Abstract

The quest for robust and manipulable Majorana zero modes in topological superconductors faces multifaceted challenges, ranging from material realization to unambiguous experimental detection and quantum control. While the topological band theory provides a fundamental classification, it often lacks a phenomenological language to describe the processes that govern the stability and response of MZMs in real materials. This paper introduces a novel theoretical framework that bridges this gap by reinterpreting the phenomenological parameters of Ginzburg-Landau theory–$\alpha$, $\beta$, and $m^{*}$–as three universal physical processes: energy competition, condensation saturation, and Cooper pair inertial mass. We establish that the stability of the topological superconducting phase hosting MZMs is governed by the delicate interplay and internal constraints among these processes. Specifically, we demonstrate that the energy competition $\alpha$ is rooted in quantum interference of matter waves, whose anisotropy is crucial for topological pairing. The saturation parameter $\beta$ acts as a confining potential, defining the energy landscape for moving MZMs. The inertial mass $m^{*}$, enhanced by orbital angular momentum-local electric field coupling ($L \times E$ coupling), dictates the collective response and sets the adiabatic conditions for braiding. This framework offers a unified process-oriented perspective to dissect key unsolved puzzles in the MZM field: it explains the material fragility of topological superconductivity, provides an energy-scale picture for non-Abelian braiding, suggests new interpretations for local probe signals, and proposes parameter engineering especially via electric field control of $m^{*}$ as a strategic path toward building MZM networks. Our work shifts the paradigm from merely describing topological properties to actively designing and manipulating the underlying physical processes that enable them.