Linear response theory for shear modulus C66 and Raman quadrupole susceptibility: evidence for nematic orbital fluctuations in Fe-based superconductors

Quadrupolar charge dynamics in the nonmagnetic FeSe1-x S x superconductors

We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic [Formula: see text] superconductor. We observe two types of long-wavelength [Formula: see text] symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at [Formula: see text], a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the [Formula: see text] symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward [Formula: see text] The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration [Formula: see text], while the pseudogap size decreases with the suppression of [Formula: see text] We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

Mössbauer spectroscopy study of nematicity in Ba(Fe0.962Cu0.038)2As2single crystal: enhanced orbital effect

The origin of the nematic order remains unclear due to the strong coupling between orbital, spin and lattice degrees of freedom in iron-based superconductors. Although the driving force of hole-doped BeFe₂As₂is still controversial, the nematic fluctuation of electron-doped compounds is generally believed to be spin fluctuation driven. Here, we present a comprehensive study of the nematic phase transition in Ba(Fe_0.962Cu_0.038)₂As₂single crystal by using Mössbauer spectroscopy. The electric field gradient and its in-plane asymmetry on Fe nucleus, which are directly determined by the occupation of individualt_2gorbital, are sensitive to the local nematicity of Fe ions. The nematic phase transition happens atT_nem≈ 73.8 K in the compound while the band splitting betweend_xz/d_yzorbitals begins far aboveT_nemand reaches 18.8 meV at 30 K. The temperature evolution of the hyperfine parameters proves the existence of electron-phonon interaction and non-Fermi-liquid behaviour nearT_nem. However, the spin-lattice relaxation signal is only evident belowT_nem. These observations show that the role of orbital degrees of freedom is more active in driving nematicity than in Co- or Ni-doped BaFe₂As₂compounds, and can be attributed to enhanced electronic localization caused by Cu doping.

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

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

Charge-induced nematicity in FeSe

The spontaneous appearance of nematicity, a state of matter that breaks rotation but not translation symmetry, is one of the most intriguing properties of the iron-based superconductors (Fe SC), and has relevance for the cuprates as well. Establishing the critical electronic modes behind nematicity remains a challenge, however, because their associated susceptibilities are not easily accessible by conventional probes. Here, using FeSe as a model system, and symmetry-resolved electronic Raman scattering as a probe, we unravel the presence of critical charge nematic fluctuations near the structural/nematic transition temperature, [Formula: see text] 90 K. The diverging behavior of the associated nematic susceptibility foretells the presence of a Pomeranchuk instability of the Fermi surface with d-wave symmetry. The excellent scaling between the observed nematic susceptibility and elastic modulus data demonstrates that the structural distortion is driven by this d-wave Pomeranchuk transition. Our results make a strong case for charge-induced nematicity in FeSe.

Sign-Reversing Orbital Polarization in the Nematic Phase of FeSe due to the C_{2} Symmetry Breaking in the Self-Energy

To understand the nematicity in Fe-based superconductors, nontrivial k dependence of the orbital polarization [ΔE_{xz}(k), ΔE_{yz}(k)] in the nematic phase, such as the sign reversal of the orbital splitting between Γ and X, Y points in FeSe, provides significant information. To solve this problem, we study the spontaneous symmetry breaking with respect to the orbital polarization and spin susceptibility self-consistently. In FeSe, due to the sign-reversing orbital order, the hole and electron pockets are elongated along the k_{y} and k_{x} axes, respectively, consistently with experiments. In addition, an electron pocket splits into two Dirac cone Fermi pockets while increasing the orbital polarization. The orbital order in Fe-based superconductors originates from the strong positive feedback between the nematic orbital order and spin susceptibility.

Nematic Resonance in the Raman Response of Iron-Based Superconductors

In a fully gapped superconductor the electronic Raman response has a pair-breaking peak at twice the superconducting gap Δ, if the Bogoliubov excitations are uncorrelated. Motivated by the iron based superconductors, we study how this peak is modified if the superconducting phase hosts a nematic-structural quantum critical point. We show that, upon approaching this point by tuning, e.g., doping, the growth of nematic correlations between the quasiparticles transforms the pair-breaking peak into a nematic resonance. The mode energy is below 2Δ, and stays finite at the quantum critical point, where its spectral weight is sharply enhanced. The latter is consistent with recent experiments on electron-doped iron based superconductors and provides direct evidence of nematic correlations in their superconducting phases.

Phonons of Fe-based superconductor Ca10Pt4As8(Fe1-x Pt x As)10

We report the results of inelastic neutron scattering measurements on particular phonons of a superconducting (SC) Ca10Pt4As8(Fe1-x Pt x As)10 with the onset transition temperature T c ~ 33 K to investigate mainly what roles orbital fluctuation plays in Cooper pairing, where we observed a slight softening of the in-plane transverse acoustic mode corresponding to the elastic constant C 66. This softening starts at temperature T well above the SC T c, as T decreases. An anomalously strong change of the scattering intensity of in-plane optical modes was observed at the M point of the pseudo tetragonal reciprocal space in the range of 35  <  ω  <  40 meV with decreasing T from far above T c. Because this ω region mainly corresponds to the motion of Fe and As atoms in the FeAs planes, the finding presents information on the coupling between the orbital fluctuation of Fe 3d electrons and the lattice system, useful for studying the possible roles of orbital fluctuation in the pairing mechanism and/or the appearance of the so-called nematic phase.