{
  "id": "2202.08610",
  "version": "v1",
  "published": "2022-02-17T11:48:19.000Z",
  "updated": "2022-02-17T11:48:19.000Z",
  "title": "Understanding the three-dimensional quantum Hall effect in generic multi-Weyl semimetals",
  "authors": [
    "Feng Xiong",
    "Carsten Honerkamp",
    "Dante M. Kennes",
    "Tanay Nag"
  ],
  "comment": "17 pages and 9 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "The quantum Hall effect in three-dimensional Weyl semimetal (WSM) receives significant attention for the emergence of the Fermi loop where the underlying two-dimensional Hall conductivity, namely, sheet Hall conductivity, shows quantized plateaus. Considering the tilted lattice models for multi Weyl semimetals (mWSMs), we systematically study the Landau levels (LLs) and magneto-Hall conductivity in the presence of parallel and perpendicular (with respect to the Weyl node's separation) magnetic field, i.e., $\\mathbf{ B}\\parallel z$ and $\\mathbf{B}\\parallel x$, to explore the impact of tilting and non-linearity in the dispersion. We make use of two (single) node low-energy models to qualitatively explain the emergence of mid-gap chiral (linear crossing of chiral) LLs on the lattice for $\\mathbf{ B}\\parallel z$ ($\\mathbf{ B}\\parallel x$). Remarkably, we find that the sheet Hall conductivity becomes quantized for $\\mathbf{ B}\\parallel z$ even when two Weyl nodes project onto a single Fermi point in two opposite surfaces, forming a Fermi loop with $k_z$ as the good quantum number. On the other hand, the Fermi loop, connecting two distinct Fermi points in two opposite surfaces, with $k_x$ being the good quantum number, causes the quantization in sheet Hall conductivity for $\\mathbf{ B}\\parallel x$. The quantization is almost lost (perfectly remained) in the type-II phase for $\\mathbf{ B}\\parallel x$ ($\\mathbf{ B}\\parallel z$). Interestingly, the jump profiles between the adjacent quantized plateaus change with the topological charge for both of the above cases. The momentum-integrated three-dimensional Hall conductivity is not quantized; however, it bears the signature of chiral LLs as resulting in the linear dependence on $\\mu$ for small $\\mu$. The linear zone (its slope) reduces (increases) as the tilt (topological charge) of the underlying WSM increases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-17T11:48:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "three-dimensional quantum hall effect",
      "generic multi-weyl semimetals",
      "sheet hall conductivity",
      "fermi loop",
      "weyl nodes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}