Majorana orthogonal transformation and Majorana zero modes in free fermionic systems

Abstract

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 $p_x+i{p}_y$ 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 $p_x+i{p}_y$ 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.

19 pages, 5 figures

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Cited by in corpus (11)

• Topological Solitons in Su-Schrieffer-Heeger Chain with periodic hopping modulation, domain walls and disorder
• Softening of Majorana edge states by long-range couplings
• Exact weak bosonic zero modes in a spin/fermion chain
• Edge state behavior in a Su-Schrieffer-Heeger like model with periodically modulated hopping
• Superconducting triangular islands as a platform for manipulating Majorana zero modes
• Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• Dynamical simulation of the injection of vortices into a Majorana edge mode
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Many-body wave function and edge magnetization of an open $p+is$ superconducting chain
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward