Majorana orthogonal transformation and Majorana zero modes in free fermionic systems

We study free fermionic models that host Majorana zero modes using the Majorana orthogonal transformation, which is a type of transformation between different fermionic models under Majorana representation of complex fermions. Using Majorana orthogonal transformation, a U(1) topological gauge theory for the doubled p(x) + ip(y) topological superconductor is obtained; the vortex Majorana zero modes and the degeneracy splitting of multiple vortices are studied using field theoretical method. For lattice Majorana hopping models, we perform real-space analysis on the Majorana zero modes. In one dimension, the decoupled Su-Schrieffer-Heeger model and the Kitaev chain are discussed as examples and building blocks for composite models. In two dimensions a simple lattice model realizing the p(x) + ip(y) superconductor is introduced, and its defect Majorana zero mode is written down explicitly. We introduce a systematic way to obtain models hosting Majorana zero modes in which composite models are constructed from two independent Majorana hopping models by Majorana orthogonal transformations. Three one-dimensional models are proposed and discussed as examples. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The study focuses on free fermionic models with Majorana zero modes using the Majorana orthogonal transformation, exploring the vortex Majorana zero modes and degeneracy splitting of multiple vortices in topological superconductors, and analyzing Majorana zero modes in lattice models. Various one-dimensional and two-dimensional models are discussed as examples and building blocks for composite models, demonstrating the systematic construction of models hosting Majorana zero modes through Majorana orthogonal transformations.