Majorana zero energy modes in silicene

TL;DR

This paper demonstrates the existence of Majorana zero energy modes in silicene under specific magnetic and electric fields, revealing complex interference patterns and robustness properties relevant for quantum information applications.

Contribution

It identifies new Majorana modes in silicene influenced by magnetic and electric fields, and analyzes their coherence and interference properties.

Findings

Majorana modes are found in silicene with specific field configurations.

Wave functions exhibit interference patterns finer than Planck's constant.

Majorana modes show different robustness and coherence behaviors under various interactions.

Abstract

Zero energy modes are shown to exist in silicene under suitably chosen magnetic as well as electric fields. Two Majorana modes are found on the application of opposite local magnetization on the silicene sub-lattices. We identify a non-Majorana zero energy mode carrying pure spin current under the influence of inhomogeneous gate electric field. In both cases, wave functions reveal subtle interference pattern in phase space, showing structures finer than the Planck constant $\hbar$. A spin system coupled through spin-spin ($\sigma_{z}\otimes\sigma_{z}$) interaction with the Majorana modes exhibits periodic revival of coherence with a minimum period $\sim $1/n. The same system shows decoherence-free evolution in the case of gate electric field. Under a momentum dependent interaction, one Majorana mode having a bound state in the continuum character is found to be more robust as compared to the other. The mode arising on application of electric field shows rapid loss of coherence for such an interaction.