Dressed Majorana Fermion in a Hybrid Nanowire

In hybrid systems where nanowires are proximity-coupled with superconductors, the low-energy theory fails to determine the topological phase with Majorana fermion (MF) when the magnetic field or proximity coupling is much stronger. To overcome this limitation, we propose a holistic approach that defines MF by considering both the motion of electrons in the nanowire and the quasiparticle excitations in the superconductor. This approach transcends the constraints of low-energy theory and offers broad applicability. Our approach reveals that the topological phase diagram depends not only on the chemical potential and Zeeman energy in the nanowire, but also on those in the superconductor, and the matched chemical potentials are more favorable for observing MF. This broader perspective provides specific experimental guidance under various conditions.