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Orbital anisotropy of heavy fermion Ce$_{2}$IrIn$_{8}$ under crystalline electric field and its energy scale

We investigate the temperature ($T$)-evolution of orbital anisotropy and its effect on spectral function and optical conductivity in Ce$_{2}$IrIn$_{8}$, using a first principles dynamical mean field theory combined with density functional theory. The orbital anisotropy develops by lowering $T$ and it is intensified below a temperature corresponding to the crystalline-electric field (CEF) splitting size. Interestingly, the depopulation of CEF excited states leaves a spectroscopic signature, "shoulder", in the $T$-dependent spectral function at the Fermi level. From the two-orbital Anderson impurity model, we demonstrate that CEF splitting size is the key ingredient influencing the emergence and the position of the "shoulder". Besides the two conventional temperature scales $T_{K}$ and $T^{*}$, we introduce an additional temperature scale to deal with the orbital anisotropy in heavy fermion systems.