Distinguishing between topological Majorana and trivial zero modes via transport and shot noise study in an altermagnet heterostructure

We theoretically investigate the transport and shot-noise properties of a one-dimensional semiconducting nanowire with Rashba spin-orbit coupling (SOC) placed in closed proximity to a bulk $s\text{\ensuremath{-}}\mathrm{wave}$ superconductor and an altermagnet with $d\text{\ensuremath{-}}\mathrm{wave}$ symmetry. Such heterostructure with vanishing net magnetization manifests itself as an alternative route to anchor Majorana zero modes (MZMs) characterized by appropriate topological index (winding number $W$). Interestingly, this system also hosts accidental zero modes (AZMs) emerged with vanishing topological index indicating their nontopological nature. Furthermore, by incorporating three terminal setup, we explore the transport and shot-noise signatures of these zero modes. At zero temperature, we obtain zero-bias peak (ZBP) in differential conductance to be quantized with value $|W|\ifmmode\times\else\texttimes\fi{}2{e}^{2}/h$ for MZMs. On the other hand, AZMs exhibit nonquantized value at zero bias. Moreover, zero-temperature shot noise manifests negative (positive) value for MZMs (AZMs) within the bulk gap. At finite temperature, shot noise exhibits negative value (negative to positive transition) concerning MZMs (AZMs). Thus, the obtained signatures clearly distinguish between the MZMs and nontopological AZMs. We extend our analysis by switching on the next-to-nearest-neighbor hopping amplitude and SOC. Our conclusion remains unaffected for this case as well. Hence, our work paves the way to differentiate between emergent MZMs and AZMs in a semiconductor/ superconductor/ altermagnet heterostructure.