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Excitonic insulator is a coherent electronic phase that results from the formation of a macroscopic population of bound particle-hole pairs—excitons. With only a few candidate materials known, the collective excitonic behavior is challenging to observe, being obscured by crystalline lattice effects. Here we use polarization-resolved Raman spectroscopy to reveal the quadrupolar excitonic mode in the candidate zero-gap semiconductor Ta₂NiSe₅disentangling it from the lattice phonons. The excitonic mode pronouncedly softens close to the phase transition, showing its electronic character, while its coupling to noncritical lattice modes is shown to enhance the transition temperature. On cooling, we observe the gradual emergence of coherent superpositions of band states at the correlated insulator gap edge, with strong departures from mean-field theory predictions. Our results demonstrate the realization of a strongly correlated excitonic state in an equilibrium bulk material.

 

Abstract We present Raman-scattering results for three materials, CeB 6 , TbInO 3 , and YbRu 2 Ge 2 , to illustrate the essential aspects of crystal-field (CF) excitations and quadrupolar fluctuations of 4 f -electron systems. For CF excitations, we illustrate how the 4 f orbits are split by spin-orbit coupling and CF potential by presenting spectra for inter- and intra-multiplet excitations over a large energy range. We discuss identification of the CF ground state and establishment of low-energy CF level scheme from the symmetry and energy of measured CF excitations. In addition, we demonstrate that the CF linewidth is a sensitive probe of electron correlation by virtue of self-energy effect. For quadrupolar fluctuations, we discuss both ferroquadrupolar (FQ) and antiferroquadrupolar (AFQ) cases. Long-wavelength quadrupolar fluctuations of the same symmetry as the FQ order parameter persists well above the transition temperature, from which the strength of electronic intersite quadrupolar interaction can be evaluated. The tendency towards AFQ ordering induces ferromagnetic correlation between neighboring 4 f -ion sites, leading to long-wavelength magnetic fluctuations. 

We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic F e S e 1 − x S x superconductor. We observe two types of long-wavelength X Y 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 T S ( x ) , a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the X Y symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward T S ( x ) . The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration x c r ≈ 0.16 , while the pseudogap size decreases with the suppression of T S ( x ) . 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.