Pith Number

pith:5AYW55EN

pith:2026:5AYW55ENWIECJGPRE772H26NV6

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Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential

Kyoung-Min Kim, Sanghoon Lee

Aligning a periodic potential at an angle to a square lattice produces a Hofstadter butterfly whose fractal spectrum contains mobility edges separating extended and localized states.

arxiv:2604.12472 v2 · 2026-04-14 · cond-mat.dis-nn

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Claims

C1strongest claim

we demonstrate their convergence within a tilt-induced quasiperiodic potential on a square lattice, giving rise to a ``mobility-edge-embedded Hofstadter butterfly'' (MEE-HB). This potential is generated by aligning a periodic potential at an angle relative to the lattice axes--a configuration readily accessible in optical lattice experiments. Using a tight-binding model, we show that the MEE-HB manifests as a fractal energy splitting pattern hosting MEs that separate extended and localized states.

C2weakest assumption

The tight-binding model and derived Harper-like equation accurately capture the physics without higher-order effects or lattice imperfections dominating, and that the effective long-range hopping is the sole origin of the mobility edges.

C3one line summary

Tilt-induced quasiperiodic potentials on square lattices generate a mobility-edge-embedded Hofstadter butterfly with fractal dimension 0.8-1.0, combining fractal spectra from 1D-like behavior with mobility edges from effective long-range hopping.

Receipt and verification

First computed	2026-05-20T00:04:31.472739Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8316ef48db2082499f127ffa3ebcdafabe1b3c6d4cc6b90055cc31e58c279de

Aliases

arxiv: 2604.12472 · arxiv_version: 2604.12472v2 · doi: 10.48550/arxiv.2604.12472 · pith_short_12: 5AYW55ENWIEC · pith_short_16: 5AYW55ENWIECJGPR · pith_short_8: 5AYW55EN

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5AYW55ENWIECJGPRE772H26NV6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e8316ef48db2082499f127ffa3ebcdafabe1b3c6d4cc6b90055cc31e58c279de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "031e5ae6ddfde34cd580f9afd4e18afc40683eb66e857347579942c82fecd43b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.dis-nn",
    "submitted_at": "2026-04-14T08:58:16Z",
    "title_canon_sha256": "54cfccf25b9825abf281868cfc9a11106ee5aae1b23935b8a2967e8e0d6bd988"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.12472",
    "kind": "arxiv",
    "version": 2
  }
}