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

## TL;DR

This paper proposes a phenomenological theory for superconductivity in YbRh₂Si₂, revealing near-degenerate $p_x+ip_y$ and $d_{x^2-y^2}$ pairing symmetries influenced by quantum critical fluctuations, with implications for its phase diagram and electronic properties.

## Contribution

It introduces a multiband Eliashberg framework combining first-principles Fermi surfaces and quantum critical magnetic interactions to analyze pairing symmetry in YbRh₂Si₂.

## Key findings

- Superconductivity is near a boundary between $p_x+ip_y$ and $d_{x^2-y^2}$-wave states.
- Two candidate phase diagrams are proposed, with different field-dependent phases.
- Pairing is dominated by the 'jungle-gym' Fermi surface, challenging previous assumptions.

## Abstract

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 $(p_x+ip_y)$ and $d_{x^2-y^2}$-wave solutions. This leads to two candidate phase diagrams: one has only a spin-triplet $(p_x+ip_y)$-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 $(p_x+ip_y)$-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$_2$.