Surface induced odd-frequency spin-triplet superconductivity as a veritable signature of Majorana bound states

Abstract: We predict surface-induced odd-frequency (odd-$\nu$) spin-triplet superconducting pairing can be a veritable signature of Majorana bound states (MBS) in a Josephson nodal $p$-wave superconductor ($p_{x}$)-spin flipper (SF)-nodal $p$-wave superconductor ($p_{x}$) junction. Remarkably, in a $p_{x}$-SF-$p_{x}$ Josephson junction three distinct phases emerge: the topological phase featuring MBS, the topological phase without MBS, and the trivial phase devoid of MBS. Surface odd-$\nu$ spin-triplet pairing is induced only in the topological regime when MBS appears. In contrast, surface-induced even-frequency (even-$\nu$) spin-triplet pairing is finite regardless of the existence of MBS. Importantly, we find the surface induced odd-$\nu$ spin-triplet pairing is immune to disorder in the topological phase featuring MBS, while in the trivial phase the surface induced even-$\nu$ spin-triplet pairing is affected by disorder. Our study offers a potential means for distinguishing the topological phase featuring MBS from both the trivial phase as well as the topological phase devoid of MBS, primarily through the observation of induced surface odd-$\nu$ spin-triplet superconductivity.