The interactions among lattice, charge, and spin degrees of freedom fundamentally shape material properties. In FeSe, symmetry-breaking perturbations serve as highly sensitive probes of these couplings. Previous work has shown that defects and isoelectronic substitution can substantially alter these interactions, giving rise to additional phonon modes. In this study, uniaxial strain is employed as a tunable symmetry-breaking control parameter to probe the intrinsic lattice response in the absence of disorder. The temperature evolution of phonon excitations was examined with fine temperature resolution in the vicinity of the nemato-structural transition temperature T_s, under strain applied along the ⟨ 110 ⟩ and ⟨ 100 ⟩ crystallographic directions. A subtle asymmetry of the A_1g^ph mode appears in the unstrained crystal within a narrow temperature window around T_s, originating from the emergence of an additional mode in the fully symmetric channel. With applied strain, this feature becomes more distinctly resolved. The anomaly is attributed to modifications of the coupling between lattice and electronic degrees of freedom driven by the ordering fluctuations right above the nematic transition. These fluctuations enhance susceptibility for phonon-electron-phonon coupling in the vicinity of the X and R points of the Brillouin zone and promote two-phonon scattering close to the A_1g^ph mode. The presence of this two-phonon scattering depends on both the strength and the direction of the applied strain, indicating a high sensitivity of FeSe to local symmetry breaking.

Abstract The emergence of phonon frequency combs exemplifies a rare and intriguing phenomenon in quantum solids. Materials with distinctive phonon band structures are especially promising for hosting such states, as their vibrational dispersion landscape across the Brillouin zone can facilitate the formation of long-lived, collective lattice excitations. In the layered Van der Waals compound $$\textrm{InSi}\textrm{Te}_{3}$$ , polarization-resolved Raman spectroscopy reveals a pronounced anharmonicity in symmetry-predicted modes and the formation of a self-organized frequency domain structure (coherent-like state), in the range of a localized high-energy $$A_{1g}$$ phonon mode near 500 cm−1. This strong phonon-phonon coupling manifests itself as an anomalous temperature dependence around 200 K, coinciding with the appearance of higher-order excitations within the phonon density of states gap. These findings position $$\textrm{InSi}\textrm{Te}_{3}$$ as an unconventional platform where intrinsic highly structured phonon spectral correlations and unusually strong anharmonic effects coexist, opening new avenues for exploring emergent vibrational phenomena in low-dimensional materials.

The emergence of phonon frequency combs exemplifies a rare and intriguing phenomenon in quantum solids. Materials with distinctive phonon band structures are especially promising for hosting such states, as their vibrational dispersion landscape across the Brillouin zone can facilitate the formation of long-lived, collective lattice excitations. In the layered Van der Waals compound [Formula: see text], polarization-resolved Raman spectroscopy reveals a pronounced anharmonicity in symmetry-predicted modes and the formation of a self-organized frequency domain structure (coherent-like state), in the range of a localized high-energy [Formula: see text] phonon mode near 500 cm-1. This strong phonon-phonon coupling manifests itself as an anomalous temperature dependence around 200 K, coinciding with the appearance of higher-order excitations within the phonon density of states gap. These findings position [Formula: see text] as an unconventional platform where intrinsic highly structured phonon spectral correlations and unusually strong anharmonic effects coexist, opening new avenues for exploring emergent vibrational phenomena in low-dimensional materials.

We present results of a Raman scattering study of the Kagome ferromagnet Co_3Sn_2S_2, with a focus on electronic and phononic excitations and their interplay. We provide a theoretical analysis of the electronic band structure, enabling a semi-quantitative explanation of the spectra. A prominent feature in the electronic spectra is a redistribution of spectral weight from low to high energies in all polarization configurations starting at the Curie temperature T_C. In the symmetry-resolved spectra, the suppression of the A_1g continuum in the ferromagnetic state arises from the redistribution of electronic states below T_C, while a strong enhancement of the A_2g continuum is linked to the dynamics of fermions near the Fermi level E_ F being characterized by spin-momentum locking near Weyl points. The A_1g phonon modulates the position of these Weyl points and couples strongly to the related fermions close to E_ F. These results allow a comprehensive understanding of the bulk band structure evolution as a function of temperature in Co_3Sn_2S_2, offering key insights for further studies of the driving force behind the long-range magnetic order and novel topological states in this compound.

