Fermionic influence superoperator for transport through Majorana zero modes

In recent years, the study of Majorana signatures in quantum transport has become a central focus in condensed matter physics. Here, we present a rigorous and systematic derivation of the fermionic superoperator describing the open quantum dynamics of electron transport through Majorana zero modes, building on the techniques introduced in Phys. Rev. B 105, 035121 (2022). The numerical implementation of this superoperator is to construct its differential equivalence, the hierarchical equations of motion (HEOM). The HEOM approach describes the system-bath correlated dynamics. Furthermore, we also develop a functional derivative scheme that provides exact expressions for the transport observables in terms of the auxiliary density operators introduced in the HEOM formulation. The superoperator formalism establishes a solid theoretical foundation for analyzing key transport signatures that may uncover the unique characteristics of Majorana physics in mesoscopic systems.