Nearly degenerate p x + i p y and d x 2 − y 2 pairing symmetry in the heavy fermion superconductor YbRh 2 Si 2

Recent discovery of superconductivity in ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$ has raised particular interest in its pairing mechanism and gap symmetry. Here we propose a phenomenological theory of its superconductivity and investigate possible gap structures by solving the multiband Eliashberg equations combining realistic Fermi surfaces from first-principles calculations and a quantum critical form of magnetic pairing interactions. The resulting gap symmetry shows sensitive dependence on the in-plane propagation wave vector of the quantum critical fluctuations, suggesting that superconductivity in ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$ is located on the border of $({p}_{x}+i{p}_{y})$ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave solutions. This leads to two candidate phase diagrams: one has only a spin-triplet $({p}_{x}+i{p}_{y})$-wave superconducting phase; the other contains multiple phases with a spin-singlet ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave state at zero field and a field-induced spin-triplet $({p}_{x}+i{p}_{y})$-wave state. In addition, the electron pairing is found to be dominated by the ``jungle-gym'' Fermi surface rather than the ``doughnut''-like one, in contrast to previous thought. This requests a more elaborate and renewed understanding of the electronic properties of ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$.