Generalized Aubry-André-Harper model with p-wave superconducting pairing

Abstract

We investigate a generalized Aubry-André-Harper (AAH) model with p-wave superconducting pairing. Both the hopping amplitudes between the nearest neighboring lattice sites and the on-site potentials in this system are modulated by a cosine function with a periodicity of $1/\alpha$. In the incommensurate case [$\alpha =(\sqrt{5}-1)/2$], due to the modulations on the hopping amplitudes, the critical region of this quasiperiodic system is significantly reduced and the system becomes more easily to be turned from extended states to localized states. In the commensurate case ($\alpha =1/2$), we find that this model shows three different phases when we tune the system parameters: Su-Schrieffer-Heeger (SSH)-like trivial, SSH-like topological, and Kitaev-like topological phases. The phase diagrams and the topological quantum numbers for these phases are presented in this work. This generalized AAH model combined with superconducting pairing provides us with a useful testfield for studying the phase transitions from extended states to Anderson localized states and the transitions between different topological phases.

9 pages, 5 figures

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• Quantum computation via Floquet topological edge modes
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• Disorder-induced Majorana zero modes in a dimerized Kitaev superconductor chain
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• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Dynamics of a quantum phase transition in the Aubry-André-Harper model with $p$-wave superconductivity
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Line nodes and surface Majorana flat bands in static and kicked p-wave superconducting Harper model
• Analytical solution of open crystalline linear 1D tight-binding models
• Simulating Z_2 topological insulators via a one-dimensional cavity optomechanical cells array
• Generalized Su-Schrieffer-Heeger model in one dimensional optomechanical arrays
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• Adatom engineering magnetic order in superconductors: Applications to altermagnetic superconductivity
• Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model
• String and conventional order parameters in the solvable modulated quantum chain
• Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain
• Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing
• Detecting topological phases via survival probabilities of edge Majorana fermions
• Quench dynamics in the Aubry-André-Harper model with \textit{p}-wave superconductivity
• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Unraveling Multifractality and Mobility Edges in Quasiperiodic Aubry-André-Harper Chains through High-Harmonic Generation
• Polynomial description of inhomogeneous topological superconducting wires
• Quasiperiodicity-induced enhancement of superconductivity in one-dimensional critical systems
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Distinct reentrant transitions in a quasi-periodic Raman lattice
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• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation