Nearly-degenerate $p_x+ip_y$ and $d_{x^2-y^2}$ pairing symmetry in the heavy fermion superconductor YbRh$_2$Si$_2$

Recent discovery of superconductivity in YbRh $_{2}$ 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 YbRh $_{2}$ Si $_{2}$ is located on the border of $(p_{x} + i p_{y})$ and $d_{x^{2} - y^{2}}$ -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 $d_{x^{2} - y^{2}}$ -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 YbRh $_{2}$ Si $_{2}$ .

Nearly-degenerate $p_{x} + i p_{y}$ and $d_{x^{2} - y^{2}}$ pairing symmetry in the heavy fermion superconductor YbRh $_{2}$ Si $_{2}$

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Nearly-degenerate $p_{x} + i p_{y}$ and $d_{x^{2} - y^{2}}$ pairing symmetry in the heavy fermion superconductor YbRh $_{2}$ Si $_{2}$

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Nearly-degenerate px+ipypx​+ipy​ and dx2−y2dx2−y2​ pairing symmetry in the heavy fermion superconductor YbRh22​Si22​

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Nearly-degenerate px+ipypx​+ipy​ and dx2−y2dx2−y2​ pairing symmetry in the heavy fermion superconductor YbRh22​Si22​

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Nearly-degenerate $p_{x} + i p_{y}$ and $d_{x^{2} - y^{2}}$ pairing symmetry in the heavy fermion superconductor YbRh $_{2}$ Si $_{2}$

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Nearly-degenerate $p_{x} + i p_{y}$ and $d_{x^{2} - y^{2}}$ pairing symmetry in the heavy fermion superconductor YbRh $_{2}$ Si $_{2}$

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