Dressed Majorana fermion in a hybrid nanowire

Abstract

The low-energy theory of hybrid nanowire systems fails to define Majorana fermion (MF) in the strong tunneling and magnetic field strength. To address this limitation, we propose a holistic approach to define MF in which the quasi-excitation in nanowire and superconductor constitutes together its own ``antiparticles''. This definition is general, beyond the constraint presented in the low-energy theory. It reveals that the Majorana phase depends not only on the chemical potential and Zeeman energy in nanowire but also on those of superconductor, and that the mismatch of chemical potential leads not to observe MF. Such a broader perspective provides more specific experimental guidance under various conditions

Figures (2)

• Figure 1: The semiconductor nanowire is partially or fully covered by the superconducting shell, which can be characterized by the one-dimensional lattice model of nanowire coupled to an s-wave superconductor. And the spectrum of its differential conductance is obtained by connecting electron leads at the ends of the nanowire.
• Figure 2: (a) The zero-energy and excitation-energy modes in the hybrid system. (b) The zero-energy wave function $\mathrm{P}_{\mathrm{SC}},\mathrm{P}_{\mathrm{NW}}$ in nanowire and SC, and their proportion $\mathrm{P}_{\mathrm{SC}}/\mathrm{P}_{\mathrm{NW}}$ change as the tunneling strength enhances. (c, d) The distribution of the localized zero-mode wave functions at each site-$n$ in nanowire and SC. (e) The zero bias peak in differential spectrum by connecting electron leads at the ends of the nanowire. The parameters are set as $N=600,t_{w}=12\Delta_{s},t_{s}=10\Delta_{s},\mu_{w}=0,\mu_{s}=4\Delta_{s},h_{w}=1.5\Delta_{s},h_{s}=0,\alpha_{w}=T=1.5\Delta_{s}.$ (f) The general Majorana phase (light purple region) deviates from the phase diagram determined by the low-energy theory (red dashed line) in $\mu_{w}-h_{w}$ space with the correction factor $Z_{0}=0.2$ and $h_{s}=0.1h_{w}$.