2020/10/31 by Joana Fraxanet, Utso Bhattacharya, Tobias Grass +3 · 38 citations
Materials Science · Physics and Astronomy · #Advanced Condensed Matter Physics #Chain (unit) #Invariant (physics) #MAJORANA #Organic and Molecular Conductors Research #Pairing #Topological Materials and Phenomena #Topological entropy in physics #Topology (electrical circuits) #Winding number #Zero mode #Zero-point energy #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevresearch.3.013148
published in Physical Review Research 3(1) (American Physical Society) · 17 pages, 12 figures, comments are welcome
openalex created_date 2020/10/22 · openalex publication_date 2021/02/15 · arxiv created 2021/02/26 · arxiv updated 2021/03/01 · openalex updated_date 2026/08/05
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-Andr-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 intimate 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-Andr-Harper potential also leads to other energy gaps at nonzero 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 of 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.