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An unconventional pairing mechanism in the heavy-fermion material$\mathrm{URu_{2}Si_{2}}$ is studied. We propose a mixed singlet-triplet$d$-density wave to be the hidden-order state in $\mathrm{URu_{2}Si_{2}}$. Theexotic order is topologically nontrivial and supports a charge $2e$ skyrmionicspin texture, which is assumed to fractionalize into merons and antimerons atthe deconfined quantum critical point. The interaction between these fractionalparticles results in a (pseudo)spin-singlet chiral $d$-wave superconductingstate, which breaks time reversal symmetry. Therefore, it is highly likely toproduce a nonzero signal of the polar Kerr effect at the onset of thesuperconductivity, consistent with recent experiments. In addition, the nodalstructures of the possible pairing functions in our model are consistent withthe thermodynamic experiments in $\mathrm{URu_{2}Si_{2}}$.

Superconducting phase within the hidden-order state of the heavy-fermion material $\mathrm{URu_{2}Si_{2}}$