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The origin of anisotropy and high density of states in the electronic structure of Cr$_2$GeC by means of polarized soft X-ray spectroscopy and ab initio calculations

The anisotropy in the electronic structure of the inherently nanolaminated ternary phase Cr$_{2}$GeC is investigated by bulk-sensitive and element selective soft x-ray absorption/emission spectroscopy. The angle-resolved absorption/emission measurements reveal differences between the in-plane and out-of-plane bonding at the (0001) interfaces of Cr$_{2}$GeC. The Cr $L_{2,3}$, C $K$, and Ge $M_{1}$, $M_{2,3}$ emission spectra are interpreted with first-principles density-functional theory (DFT) including core-to-valence dipole transition matrix elements. For the Ge $4s$ states, the x-ray emission measurements reveal two orders of magnitude higher intensity at the Fermi level than DFT within the General Gradient Approximation (GGA) predicts. We provide direct evidence of anisotropy in the electronic structure and the orbital occupation that should affect the thermal expansion coefficient and transport properties. As shown in this work, hybridization and redistribution of intensity from the shallow $3d$ core levels to the $4s$ valence band explain the large Ge density of states at the Fermi level.