{
  "id": "2309.14429",
  "version": "v1",
  "published": "2023-09-25T18:00:05.000Z",
  "updated": "2023-09-25T18:00:05.000Z",
  "title": "Fractional Chern Insulators vs. Non-Magnetic States in Twisted Bilayer MoTe$_2$",
  "authors": [
    "Jiabin Yu",
    "Jonah Herzog-Arbeitman",
    "Minxuan Wang",
    "Oskar Vafek",
    "B. Andrei Bernevig",
    "Nicolas Regnault"
  ],
  "comment": "16+32 pages, 10+28 figures, 2+1 tables",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "Fractionally filled Chern bands with strong interactions may give rise to fractional Chern insulator (FCI) states, the zero-field analogue of the fractional quantum Hall effect. Recent experiments have demonstrated the existence of FCIs in twisted bilayer MoTe$_2$ without external magnetic fields -- most robust at $\\nu=-2/3$ -- as well as Chern insulators (CIs) at $\\nu=-1$. Although the appearance of both of these states is theoretically natural in an interacting topological system, experiments repeatedly observe nonmagnetic states (lacking FCIs) at $\\nu=-1/3$ and $-4/3$, a puzzling result which has not been fully theoretically explained. In this work, we perform Hartree-Fock and exact diagonalization calculations to test whether the standard MoTe$_2$ moir\\'e model with the (greatly varying) parameter values available in the literature can reproduce the non-magnetic states at $\\nu=-1/3$ and $-4/3$ in unison with the FCI at $\\nu=-2/3$ and CI state at $\\nu = -1$. We focus on the experimentally relevant twist angles and, crucially, include remote bands. We find that the parameters proposed in [Wang et al. (2023)] can nearly capture the experimental phenomena at $\\nu=-1/3,-2/3,-1,-4/3$ simultaneously, though the predicted ground states at $\\nu=-1/3$ are still mostly fully-spin-polarized and a larger dielectric constant $\\epsilon>10$ than is typical of hexagonal boron nitride (h-BN) substrate $\\epsilon\\sim 6$ is required. Our results show the importance of remote bands in identifying the competing magnetic orders and lay the groundwork for further study of the realistic phase diagram.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-25T18:00:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional chern insulator",
      "twisted bilayer mote",
      "non-magnetic states",
      "fractional quantum hall effect",
      "remote bands"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}