Inelastic light scattering studies on single crystal of electron-doped Ca(Fe0.95Co0.05)2As2 superconductor, covering the tetragonal to orthorhombic structural transition as well as magnetic transition at TSM ~ 140 K and superconducting transition temperature Tc ~ 23 K, reveal evidence for superconductivity-induced phonon renormalization; in particular the phonon mode near 260 cm-1 shows hardening below Tc, signaling its coupling with the superconducting gap. All the three Raman active phonon modes show anomalous temperature dependence between room temperature and Tc i.e phonon frequency decreases with lowering temperature. Further, frequency of one of the modes shows a sudden change in temperature dependence at TSM. Using first-principles density functional theory-based calculations, we show that the low temperature phase (Tc < T < TSM) exhibits short-ranged stripe anti-ferromagnetic ordering, and estimate the spin-phonon couplings that are responsible for these phonon anomalies.
The interplay between spin dynamics and lattice vibration has been suggested as an important part of the puzzle of high-temperature superconductivity. Here we report the strong interaction between spin fluctuation and phonon in SmFeAsO, a parent compound of the iron arsenide family of superconductors, revealed by low-temperature Raman spectroscopy. Anomalous zone-boundary-phonon Raman scattering from spin superstructure was observed at temperatures below the antiferromagnetic ordering point, which offers compelling evidence on spin dependent electron-phonon coupling in pnictides.
We investigate non-resonant Raman response for iron-based superconductors using the framework of an effective S4 model that was recently proposed to capture the essential electronic and magnetic properties of Iron based superconductors. We compute the momentum matrix elements and the resulting Raman vertices exactly for different polarization geometries and amazingly find that a simple coskxcosky superconducting gap function is in good agreement with experimental data measured in both iron-pnictides and iron-chalcogenides. The Raman peaks are also matched quantitatively with the measured super…
We performed model calculations of Raman responses for multiband 2D superconductors. The multiband effects of screening in the A_{1g} symmetry channel were investigated analytically and numerically for a band structure model mimicing ARPES data on iron-pnictide materials. An acceptable agreement between our model calculations and recent experimental data is demonstrated by modification of the band structure parameters.
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 convent…
We performed a Raman scattering study of thin films of LiTi$_2$O$_4$ spinel oxide superconductor. We detected four out of five Raman active modes, with frequencies in good accordance with our first-principles calculations. Three T$_{2g}$ modes show a Fano lineshape from 5 K to 295 K, which suggests an electron-phonon coupling in LiTi$_2$O$_4$. Interestingly, the electron-phonon coupling shows an anomaly across the negative to positive magnetoresistance transition at 50 K, which may be due to the unset of other competing orders. The strength of the electron-phonon interaction estimated from the…
We report inelastic light scattering studies on Ca(Fe0.97Co0.03)2As2 in a wide spectral range of 120-5200 cm-1 from 5K to 300K, covering the tetragonal to orthorhombic structural transition as well as magnetic transition at Tsm ~ 160K. The mode frequencies of two first-order Raman modes B1g and Eg, both involving displacement of Fe atoms, show sharp increase below Tsm. Concomitantly, the linewidths of all the first-order Raman modes show anomalous broadening below Tsm, attributed to strong spin-phonon coupling. The high frequency modes observed between 400-1200 cm-1 are attributed to the elect…
Inelastic light (Raman) scattering has been used to study electronic excitations and phonon anomalies in detwinned, slightly overdoped YBa$_2$Cu$_3$O$_{6.95}$ and moderately overdoped Y$_{0.85}$Ca$_{0.15}$Ba$_2$Cu$_3$O$_{6.95}$ single crystals. In both samples modifications of the electronic pair-breaking peaks when interchanging the a- and b-axis were observed. The lineshapes of several phonon modes involving plane and apical oxygen vibrations exhibit pronounced anisotropies with respect to the incident and scattered light field configurations. Based on a theoretical model that takes both ele…
We use polarization-resolved Raman scattering to study lattice dynamics in NaFe$_{0.53}$Cu$_{0.47}$As single crystals. We identify 4 $A_{1g}$ phonon modes at 125, 172, 183 and 197 cm$^{-1}$, and 4 $B_{3g}$ phonon modes at 101, 138, 173, 226 cm$^{-1}$. The phonon spectra are consistent with the $Ibam$ group, which confirms that the Cu and Fe atoms form a stripe order. The temperature dependence of the phonon spectra suggests weak electron-phonon and magneto-elastic interactions.
