Electronic structures of the quantum critical superconductor β-YbAlB4 and its polymorph α-YbAlB4 are investigated by using bulk-sensitive hard x-ray photoemission spectroscopy. From the Yb 3d core level spectra, the values of the Yb valence are estimated to be ∼2.73 and ∼2.75 for α- and β-YbAlB4, respectively, thus providing clear evidence for valence fluctuations. The valence band spectra of these compounds also show Yb2 + peaks at the Fermi level. These observations establish an unambiguous case of a strong mixed valence at quantum criticality for the first time among heavy fermion systems, calling for a novel scheme for a quantum critical model beyond the conventional Doniach picture in β-YbAlB4.
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