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The isostructural transition in the tetragonal phase, with sizable change inthe anion-height, is realized in heavily H-doped LaFeAsO and (La,P) co-dopedCaFe$_2$As$_2$. In these compounds, the superconductivity with higher-Tc (40~50K) is realized near the isostructural transition. To reveal the origin of theanion-height instability and its important role in realizing the higher-Tcstate, we develop the orbital-spin fluctuation theory by including the vertexcorrection. It is found that the non-nematic orbital fluctuations, which inducethe anion-height instability, can develop near the magnetic quantum criticalpoint, in addition to the conventional nematic orbital fluctuations. Thenon-nematic orbital order triggers the isostructural transition, and itsfluctuation would be a key ingredient to realize higher-Tc superconductivity oforder 50 K.

High-Tc Superconductivity near the Anion Height Instability in Fe-based Superconductors: Analysis of LaFeAsO$_{1-x}$H$_x$