Critical current of the spin-triplet superconducting phase in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

There have been two different proposals for the spin-triplet order parameter of the superconducting phase in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$: an $f$-wave order parameter and the multigap model where some of the bands have the line node. In an effort to propose an experiment that can distinguish these two cases, we study the behavior of the supercurrent and compute the critical current for these order parameters when the sample is a thin film with the thickness $d⪡\xi$ where $\xi$ is the coherence length. It is found that the supercurrent behaves very differently in two models. This will serve as a sharp test for the identification of the correct order parameter.

Figure 1

The supercurrent as a function of $s∕\Delta \left(0\right)$ with the current (a) in the $ab$-plane for both of the $f$- and $f^{\prime }$-waves, (b) along the $c$-axis for the $f$-wave, and (c) along the $c$-axis for the $f^{\prime }$-wave. The unit of the supercurrent is $(en∕m{v}_F)\Delta \left(0\right)$ and $(en∕m)(v_{Fc}∕v_F^2)\Delta \left(0\right)$ for the current in the plane and along the $c$-axis, respectively.