{
  "abstract": "Transition-metal trichalcogenides MX$_3$ are quasi-one-dimensional van der Waals materials whose layers form through lateral chain binding, giving them an interlayer cleavage plane and in-plane electronic anisotropy. Among them, ZrSe$_3$ is stable under ambient conditions and semiconducting. Exfoliated crystals expose four crystallographic planes, and electrocatalytic measurements on an individual crystal assigned the hydrogen evolution activity to the high-energy (210) facet rather than to the basal plane. Those non-basal surfaces remain uncharacterized, since the available calculations treat either the bulk crystal or the free-standing basal monolayer. Here, we compute the surface energies and the equilibrium morphology of these four surfaces with a dispersion-corrected semilocal functional, and their band-edge alignment with the HSE06 hybrid functional including spin-orbit coupling. The surface energies span nearly an order of magnitude, from \\SI{0.097}{\\joule\\per\\meter\\squared} for (001) to \\SI{0.869}{\\joule\\per\\meter\\squared} for (010), and the Wulff shape exposes the four observed planes with area fractions of \\SI{17.1}{\\percent}, \\SI{4.4}{\\percent}, \\SI{71.4}{\\percent}, and \\SI{7.0}{\\percent}. The ionization potential varies by \\SI{0.45}{\\electronvolt} between facets and the electron affinity by \\SI{0.80}{\\electronvolt}, the gap of (210) falls from 1.43 to \\SI{0.94}{\\electronvolt} between 10 and \\SI{23}{\\angstrom}, and (010) remains metallic. The facets separate according to whether the cut preserves or distorts the Se-Se dimer, and the distorted dimers concentrate the frontier states. Because the same dimer governs the bulk electronic structure of the MX$_3$ family, the criterion transfers to the related trichalcogenides.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36150",
  "author_total": 7,
  "authors": [
    {
      "name": "Sandro G Holanda"
    },
    {
      "name": "Bruno Ipaves"
    },
    {
      "name": "Astrid Campos-Mata"
    },
    {
      "name": "Shreyasi Chattopadhyay"
    },
    {
      "name": "Pulickel M Ajayan"
    },
    {
      "name": "Douglas S Galvao"
    },
    {
      "name": "Marcelo L Pereira Junior"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9eya75ne6x02h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36150",
  "fulltext_url": null,
  "id": "9eya75ne6x02h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36150",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "openalex",
      "2505|2D Materials and Applications"
    ]
  ],
  "openalex": "W7214893992",
  "pdf_url": "https://arxiv.org/pdf/2609.36150",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9eya75ne6x02h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36150",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36150"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Facet- and thickness-dependent band-edge alignment at ZrSe\\texorpdfstring{$_3$}{3} surfaces: hybrid-functional calculations with spin-orbit coupling",
  "title_text": "Facet- and thickness-dependent band-edge alignment at ZrSe\\texorpdfstring{_3}{3} surfaces: hybrid-functional calculations with spin-orbit coupling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/9eya75ne6x02h",
  "venue": "arXiv",
  "versions": []
}