Superconducting phase within the hidden-order state of the heavy-fermion material $\mathrm{U}\mathrm{R}{\mathrm{u}}_2\mathrm{S}{\mathrm{i}}_2$

An unconventional pairing mechanism in the heavy-fermion material $\mathrm{U}\mathrm{R}{\mathrm{u}}_2\mathrm{S}{\mathrm{i}}_2$ is studied. We propose a mixed singlet-triplet $d$-density wave to be the hidden-order state in $\mathrm{U}\mathrm{R}{\mathrm{u}}_2\mathrm{S}{\mathrm{i}}_2$. The exotic order is topologically nontrivial and supports a charge $2e$ skyrmionic spin texture, which is assumed to fractionalize into merons and antimerons at the deconfined quantum critical point. The interaction between these fractional particles results in a (pseudo)spin-singlet chiral $d$-wave superconducting state, which breaks time reversal symmetry. Therefore, it is highly likely to produce a nonzero signal of the polar Kerr effect at the onset of the superconductivity, consistent with recent experiments. In addition, the nodal structures of the possible pairing functions in our model are consistent with the thermodynamic experiments in $\mathrm{U}\mathrm{R}{\mathrm{u}}_2\mathrm{S}{\mathrm{i}}_2$.