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.

arXiv comment19 pages, 5 figures

References in corpus (57)

• Topological Insulators
• Topological insulators and superconductors
• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Helical liquids and Majorana bound states in quantum wires
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Periodic table for topological insulators and superconductors
• Search for Majorana fermions in superconductors
• Majorana fermions in a tunable semiconductor device
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Majorana Zero Modes and Topological Quantum Computation
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Topological phases of fermions in one dimension
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Majorana fermions in chains of magnetic atoms on a superconductor
• The effects of interactions on the topological classification of free fermion systems
• Topological superconducting phase in helical Shiba chains
• Chiral Majorana edge state in a quantum anomalous Hall insulator-superconductor structure
• Fermion zero modes on vortices in chiral superconductors
• Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
• Superconductors are topologically ordered
• Random-matrix theory of Majorana fermions and topological superconductors
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Stability of half-quantum vorticies in p_x+ip_y superconductors
• Zero modes of two-dimensional chiral p-wave superconductors
• An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors
• Topological order in the Kitaev/Majorana chain in the presence of disorder and interactions
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Surface states and chiral symmetry on the lattice
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Topological phases, edge modes, and the Hofstadter butterfly in coupled Su-Schrieffer-Heeger systems
• Multihole edge states in Su-Schrieffer-Heeger chains with interactions
• Topological Majorana and Dirac zero modes in superconducting vortex cores
• Splitting and oscillation of Majorana zero modes in the p-wave BCS-BEC evolution with plural vortices
• Robustness of Majorana edge modes and topological order -- exact results for the symmetric interacting Kitaev chain with disorder
• Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models
• Equivalence of Topological Insulators and Superconductors
• Engineering Topological Models with a General-Purpose Symmetry-to-Hamiltonian Approach

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• 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