Details
| Originalsprache | Englisch |
|---|---|
| Fachzeitschrift | Annalen der Physik |
| Publikationsstatus | Elektronisch veröffentlicht (E-Pub) - 10 März 2025 |
Abstract
Random defects do not constitute the unique source of electron localization in two dimensions. Lattice quasidisorder generated from two inplane superimposed rotated, main and secondary, square lattices, namely monolayers where moiré patterns are formed, leads to a sharp localized to delocalized single-particle transition. This is demonstrated here for both, discrete and continuum models of moiré patterns that arise as the twisting angle (Formula presented.) between the main and the secondary lattices is varied in the interval (Formula presented.). Localized to delocalized transition is recognized as the moiré patterns depart from being perfect square crystals to non-crystalline structures. Extended single-particle states are found for rotation angles associated with Pythagorean triples that produce perfectly periodic structures. Conversely, angles not arising from such Pythagorean triples lead to non-commensurate or quasidisordered structures, thus originating localized states. These conclusions are drawn from a stationary analysis where the standard inverse participation ratio (IPR) parameter measuring localization allowed to detect the transition. While both, ground state and excited states are analyzed for the discrete model, where the secondary lattice is considered as a perturbation of the main one, the sharp transition is tracked back for the fundamental state in the continuous scenario where the secondary lattice is not a perturbation any more.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
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in: Annalen der Physik, 10.03.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Localized and Extended Phases in Square Moiré Patterns
AU - Madroñero, C.
AU - Domínguez‐Castro, G. A.
AU - Paredes, R.
PY - 2025/3/10
Y1 - 2025/3/10
N2 - Random defects do not constitute the unique source of electron localization in two dimensions. Lattice quasidisorder generated from two inplane superimposed rotated, main and secondary, square lattices, namely monolayers where moiré patterns are formed, leads to a sharp localized to delocalized single-particle transition. This is demonstrated here for both, discrete and continuum models of moiré patterns that arise as the twisting angle (Formula presented.) between the main and the secondary lattices is varied in the interval (Formula presented.). Localized to delocalized transition is recognized as the moiré patterns depart from being perfect square crystals to non-crystalline structures. Extended single-particle states are found for rotation angles associated with Pythagorean triples that produce perfectly periodic structures. Conversely, angles not arising from such Pythagorean triples lead to non-commensurate or quasidisordered structures, thus originating localized states. These conclusions are drawn from a stationary analysis where the standard inverse participation ratio (IPR) parameter measuring localization allowed to detect the transition. While both, ground state and excited states are analyzed for the discrete model, where the secondary lattice is considered as a perturbation of the main one, the sharp transition is tracked back for the fundamental state in the continuous scenario where the secondary lattice is not a perturbation any more.
AB - Random defects do not constitute the unique source of electron localization in two dimensions. Lattice quasidisorder generated from two inplane superimposed rotated, main and secondary, square lattices, namely monolayers where moiré patterns are formed, leads to a sharp localized to delocalized single-particle transition. This is demonstrated here for both, discrete and continuum models of moiré patterns that arise as the twisting angle (Formula presented.) between the main and the secondary lattices is varied in the interval (Formula presented.). Localized to delocalized transition is recognized as the moiré patterns depart from being perfect square crystals to non-crystalline structures. Extended single-particle states are found for rotation angles associated with Pythagorean triples that produce perfectly periodic structures. Conversely, angles not arising from such Pythagorean triples lead to non-commensurate or quasidisordered structures, thus originating localized states. These conclusions are drawn from a stationary analysis where the standard inverse participation ratio (IPR) parameter measuring localization allowed to detect the transition. While both, ground state and excited states are analyzed for the discrete model, where the secondary lattice is considered as a perturbation of the main one, the sharp transition is tracked back for the fundamental state in the continuous scenario where the secondary lattice is not a perturbation any more.
KW - bilayer moiré lattice
KW - disorder in 2D lattices
KW - localized and extended states
KW - pythagorean angles
UR - http://www.scopus.com/inward/record.url?scp=105000236687&partnerID=8YFLogxK
U2 - 10.1002/andp.202400309
DO - 10.1002/andp.202400309
M3 - Article
JO - Annalen der Physik
JF - Annalen der Physik
SN - 0003-3804
ER -