Disorder Protected and Induced Local Zero-Modes in Longer-Range Kitaev Chains

Abstract

We study the effects of disorder on a Kitaev chain with longer-range hopping and pairing terms which is capable of forming local zero energy excitations and, hence, serves as a minimal model for localization-protected edge qubits. The clean phase diagram hosts regions with 0, 1, and 2 Majorana zero-modes (MZMs) per edge. Using a semi-analytic approach corroborated by numerical calculations of the entanglement degeneracy, we show how phase boundaries evolve under the influence of disorder. While in general the 2 MZM region is stable with respect to moderate disorder, stronger values drive transition towards the topologically trivial phase. We uncover regions where the addition of disorder induces local zero-modes absent for the corresponding clean system. Interestingly, we discover that disorder destroys any direct transition between phases with zero and two MZMs by creating a tricritical point at the 2-0 MZM boundary of the clean system. Finally, motivated by recent experiments, we calculate the characteristic signatures of the disorder phase diagram as measured in dynamical local and non-local qubit correlation functions. Our work provides a minimal starting point to investigate the coherence properties of local qubits in the presence of disorder.

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• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Structural disorder-induced topological phase transitions in quasicrystals
• Entanglement and Disordered-Enhanced Topological Phase in the Kitaev Chain
• Effect of impurities and disorder on the braiding dynamics of Majorana zero modes
• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Aharonov-Bohm interference as a probe of Majorana fermions
• Quantum information spreading in random spin chains with topological order
• Phase diagram of the disordered Kitaev chain with long range pairing connected to external baths
• Topological phases in the presence of disorder and longer-range couplings
• Genuine topological Anderson insulator from impurity induced chirality reversal
• Recent progress on disorder-induced topological phases
• Charge current and phase diagram of the disordered open longer-range Kitaev chain
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal