{
  "id": "2409.11514",
  "version": "v1",
  "published": "2024-09-17T19:38:23.000Z",
  "updated": "2024-09-17T19:38:23.000Z",
  "title": "Perturbation theory for dispersion relations of spacetime-periodic materials",
  "authors": [
    "Erik Orvehed Hiltunen"
  ],
  "comment": "6 pages, 3 figures",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We consider Bloch states of weak spacetime-periodic perturbations of homogeneous materials in one spatial dimension. The interplay of space- and time-periodicity leads to an infinitely degenerate dispersion relation in the free case. We consider a general perturbation term, and, as a consequence of the infinite degeneracy, we show that the effective equations are given by the eigenvalue problem of an infinite matrix. Our method can be viewed as a time-modulated generalisation of the nearly-free electron model. Based on this result, we find that the infinite degeneracy may split into a family of non-degenerate bands. Our results are illustrated with numerical calculations, and we observe close agreement between the perturbation theory and the numerically computed full solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-17T19:38:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perturbation theory",
      "spacetime-periodic materials",
      "infinite degeneracy",
      "weak spacetime-periodic perturbations",
      "nearly-free electron model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}