Effect of Anisotropic Hybridization in YbAlB$_4$ Probed by Linear Dichroism in Core-Level Hard X-ray Photoemission Spectroscopy

We have probed the crystalline electric-field ground states of pure $|J = 7/2, J_z = pm 5/2rangle$ as well as the anisotropic $c$-$f$ hybridization in both valence fluctuating systems $alpha$- and $beta$-YbAlB$_4$ by linear polarization dependence of angle-resolved core level photoemission spectroscopy. Interestingly, the small but distinct difference between abyb was found in the polar angle dependence of linear dichroism, indicating the difference in the anisotropy of $c$-$f$ hybridization which may be essential to a heavy Fermi liquid state in $alpha$-YbAlB$_4$ and a quantum critical state in $beta$-YbAlB$_4$.