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Abstract The superconducting critical temperature T c of intercalated iron-selenide superconductor (Li,Fe)OHFeSe (FeSe11111) can be increased to 42 from 8 K of bulk FeSe. It shows remarkably similar electronic properties as the high- T c monolayer FeSe and provides a bulk counterpart to investigate the origin of enhanced superconductivity. Unraveling the nature of excitations is crucial for understanding the pairing mechanism in high- T c iron selenides. Here we use resonant inelastic x-ray scattering (RIXS) to investigate the excitations in FeSe11111. Our high-quality data exhibit several Raman-like excitations, which are dispersionless and isotropic in momentum transfer in both superconducting 28 K and 42 K samples. Using atomic multiplet calculations, we assign the low-energy ~0.3 and 0.7 eV Raman peaks as local e g  −  e g and e g  −  t 2 g orbital excitations. The intensity of these two features decreases with increasing temperature, suggesting a dominating contribution of the orbital fluctuations. Our results highlight the importance of the orbital degree of freedom for high- T c iron selenides.

For a local complete intersection subvariety $X = V (I)$ in $P^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of vector bundles on the formal completion of $P^n$ along $X$ can be effectively computed as the cohomology on any sufficiently high thickening $X_t = V (I^t)$; the main ingredient here is a positivity result for the normal bundle of $X$. Furthermore, we show that the Kodaira vanishing theorem holds for all thickenings $X_t$ in the same range of cohomological degrees; this extends the known version of Kodaira vanishing on $X$, and the main new ingredient is a version of the Kodaira- Akizuki-Nakano vanishing theorem for $X$, formulated in terms of the cotangent complex.