Intrinsically $s$-wave-like property of triplet superconductors with spin-orbit coupling

We have studied a general property of unconventional superconductors (USs) with spin-orbit coupling by solving the Bogoliubov–de Gennes equation and found that the two of four eigenfunctions for triplet pairing coincide with those for $s$-wave pairing when a relation holds between pairing symmetry and spin-orbit coupling, indicative of an intrinsically $s$-wave-like property of triplet superconductors. Applying the result, we have studied the tunneling conductance in normal metal/insulator/unconventional superconductor junctions with a pairing symmetry $\mathbf{d}\left(\mathbf{k}\right)\propto \widehat{\mathbf{x}}{k}_y-\widehat{\mathbf{y}}{k}_x$. The effect of Rashba spin-orbit coupling (RSOC) is taken into account. We have found that the RSOC induces a peak at the energy gap like $s$-wave superconductors in the tunneling spectrum, which stems from the intrinsically $s$-wave-like property of a triplet component of the US. As a result, the tunneling spectrum has $s$- and $p$-wave-like features. This may serve as a tool for determining the pairing symmetry of USs without inversion symmetry.

Figure 1

(Color online) Normalized tunneling conductance with $g=0.1$ for (a) $Z=10$ and (b) $Z=0$.

Figure 2

(Color online) Normalized tunneling conductance with $g=0.01$ for (a) $Z=10$ and (b) $Z=0$.

Figure 3

(Color online) Normalized tunneling conductance for $Z=10$ and $g=0.1$.

Figure 4

(Color online) Normalized tunneling conductance for other pairing symmetries with $Z=10$ and $g=0.1$. (a) $\mathbf{d}\left(\mathbf{k}\right)=-(\Delta ∕\mid \mathbf{k}\mid )k_x\widehat{\mathbf{y}}$ and (b) $\mathbf{d}\left(\mathbf{k}\right)=-(\Delta ∕\mid \mathbf{k}\mid )k_y\widehat{\mathbf{y}}$.