Anomalous upper critical field of two-gap superconductor Lu$_2$Fe$_3$Si$_5$

Ternary-iron silicide superconductor Lu$_2$Fe$_3$Si$_5$ with $T_c$ = 6 K has attracted attention because of the anomalous superconducting properties, such as a large residual linear term in the superconducting specific heat and a reduced normalized specific heat jump at $T_c$ smaller than the BCS value. Our recent specific-heat study has revealed that these anomalies stem from the two distinct superconducting gaps. In order to clarify the details of the two-gap superconductivity in Lu$_2$Fe$_3$Si$_5$, we have prepared the high-quality single crystal and investigated the upper critical field $H_{c2}$ obtained by resistivity measurements. We find that $H_{c2}$ increases linearly with decreasing temperature down to $T_c/3$, and $H_{c2}(T=0)$ exceeds the orbital depairing field described by the simple WHH theory. We also find that the angular dependence of $H_{c2}$ is well described by anisotropic GL model unlike the case of typical two-gap superconductor MgB$_2$. We discuss the origin of these differences based on the nature of two gaps in the two superconductors.