{
  "id": "2111.01178",
  "version": "v2",
  "published": "2021-11-01T18:11:43.000Z",
  "updated": "2022-04-23T17:40:42.000Z",
  "title": "Quality factor for zero-bias conductance peaks in Majorana nanowire",
  "authors": [
    "Yi-Hua Lai",
    "Sankar Das Sarma",
    "Jay D. Sau"
  ],
  "comment": "19 pages, 8 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.supr-con"
  ],
  "abstract": "Despite recent experimental progress towards observing large zero-bias conductance peaks (ZBCP) as signatures of Majorana modes, confusion remains about whether Majorana modes have been observed. This is in part due to the theoretical prediction of fine-tuned trivial zero-bias peaks that occur because of uncontrolled quantum dots or disorder potentials. While many aspects of the topological phase can be somewhat fine-tuned because the topological phase space is often small, the quantized height of ZBCPs associated with a Majorana mode is known to be robust at sufficiently low temperatures even as the tunnel barrier is pinched off to vanishingly small normal-state conductance. In this work, we study whether this counter-intuitive robustness of the ZBCP height can be used to distinguish Majorana modes from non-topological ZBCPs. To this end, we introduce a dimensionless quality factor $F$ to quantify the robustness of the ZBCP height based on the range of normal-state conductance over which the ZBCP height remains within a pre-specified range of quantization. By computing this quality factor $F$ together with the topological characteristics for a wide range of models and parameters, we find that Majoranas are significantly more robust compared with non-topological ZBCPs in the ideal low-temperature limit. Even at a temperature as high as the experimentally used 20 mK, we find that we can set a threshold value of $F\\sim 2$ so that ZBCPs associated with a quality factor $F>2$ are likely topological and $F\\ll 2$ are topologically trivial. More precisely, the value of $F$ is operationally related to the degree of separation of the Majorana modes in the system although $F$ uses only the experimentally measured tunnel conductance properties. Finally, we discuss how the quality factor $F$ measured in a transport setup can help estimate the quality of topological qubits made from Majorana modes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-23T17:40:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quality factor",
      "majorana mode",
      "majorana nanowire",
      "large zero-bias conductance peaks",
      "measured tunnel conductance properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}