{
  "id": "1403.7262",
  "version": "v2",
  "published": "2014-03-28T01:06:16.000Z",
  "updated": "2014-11-03T02:56:28.000Z",
  "title": "Topological Effects in Chiral Symmetric Driven Systems",
  "authors": [
    "Derek Y. H. Ho",
    "Jiangbin Gong"
  ],
  "comment": "37 pages, 5 figures, to appear in Physical Review B",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.quant-gas",
    "quant-ph"
  ],
  "abstract": "Recent years have seen a strong interest in topological effects within periodically driven systems. In this work, we explore topological effects in two closely related 2-dimensional driven systems described by Floquet operators possessing chiral symmetry (CS). Our numerical and analytical results suggest the following. Firstly, the CS is associated with the existence of the anomalous counter-propagating (ACP) modes reported recently. Specifically, we show that a particular form of CS protects the ACP modes occurring at quasienergies of $\\pm \\pi$. We also find that these modes are only present along selected boundaries, suggesting that they are a weak topological effect. Secondly, we find that CS can give rise to protected $0$ and $\\pi$ quasienergy modes, and that the number of these modes may increase without bound as we tune up certain system parameters. Like the ACP modes, these $0$ and $\\pi$ modes also appear only along selected boundaries and thus appear to be a weak topological effect. To our knowledge, this work represents the first detailed study of weak topological effects in periodically driven systems. Our findings add to the still-growing knowledge on driven topological systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-28T01:06:16.000Z",
      "title": "Effects of Symmetry on Bulk-Edge Correspondence in Periodically Driven Systems",
      "abstract": "Topological states of matter in periodically driven systems have been attracting great theoretical and experimental interests, but more insights need to be gained to better understand the issue of bulk-edge correspondence in driven systems. To that end, this work investigates in detail how specific properties of chiral symmetry operators may lead to a big difference in the behavior of the edge states. In particular, we exploit two dynamical models, namely, a variant of the so-called kicked-rotor model in the quantum chaos literature and the kicked Harper model, both possessing fractal-like quasi-energy spectra closely resembling the Hofstadter butterfly. Despite the topological equivalence between the two dynamical systems [H. Wang, D. Y. H. Ho, W. Lawton, J. Wang and J. B. Gong, Phys. Rev. E 88, 052920 (2013)] and the fact that these two systems can be mapped onto each other, we show that different chiral symmetry properties have remarkably different consequences. In (only) one model there can exist an arbitrary number of edge modes with 0 or pi quasi-energy values accompanied by a proliferation of Dirac points, but (only) in the other model there can be counter-propagating chiral edge modes at the same boundary. Our results should be useful towards the ongoing efforts to topologically classify periodically driven systems, and should further motivate experimental studies of topological states using quantum systems under external control fields.",
      "comment": "35 pages, 5 figures, comments are welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-03T02:56:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Vf",
      "05.30.Rt",
      "05.45.-a",
      "03.75.-b"
    ],
    "keywords": [
      "bulk-edge correspondence",
      "classify periodically driven systems",
      "quasi-energy spectra closely resembling",
      "fractal-like quasi-energy spectra",
      "edge modes"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevB.90.195419",
      "journal": "Physical Review B",
      "year": 2014,
      "month": "Nov",
      "volume": 90,
      "number": 19,
      "pages": 195419
    },
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvB..90s5419H"
    }
  }
}