Topologically ordered states, such as chiral spin liquids, have been proposed as candidates that host fractionalized excitations. However, detecting chiral character or proximity to these non-trivial states remains a challenge. Resonant Raman scattering can be a powerful tool for detecting chiral fluctuations, as the A_2g channel probes excitations with broken time-reversal symmetry and local chiral order. Here, we use exact diagonalization to characterize the resonant A_2g channel, alongside two-magnon scattering in B_1g and E_g channels, for the Hubbard model on lattices with increasing levels of geometric spin frustration, where tuning the incident energy near the Mott gap reveals strong chiral spin excitation intensity. Increased spin frustration in the Mott insulator results in an overall softening of the Raman A_2g response, indicating a tendency toward low energy chiral-chiral fluctuations in Mott insulators with magnetic frustration and proximity to chiral spin liquid states that can potentially be tuned by external perturbations.

The formation of charge density waves (CDW) is a long-standing open problem particularly in dimensions higher than one. Various observations in the vanadium antimonides discovered recently, such as the missing Kohn anomaly in the acoustic phonons or the latent heat at the transition T_ CDW = 95 K , further underpin this notion. Here, we study the Kagome metal CsV_3Sb_5 using polarized inelastic light scattering. The electronic energy gap 2Δ as derived from the redistribution of the continuum is much larger than expected from mean-field theory and reaches values above 20 for 2Δ/k_ BT_ CDW. The A_1g phonon has a discontinuity at T_ CDW and a precursor starting 20 K above T_ CDW. Density functional theory qualitatively reproduces the redistribution of the electronic continuum at the CDW transition and the phonon energies of the pristine and distorted structures. The linewidths of all A_1g and E_2g phonon lines including those emerging below T_ CDW were analyzed in terms of anharmonic symmetric decay revealing strong phonon-phonon coupling. In addition, we observe two CDW amplitude modes (AMs): one in A_1g symmetry and one in E_2g symmetry. The temperature dependence of both modes deviates from the prediction of mean-field theory. The A_1g AM displays an asymmetric Fano-type lineshape, suggestive of strong electron-phonon coupling. The asymmetric A_1g AM, along with the discontinuity of the A_1g phonon, the large phonon-phonon coupling parameters and the large gap ratio, indicate the importance of anharmonic strong phonon-phonon and electron-phonon coupling for the CDW formation in CsV_3Sb_5.

This review summarizes studies of the energy gap and selected electronic properties of CuO2 superconductors. The main focus is placed on results of inelastic light scattering experiments starting as early as 1987 just a year after the discovery of superconductivity in copper–oxygen compounds by Georg Bednorz and Alex Muller. I add a few historical and personal remarks on superconductivity in general and on the contribution of the eminent scientist Karl Alex Muller who passed away in January 2023.

Tip-enhanced Raman spectroscopy (TERS) combines inelastic light scattering well below the diffraction limit down to the nanometer range and scanning probe microscopy and, possibly, spectroscopy. In this way, topographic and spectroscopic as well as single- and two-particle information may simultaneously be collected. While single molecules can now be studied successfully, bulk solids are still not meaningfully accessible. It is the purpose of the work presented here to outline approaches toward this objective. We describe a home-built, liquid helium cooled, ultrahigh vacuum TERS. The setup is based on a scanning tunneling microscope and, as an innovation, an off-axis parabolic mirror having a high numerical aperture of ∼0.85 and a large working distance. The system is equipped with a fast load-lock chamber, a chamber for the in situ preparation of tips, substrates, and samples, and a TERS chamber. Base pressure and temperature in the TERS chamber were ∼3 × 10-11 mbar and 15 K, respectively. Polarization dependent tip-enhanced Raman spectra of the vibration modes of carbon nanotubes were successfully acquired at cryogenic temperature. The new features described here including very low pressure and temperature and the external access to the light polarizations, thus the selection rules, may pave the way toward the investigation of bulk and surface materials.

Connections between crystal chemistry and critical temperature Tc have been in the focus of superconductivity, one of the most widely studied phenomena in physics, chemistry, and materials science alike. In most Fe-based superconductors, materials chemistry and physics conspire so that Tc correlates with the average anion height above the Fe plane, i.e., with the geometry of the FeAs4 or FeCh4 (Ch = Te, Se, or S) tetrahedron. By synthesizing Fe1-ySe1-xSx (0 ≤ x ≤ 1; y ≤ 0.1), we find that in alloyed crystals Tc is not correlated with the anion height like it is for most other Fe superconductors. Instead, changes in Tc(x) and tetragonal-to-orthorhombic (nematic) transition Ts(x) upon cooling are correlated with disorder in Fe vibrations in the direction orthogonal to Fe planes, along the crystallographic c-axis. The disorder stems from the random nature of S substitution, causing deformed Fe(Se,S)4 tetrahedra with different Fe-Se and Fe-S bond distances. Our results provide evidence of Tc and Ts suppression by disorder in anion height. The connection to local crystal chemistry may be exploited in computational prediction of new superconducting materials with FeSe/S building blocks.

Polarization- and temperature-dependent Raman data along with theoretical simulations are presented for the Kagome ferromagnet Fe_3Sn_2. Eight out of nine expected phonon modes were identified. The experimental energies compare well with those from the simulations. The analysis of the line widths indicates relatively strong phonon-phonon coupling in the range 0.1 to 1. The temperature-dependent frequencies of three A_1g modes show weak anomalies at approximately 100 K. In contrast, the linewidths of all phonon modes follow the conventional exponential broadening up to room temperature except for the softest A_1g mode, whose width exhibits a kink close to 100 K and becomes nearly constant for T > 100 K. These features are indicative of a spin reorientation taking place in the temperature range above 100 K which might arise from spin-phonon coupling. The low-energy part of the electronic continuum in E_g symmetry depends strongly on temperature. The possible reasons include particle-hole excitation tracking the resistivity, a spin-dependent gap or spin fluctuations.

Quantum critical fluctuations may prove to play an instrumental role in the formation of unconventional superconductivity. Here, we show that the characteristic scaling of a marginal Fermi liquid is present in inelastic light scattering data of an Fe-based superconductor tuned through a quantum critical point (QCP) by chemical substitution or doping. From the doping dependence of the imaginary time dynamics we are able to distinguish regions dominated by quantum critical behavior from those having classical critical responses. This dichotomy reveals a connection between the marginal Fermi liquid behavior and quantum criticality. In particular, the overlap between regions of high superconducting transition temperatures and quantum critical scaling suggests a contribution from quantum fluctuations to the formation of superconductivity.

A Raman scattering study covering the entire substitution range of the FeSe$_{1-x}$S$_x$ solid solution is presented. Data were taken as a function of sulfur concentration $x$ for $0\le x \le 1$, of temperature and of scattering symmetry. All type of excitations including phonons, spins and charges are analyzed in detail. It is observed that the energy and width of iron-related B$_{1g}$ phonon mode vary continuously across the entire range of sulfur substitution. The A$_{1g}$ chalcogenide mode disappears above $x=0.23$ and reappears at a much higher energy for $x=0.69$. In a similar way the spectral features appearing at finite doping in A$_{1g}$ symmetry vary discontinuously. The magnetic excitation centered at approximately 500 cm$^{-1}$ disappears above $x=0.23$ where the A$_{1g}$ lattice excitations exhibit a discontinuous change in energy. The low-energy mode associated with fluctuations displays maximal intensity at the nemato-structural transition and thus tracks the phase boundary.

