, the data suggest that these kinks originate from strong electron-phonon coupling present in [Formula: see text]. Considering that the kink structures of [Formula: see text] are similar to those of the other three members of the Ruddlesden Popper structured ruthenates, the possible universality of strong coupling of electrons to oxygen-related phonons in [Formula: see text] compounds is proposed.

Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering

Helium-atom scattering (HAS) spectroscopy from conducting surfaces has been shown to provide direct information on the electron–phonon interaction, more specifically the mass-enhancement factor λ from the temperature dependence of the Debye–Waller exponent, and the mode-selected electron–phonon coupling constants λQν from the inelastic HAS intensities from individual surface phonons. The recent applications of the method to superconducting ultra-thin films, quasi-1D high-index surfaces, and layered transition-metal and topological pnictogen chalcogenides are briefly reviewed.

Direct observation of large electron-phonon interaction effect on phonon heat transport

As a foundational concept in many-body physics, electron-phonon interaction is essential to understanding and manipulating charge and energy flow in various electronic, photonic, and energy conversion devices. While much progress has been made in uncovering how phonons affect electron dynamics, it remains a challenge to directly observe the impact of electrons on phonon transport, especially at environmental temperatures. Here, we probe the effect of charge carriers on phonon heat transport at room temperature, using a modified transient thermal grating technique. By optically exciting electron-hole pairs in a crystalline silicon membrane, we single out the effect of the phonon-carrier interaction. The enhanced phonon scattering by photoexcited free carriers results in a substantial reduction in thermal conductivity on a nanosecond timescale. Our study provides direct experimental evidence of the elusive role of electron-phonon interaction in phonon heat transport, which is important for understanding heat conduction in doped semiconductors. We also highlight the possibility of using light to dynamically control thermal transport via electron-phonon coupling.

Strong Electron-Phonon Interaction in 2D Vertical Homovalent III-V Singularities

Highly polar materials are usually preferred over weakly polar ones to study strong electron-phonon interactions and its fascinating properties. Here, we report on the achievement of simultaneous confinement of charge carriers and phonons at the vicinity of a 2D vertical homovalent singularity (antiphase boundary, APB) in an (In,Ga)P/SiGe/Si sample. The impact of the electron-phonon interaction on the photoluminescence processes is then clarified by combining transmission electron microscopy, X-ray diffraction, ab initio calculations, Raman spectroscopy, and photoluminescence experiments. 2D localization and layer group symmetry properties of homovalent electronic states and phonons are studied by first-principles methods, leading to the prediction of a type-II band alignment between the APB and the surrounding semiconductor matrix. A Huang-Rhys factor of 8 is finally experimentally determined for the APB emission line, underlining that a large and unusually strong electron-phonon coupling can be achieved by 2D vertical quantum confinement in an undoped III-V semiconductor. This work extends the concept of an electron-phonon interaction to 2D vertically buried III-V homovalent nano-objects and therefore provides different approaches for material designs, vertical carrier transport, heterostructure design on silicon, and device applications with weakly polar semiconductors.

Direct Measurement of Electron-Phonon Coupling with Time-Resolved ARPES

Time- and angular- resolved photoelectron spectroscopy is a powerful technique to measure electron dynamics in solids. Recent advances in this technique have facilitated band and energy resolved observations of the effect that excited phonons, have on the electronic structure. Here, we show with the help of ab initio simulations that the Fourier analysis of the time-resolved measurements of solids with excited phonon modes enables the determination of the band- and mode-resolved electron-phonon coupling directly from the experimental data without any additional input from theory. Such an observation is not restricted to regions of strong electron-phonon coupling and does not require strongly excited or hot phonons, but can be employed to monitor the dynamical renormalization of phonons in driven phases of matter.

Disparate Exciton-Phonon Couplings for Zone-Center and Boundary Phonons in Solid-State Graphite

The exciton-phonon coupling in highly oriented pyrolytic graphite is studied using resonant inelastic x-ray scattering (RIXS) spectroscopy. With ∼70  meV energy resolution, multiple low energy excitations associated with coupling to phonons can be clearly resolved in the RIXS spectra. Using resonance dependence and the closed form for RIXS cross section without considering the intermediate state mixing of phonon modes, the dimensionless coupling constant g is determined to be 5 and 0.35, corresponding to the coupling strength of 0.42  eV+/-20  meV and 0.20  eV+/-20  meV, for zone center and boundary phonons, respectively. The reduced g value for the zone-boundary phonon may be related to its double resonance nature.