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.

arXiv commentComments are welcome

References in corpus (80)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Anderson Transitions
• Many-body localization, thermalization, and entanglement
• Anderson localization of a non-interacting Bose-Einstein condensate
• Topological superconductors: a review
• Colloquium: Topological Band Theory
• The many-body localization phase transition
• Topological States and Adiabatic Pumping in Quasicrystals
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• 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
• Theory of the topological Anderson insulator
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Ballistic Majorana nanowire devices
• Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
• Distinguishing a Majorana zero mode using spin resolved measurements
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Majorana edge states in interacting one-dimensional systems
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• High-resolution studies of the Majorana atomic chain platform
• One-dimensional quasicrystals with power-law hopping
• Exponential localization in one-dimensional quasiperiodic optical lattices
• Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
• Experimental Observation of Higher-Order Topological Anderson Insulators
• Weak-Pairing Higher Order Topological Superconductors
• Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Matter-wave diffraction from a quasicrystalline optical lattice
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• 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
• Exploring a proximity-coupled Co chain on Pb(110) as a possible Majorana platform
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
• Engineering a flux-dependent mobility edge in disordered zigzag chains
• Bose-Einstein Condensates in Optical Quasicrystal Lattices
• Anomalous mobility edges in one-dimensional quasiperiodic models
• Quantum criticality of quasi one-dimensional topological Anderson insulators
• Observation of topological edge modes in a quasi-periodic acoustic waveguide
• Experimental Demonstration of Dynamic Topological Pumping Across Incommensurate Bilayered Acoustic Metamaterials
• Flatband Engineering of Mobility Edges
• Realization and detection of non-ergodic critical phases in optical Raman lattice
• Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Emergence of multiple localization transitions in a one-dimensional quasiperiodic lattice
• Hidden dualities in 1D quasiperiodic lattice models
• Local and nonlocal order parameters in the Kitaev chain
• Critical properties of the many-particle (interacting) Aubry-André model ground-state localization-delocalization transition
• Non-power-law universality in one-dimensional quasicrystals
• Generalized Aubry-André-Harper model with modulated hopping and $p$-wave pairing
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• Disorder-induced Majorana zero modes in a dimerized Kitaev superconductor chain
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• 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