Received 26 July 2022Accepted 5 October 2022DOI:https://doi.org/10.1103/PhysRevLett.129.199702Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasSuperconducting fluctuationsSuperconducting gapSuperconducting order parameterPhysical SystemsCupratesHigh-temperature superconductorsTechniquesBCS theoryBethe-Salpeter equationCollective modelsDiagrammatic methodsMethods in superconductivityRaman spectroscopyRandom phase approximationCondensed Matter, Materials & Applied Physics

In superconductors the Anderson-Higgs mechanism allows for the existence of a collective amplitude (Higgs) mode which can couple to eV-light mainly in a non-linear Raman-like process. The experimental non-equilibrium results on isotropic superconductors have been explained going beyond the BCS theory including the Higgs mode. Furthermore, in anisotropic d-wave superconductors strong interaction effects with other modes are expected. Here we calculate the Raman contribution of the Higgs mode from a new perspective, including many-body Higgs oscillations effects and their consequences in conventional, spontaneous Raman spectroscopy. Our results suggest a significant contribution to the intensity of the A1g symmetry Raman spectrum in d-wave superconductors. In order to test our theory, we predict the presence of measurable characteristic oscillations in THz quench-optical probe time-dependent reflectivity experiments.

We present a polarization-resolved, high-resolution Raman scattering study of the three consecutive charge density wave (CDW) regimes in 1T-TaS2 single crystals, supported by ab initio calculations. Our analysis of the spectra within the low-temperature commensurate (C-CDW) regime shows P (3) over bar symmetry of the system, thus excluding the previously proposed triclinic stacking of the "star-of-David" structure, and promoting trigonal or hexagonal stacking instead. The spectra of the high-temperature incommensurate (IC-CDW) phase directly project the phonon density of states due to the breaking of the translational invariance, supplemented by sizable electron-phonon coupling. Between 200 and 352 K, our Raman spectra show contributions from both the IC-CDW and the C-CDW phases, indicating their coexistence in the so-called nearly commensurate (NC-CDW) phase. The temperature dependence of the symmetry-resolved Raman conductivity indicates the stepwise reduction of the density of states in the CDW phases, followed by a Mott transition within the C-CDW phase. We determine the size of the Mott gap to be Omega(gap) approximate to 170-190 meV, and track its temperature dependence.

The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here, we compare results from determinant quantum Monte Carlo simulations of the Hubbard model to experimental results from Raman spectroscopy in $\text{La}_{2-x}\text{Sr}_{x}\text{CuO}_{4}$, which show a prominent increase in the $B_{1g}$ response around 10% hole doping as the temperature decreases, indicative of a rise in nematic fluctuations at low energy. Our results support a picture of nematic fluctuations with $B_{1g}$ symmetry occurring in underdoped cuprates, which may arise from melted stripes at elevated temperatures.

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.

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.

Theoretical analysis typically involves imaginary-time correlation functions. Inferring real-time dynamical response functions from this information is notoriously difficult. However, as we articulate here, it is straightforward to compute imaginary-time correlators from the measured frequency dependence of (real-time) response functions. In addition to facilitating comparison between theory and experiment, the proposed approach can be useful in extracting certain aspects of the (long-time relaxational) dynamics from a complex data set. We illustrate this with an analysis of the nematic response inferred from Raman scattering spectroscopy on the iron-based superconductor Ba(Fe1-xCox)(2)As-2, which includes a new method for identifying a putative quantum-critical contribution to that response.

Connections between crystal chemistry and critical temperature T_c have been in the focus of superconductivity, one of the most widely studied phenomena in physics, chemistry and materials science alike. In most Fe-based superconductors, materials chemistry and physics conspire so that T_c correlates with the average anion height above the Fe plane, i. e. with the geometry of the FeAs4 or FeCh4 (Ch = Te, Se, or S) tetrahedron. By synthesizing Fe_1-ySe_1-xS_x (0≤x≤1, y≤0.1), we find that in alloyed crystals T_c is not correlated with the anion height like it is for most other Fe superconductors. Instead, changes in T_c(x) and tetragonal-to-orthorombic (nematic) transition T_s(x) upon cooling are correlated with disorder in Fe vibrations in the direction orthogonal to Fe planes, along the crystallographic c-axis. The disorder stems from the random nature of S substitution, causing deformed Fe(Se,S)4 tetrahedra with different Fe-Se and Fe-S bond distances. Our results provide evidence of T_c and T_s suppression by disorder in anion height. The connection to local crystal chemistry may be exploited in computational prediction of new superconducting materials with Fe/S building blocks.