{
  "id": "1901.09399",
  "version": "v1",
  "published": "2019-01-27T16:19:52.000Z",
  "updated": "2019-01-27T16:19:52.000Z",
  "title": "Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices",
  "authors": [
    "Hui Jiang",
    "Li-Jun Lang",
    "Chao Yang",
    "Shi-Liang Zhu",
    "Shu Chen"
  ],
  "comment": "9 pages, 5 figures, comments are welcome",
  "categories": [
    "cond-mat.mes-hall",
    "physics.optics",
    "quant-ph"
  ],
  "abstract": "Non-Hermiticity from non-reciprocal hoppings has been shown recently to demonstrate the non-Hermitian skin effect (NHSE) under open boundary conditions (OBCs). Here we study the interplay of this effect and the Anderson localization in a \\textit{non-reciprocal} quasiperiodic lattice, dubbed non-reciprocal Aubry-Andr\\'{e} model, and a \\textit{rescaled} transition point is exactly proved. The non-reciprocity can induce not only the NHSE, but also the asymmetry in localized states with two Lyapunov exponents for both sides. Meanwhile, this transition is also topological, characterized by a winding number associated with the complex eigenenergies under periodic boundary conditions (PBCs), establishing a \\textit{bulk-bulk} correspondence. This interplay can be realized by an elaborately designed electronic circuit with only linear passive RLC devices instead of elusive non-reciprocal ones, where the transport of a continuous wave undergoes a transition between insulating and amplifying. This initiative scheme can be immediately applied in experiments to other non-reciprocal models, and will definitely inspires the study of interplay of NHSEs and more other quantum/topological phenomena.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-27T16:19:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-hermitian skin effect",
      "non-reciprocal quasiperiodic lattices",
      "anderson localization",
      "open boundary conditions",
      "transition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}