We report interesting anomalies in the temperature dependent Raman spectra of FeSe$_{0.82}$ measured from 3K to 300K in the spectral range from 60 to 1800 cm$^{-1}$ and determine their origin using complementary first-principles density functional calculations. A phonon mode near 100 cm$^{-1}$ exhibits a sharp increase by $\sim$ 5% in frequency below a temperature T$_s$ ($\sim$ 100 K) attributed to strong spin-phonon coupling and onset of short-range antiferromagnetic order. In addition, two high frequency modes are observed at 1350 cm$^{-1}$ and 1600 cm$^{-1}$, attributed to electronic Raman …
We present Raman measurements on the iron-pnictide superconductors CeFeAsO_{1-x}F_{x} and NdFeAsO{1-x}F_{x}. Modeling the Fe-As plane in terms of harmonic and a cubic anharmonic Fe-As interaction we calculate the temperature dependence of the energy and lifetime of the Raman active Fe B_{1g} mode and fit to the observed energy shift. The shifts and lifetimes are in good agreement with those measured also in other Raman studies which demonstrate that the phonon spectrum is well represented by phonon-phonon interactions without any significant electronic contribution. We also estimate the anharm…
Time resolved measurements provide a new way to disentangle complex interactions in quantum materials due to their different timescales. We used pump-probe Raman scattering to investigate the apical oxygen vibration in YBa$_2$Cu$_3$O$_{6+x}$ under nonequilibrium conditions. Time-dependence of the phonon population demonstrated strong electron-phonon coupling. Most importantly, the phonon shifts to a higher energy due to transient smearing of the Fermi surface in a remarkable agreement with diagrammatic theory. We also discuss new insights into photoinduced superconductivity reported at lower d…
Mechanism of unconventional superconductivity is still unknown even if more than 25 years have been passed since the discovery of high-Tc cuprate superconductors by J.G. Bednorz and K. A. Muller. Here, we explore the cuprate phase diagram by electronic Raman spectroscopy and shed light on the superconducting state in hole doped cuprates. Namely, how superconductivity and the critical temperature Tc are impacted by the pseudogap.
In a recent manuscript Phys. Rev. Lett. 127, 197001 (2021) Puviani et al. claim that the Higgs mode gives an enhancement of the Raman response in the symmetric $A_{1g}$ Raman channel of cuprates. Here we report a series of technical mistakes in their derivation that completely invalidate this conclusion. In particular, the Raman response function contains two renormalized vertices, with a clearly overcounting of diagrams and uncontrolled results for the Higgs-mode contribution.
The electronic Raman response in the electron-doped cuprate superconductors is studied based on the $t$-$t'$-$J$ model. It is shown that although the domelike shape of the doping dependent peak energy in the $B_{2g}$ symmetry is a common feature for both electron-doped and hole-doped cuprate superconductors, there are pronounced deviations from a cubic response in the $B_{1g}$ channel and a linear response in the $B_{2g}$ channel for the electron-doped case in the low energy limit. It is also shown that these pronounced deviations are mainly caused by a nonmonotonic d-wave gap in the electron-…
We report temperature-dependent Raman spectra of CeFeAsO0.9F0.1 from 4 K to 300 K in spectral range of 60 to 1800 cm-1 and interpret them using estimates of phonon frequencies obtained from first-principles density functional calculations. We find evidence for a strong coupling between the phonons and crystal field excitations; in particular Ce3+ crystal field excitation at 432 cm-1 couples strongly with Eg oxygen vibration at 389 cm-1 . Below the superconducting transition temperature, the phonon mode near 280 cm-1 shows softening, signaling its coupling with the superconducting gap. The rati…
We have performed polarized Raman scattering measurements on the newly discovered superconductor Nd(O,F)BiS$_2$ ($T_c = 4$ K). We observe 2 Raman active modes, with frequencies in accordance with first-principles calculations. One A$_{1g}$ phonon mode at 112.4 cm$^{-1}$ exhibits a Fano line shape due to electron-phonon coupling. We find a resonance for this mode at 2.45 eV excitation energy. We estimate a 0.68 contribution of this mode to the electron-phonon coupling constant $λ$. Our Raman results suggest that the BiS$_2$-based superconductors are possibly phonon-mediated BCS superconductors.
Temperature dependence and resonance effects in Raman scattering of phonons in NdFeAsO$_{x}$F$_{1-x}$ single crystals
本文报道了氧铌酸铁超导体NdFeAsO $_{1-x}$ F $x$单晶的平面偏振喇曼散射光谱。该光谱表现出尖锐和对称的声子线与氟掺杂$x$弱的依赖性。温度依赖性没有显示任何声子异常的超导转变。铁相关的声子强度显示出强烈的共振增强低于2eV。我们将共振增强与在光学电导率中观察到的约2 eV的带间跃迁的存在相关联。我们的研究结果指出，在铁氧铌酸盐超导体的拉曼活性声子和电子激发之间的一个相当弱的耦合。
Certain significant fallacies are involved in discussions of the high-Tc mechanism unsolved for over 30 years in cuprate superconductors. These fallacies are explored with the aim of unravelling this mechanism. Moreover, using polarised electronic Raman scattering in inhomogeneous underdoped cuprate superconductors, the intrinsic nonlinear Raman spectrum is obtained by subtracting the pseudogap characteristic of a nonlinear from the linear Raman spectrum measured in the B2g mode of the node area below the critical temperature. The intrinsic nonlinear behaviour implies the existence of the noda…
We report a Raman scattering study of nematic degrees of freedom in the iron-based superconductor parent compound BaFe$_2$As$_2$ under tunable uniaxial strain. We demonstrate that the polarization resolved arsenic (As) phonon intensity can be used to monitor the nematic order parameter as a function of both temperature and strain. At low temperature in the nematic ordered phase we use it to track the continuous and reversible orientation of nematic domains under variable strain. At higher temperature, the evolution of the As phonon intensity under strain reflects an enhanced nematic susceptibi…
We performed a polarized Raman scattering study of quasi-one-dimensional superconductor K$_2$Cr$_3$As$_3$. We detect two A$_1^\prime$ phonons and three E$^\prime$ phonons. One of the A$_1^\prime$ modes exhibits a nearly temperature-independent Fano lineshape. Based on our first-principles calculations, we ascribe this mode to the in-phase vibrations of Cr atoms within one layer. This observation strongly suggests that the magnetic fluctuations in K$_2$Cr$_3$As$_3$ are coupled to the electronic structure \emph{via} the lattice.
Iron-based superconducting layered compounds have the second highest transition temperature after cuprate superconductors. Their discovery is a milestone in the history of high-temperature superconductivity and will have profound implications for high-temperature superconducting mechanism as well as industrial applications. Raman scattering has been extensively applied to correlated electron systems including the new superconductors due to its unique ability to probe multiple primary excitations and their coupling. In this review, we will give a brief summary of the existing Raman experiments …
Recently discovered magnetic topological insulators $T$Bi$_{2}$Te$_{4}$ ($T=$Mn, Fe) crystallize into the $R\bar{3}m$ rhombohedral structure and exhibit the antiferromagnetic order. Here, we discuss the lattice dynamics of these compounds to confirm the stability of these systems. We show that the phonon dispersion does not contain soft modes, so both compounds are dynamically stable in the $R\bar{3}m$ phase. We perform theoretical analyses of the mode activity at $Γ$ point for the discussed compounds. In the case of the Raman active modes, our results are in agreement with the experimentally …
We discuss how to analyze the optical conductivity and Raman spectra of multi-orbital systems using the velocity and the Raman vertices in a similar way Raman vertices were used to disentangle nodal and antinodal regions in cuprates. We apply this method to iron superconductors in the magnetic and non-magnetic states, studied at the mean field level. We find that the anisotropy in the optical conductivity at low frequencies reflects the difference between the magnetic gaps at the X and Y electron pockets. Both gaps are sampled by Raman spectroscopy. We also show that the Drude weight anisotrop…
We report the first systematic measurements of the Raman scattering by electrons in elemental metals of Al, Mo, Nb, Os, Pb, Re, Ta, Ti, V, W and metallic compound La$B_6$. Experimental spectra are modelled on the base of the band structures, calculated within the density functional theory, taking properly into account the effects of electron-phonon scattering. The agreement between our measured and calculated spectra is excellent for the variety of metals, thus providing estimates for the electron-phonon coupling constants and temperature-dependent relaxation rates. The method can be applied f…
The emergence of the nematic order and fluctuations has been discussed as a central issue in Fe-based superconductors. To clarify the origin of the nematicity, we focus on the shear modulus $C_{66}$ and the Raman quadrupole susceptibility $χ_{x^2-y^2}^{Raman}$. Due to the Aslamazov-Larkin vertex correction, the nematic-type orbital fluctuations are induced, and they enhances both $1/C_{66}$ and $χ_{x^2-y^2}^{Raman}$ strongly. However, $χ_{x^2-y^2}^{Raman}$ remains finite even at the structure transition temperature $T_S$, because of the absence of the band Jahn-Teller effect and the Pauli (=in…
We report Raman scattering measurement of charge nematic fluctuations in the tetragonal phase of BaFe$_2$As$_2$ and Sr(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (x=0.04) single crystals. In both systems, the observed nematic fluctuations are found to exhibit divergent Curie-Weiss like behavior with very similar characteristic temperature scales, indicating a universal tendency towards charge nematic order in 122 iron-based superconductors.
Electron-phonon coupling (EPC) is one of the most common and fundamental interactions in solids. It not only dominates many basic dynamic processes like resistivity, thermal conductivity etc, but also provides the pairing glue in conventional superconductors. But in high-temperature superconductors (HTSC), it is still controversial whether or not EPC is in favor of paring. Despite the controversies, many experiments have provided clear evidence for EPC in HTSC. In this paper, we briefly review EPC in cuprate and iron-based superconducting systems revealed by Raman scattering. We introduce how …
