Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential

Abstract

We investigate localization and topological properties of a dimerized Kitaev chain with p-wave superconducting correlations and a quasiperiodically modulated chemical potential. With regard to the localization studies, we demonstrate the existence of distinct phases, such as, the extended phase, the critical (intermediate) phase, and the localized phase that arise due to the competition between the dimerization and the onsite quasiperiodic potential. Most interestingly, the critical phase comprises of two different mobility edges that are found to exist between the extended to the localized phase, and between the critical (multifractal) and localized phases. We perform our analysis employing the inverse and the normalized participation ratios, fractal dimension, and the level spacing. Subsequently, a finite-size analysis is done to provide support of our findings. Furthermore, we study the topological properties of the zero-energy edge modes via computing the real-space winding number and number of the Majorana zero modes present in the system. We specifically illustrate that our model exhibits a phase transition from a topologically trivial to a non-trivial phase (topological Anderson phase) beyond a critical dimerization strength under the influence of the quasiperiodic potential strength. Finally, in presence of a large potential, we demonstrate that the system undergoes yet another transition from the topologically non-trivial to an Anderson localized phase. Thus, we believe that our results will aid exploration of fundamentally different physics pertaining to the critical and the topological Anderson phases.

Comments are welcome

References in corpus (36)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Anderson Transitions
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Topological Anderson Insulator
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Localization and delocalization of light in photonic moire lattices
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Distinguishing a Majorana zero mode using spin resolved measurements
• Majorana edge states in interacting one-dimensional systems
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Experimental Observation of Higher-Order Topological Anderson Insulators
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains
• Reentrant Localization Transition in a Quasiperiodic Chain
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Anomalous mobility edges in one-dimensional quasiperiodic models
• Experimental Demonstration of Dynamic Topological Pumping Across Incommensurate Bilayered Acoustic Metamaterials
• Realization and detection of non-ergodic critical phases in optical Raman lattice
• Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Emergence of multiple localization transitions in a one-dimensional quasiperiodic lattice
• Hidden dualities in 1D quasiperiodic lattice models
• Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Exact solutions and topological phase diagram in interacting dimerized Kitaev topological superconductors
• Critical analysis of the re-entrant localization transition in a one-dimensional dimerized quasiperiodic lattice
• Self-consistent theory of mobility edges in quasiperiodic chains

Cited by in corpus (9)

• Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Sub-symmetry Protected Topology in Topological Insulators and Superconductors
• Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
• Density matrix renormalization group study of the interacting Kitaev chain with quasi-periodic disorder
• Multiple reentrant topological windows induced by generalized Bernoulli disorder
• Recent progress on disorder-induced topological phases
• Localization and Topology in Noncentrosymmetric Superconductors with Disorder
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance