Robustness of Majorana edge states of short-length Kitaev chains coupled with environment

Abstract

Recently, the two-site Kitaev model hosting Majorana edge states was experimentally realized based on double quantum dots. In this context, we construct two-band effective models describing Majorana edge states of a finite-length Kitaev chain by using the isospectral matrix reduction method. We analytically estimate the robustness of Majorana edge states as a function of model parameters. We also study effects of coupling to an environment based on non-Hermitian Hamiltonians derived from the Lindblad equation. We study three types of dissipation, a local one, an adjacent one and a global one. It is found that the Majorana zero-energy edge states acquire nonzero energy such as $E\propto \pm {\left(i\gamma \right)}^L$ for the local dissipation, where $\gamma$ is the magnitude of the dissipation and $L$ is the length of the chain. On the other hand, the Majorana zero-energy edge states acquire nonzero energy such as $E\propto \pm i\gamma$ irrespective of the length $L$ for the global dissipation. Hence, the Majorana edge states are robust against the local dissipation but not against the global one. Our results will be useful for future studies on Majorana edge states based on quantum dots.

arXiv comment7 pages, 5 pages

References in corpus (37)

• Topological insulators and superconductors
• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Unpaired Majorana fermions in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Topological superconductors: a review
• Symmetry and Topology in Non-Hermitian Physics
• Fermionic quantum computation
• Topology by Dissipation in Atomic Quantum Wires
• Realization of a minimal Kitaev chain in coupled quantum dots
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Parity-time-symmetric topological superconductor
• Dissipative spin chain as a non-Hermitian Kitaev ladder
• Tunable superconducting coupling of quantum dots via Andreev bound states in semiconductor-superconductor nanowires
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Roadmap towards Majorana qubits and nonabelian physics in quantum dot-based minimal Kitaev chains
• Majorana Edge Modes with Gain and Loss
• Majorana braiding with thermal noise
• Exact eigenvectors and eigenvalues of the finite Kitaev chain and its topological properties
• Crossed Andreev reflection and elastic co-tunneling in a three-site Kitaev chain nanowire device
• Quench dynamics and parity blocking in Majorana wires
• Probing Majorana localization in minimal Kitaev chains through a quantum dot
• Fusion protocol for Majorana modes in coupled quantum dots
• Non-Hermitian Majorana modes protect degenerate steady states
• Majoranas in Noisy Kitaev Wires
• Minimal Kitaev-transmon qubit based on double quantum dots
• Minimal quantum dot based Kitaev chain with only local superconducting proximity effect
• Monte Carlo studies of the properties of the Majorana quantum error correction code: is self-correction possible during braiding?
• Adversarial Hamiltonian learning of quantum dots in a minimal Kitaev chain
• Time-dependent Correlation Functions in Open Quadratic Fermionic Systems
• Chiral zero modes in superconducting nanowires with Dresselhaus spin-orbit coupling
• Emergent non-Hermitian models
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Kitaev chain with a quantum dot
• Majorana excitons in a Kitaev chain of semiconductor quantum dots in a nanowire

Cited by in corpus (12)

• Observation of edge and bulk states in a three-site Kitaev chain
• Non-Hermitian multiterminal phase-biased Josephson junctions
• Fate of poor man's Majoranas in the long Kitaev chain limit
• Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length
• Non-Hermitian minimal Kitaev chains
• Scaling up a sign-ordered Kitaev chain without magnetic flux control
• Majorana zero-modes in a dissipative Rashba nanowire
• Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• AI-enhanced tuning of quantum dot Hamiltonians toward Majorana modes
• Quantum capacitance and parity switching of a quantum-dot-based Kitaev chain