Anisotropic heavy Fermi-liquid formation in the valence fluctuating $alpha$-YbAlB$_4$

$alpha$-YbAlB$_4$ is the locally isostructural polymorph of $beta$-YbAlB$_4$, the first example of an Yb-based heavy fermion superconductor which exhibits pronounced non-Fermi-liquid behavior above $T_{rm c}$. Interestingly, both $alpha$-YbAlB$_4$ and $beta$-YbAlB$_4$ have strongly intermediate valence. Our single crystal study of the specific heat, magnetization and resistivity has confirmed the Fermi liquid ground state of $alpha$-YbAlB$_4$ ~in contrast with the quantum criticality observed in $beta$-YbAlB$_4$. Both systems exhibit Kondo lattice behavior with the characteristic temperature scale $T^* sim$ 8 K in addition to a valence fluctuation scale $sim 200$ K. Below $T^*$, $alpha$-YbAlB$_4$ a heavy Fermi liquid state with an electronic specific heat coefficient $gammasim$ 130 mJ/mol K$^2$ and a large Wilson ratio more than 7, which indicates ferromagnetic correlation between Yb moments. A large anisotropy in the resistivity suggests that the hybridization between 4$f$ and conduction electrons is much stronger in the $ab$-plane than along the c-axis. The strongly anisotropic hybridization as well as the large Wilson ratio is the key to understand the unusual Kondo lattice behavior and heavy fermion formation in mixed valent compounds.