Strong in-plane anisotropy in the electronic structure of fixed-valence β − LuAlB 4

The origin of intrinsic quantum criticality in the heavy-fermion superconductor $\\ensuremath{\\beta}\\ensuremath{-}{\\mathrm{YbAlB}}_{4}$ has been attributed to strong Yb valence fluctuations and its peculiar crystal structure. Here, we assess these contributions individually by studying the isostructural but fixed-valence compound $\\ensuremath{\\beta}\\ensuremath{-}{\\mathrm{LuAlB}}_{4}$. Quantum oscillation measurements and density functional theory calculations reveal a Fermi surface in $\\ensuremath{\\beta}\\ensuremath{-}{\\mathrm{LuAlB}}_{4}$ markedly different from that of $\\ensuremath{\\beta}\\ensuremath{-}{\\mathrm{YbAlB}}_{4}$, consistent with a ``large\u0027\u0027 Fermi surface in the latter. We also find an unexpected in-plane anisotropy of the electronic structure, in contrast to the isotropic Kondo hybridization in $\\ensuremath{\\beta}\\ensuremath{-}{\\mathrm{YbAlB}}_{4}$.