Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation

Abstract

We present a detailed study of the topological properties of the Kitaev chain with long-range pairing terms and in the presence of an Aubry-André-Harper on-site potential. Specifically, we consider algebraically decaying superconducting pairing amplitudes; the exponent of this decay is found to determine a critical pairing strength, below which the chain remains topologically trivial. Above the critical pairing, topological edge modes are observed in the central gap. For sufficiently fast decay of the pairing, these modes are identified as Majorana zero-modes. However, if the pairing term decays slowly, the modes become massive Dirac modes. Interestingly, these massive modes still exhibit a true level crossing at zero energy, which points towards an initimate relation to Majorana physics. We also observe a clear lack of bulk-boundary correspondence in the long-range system, where bulk topological invariants remain constant, while dramatic changes appear in the behavior at the edge of the system. In addition to the central gap around zero energy, the Aubry-André-Harper potential also leads to other energy gaps at non-zero energy. As for the analogous short-range model, the edge modes in these gaps can be characterized through a 2D Chern invariant. However, in contrast to the short-range model, this topological invariant does not correspond to the number of edge mode crossings anymore. This provides another example for the weakening of the bulk-boundary correspondence occurring in this model. Finally, we discuss possible realizations of the model with ultracold atoms and condensed matter systems.

17 pages, 12 figures, comments are welcome

References in corpus (30)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• A High Phase-Space-Density Gas of Polar Molecules
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Bose-Einstein condensation of chromium
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Bose-Einstein Condensation of Erbium
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Cold molecules: Progress in Quantum Engineering of Chemistry and Quantum Matter
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Non-standard Hubbard models in optical lattices: a review
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Entanglement entropy for the long range Ising chain
• Kitaev chains with long-range pairing
• Anderson localization in Bose-Einstein condensates
• Nearly-linear light cones in long-range interacting quantum systems
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Multipartite entanglement in topological quantum phases
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Generalized Aubry-André-Harper model with p-wave superconducting pairing
• Bose-Einstein condensates with attractive 1/r interaction: The case of self-trapping
• Topological superconductivity at finite temperatures in proximitized magnetic nanowires

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• Unraveling Multifractality and Mobility Edges in Quasiperiodic Aubry-André-Harper Chains through High-Harmonic Generation
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• Topological states constructed by two different trivial quantum wires
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