Possible $d$-wave superconductivity in borocarbides: Upper critical field of ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ and ${\mathrm{LuNi}}_2{\mathrm{B}}_2\mathrm{C}$

The upper critical field of a three-dimensional version of $d$-wave superconductors in a variety of field configurations is analyzed theoretically within the weak-coupling model. The present theory describes the main features of upper critical fields observed recently in ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ and ${\mathrm{LuNi}}_2{\mathrm{B}}_2\mathrm{C}.$ This strongly suggests that the underlying superconductivity in borocarbides should be of $d$ wave type.