Quasicrystals are Functionally Graded Materials
Abstract
Quasicrystals exhibit long-range order without translational periodicity, posing challenges to compute their electronic properties. Here we show that a quasicrystal can be represented exactly as a periodic approximant with a spatially graded phason, establishing a connection to functionally graded materials. Building on this connection, we develop a controlled quantum theory of quasicrystals. We derive a state-dependent control parameter governed by the quantum metric of local Bloch states, determining when finite approximations are reliable. We further construct a Hamiltonian that correctly predicts Bragg gap positions, quasimomentum equivalence, and quasiperiodic eigenstates to all orders in phason strain within a finite Fourier window. We verify the theory numerically and propose a diffraction-based experimental test of the gap shift induced by phason strain. Our framework opens a route to predicting the electronic structure and functional properties of quasicrystals using methods developed for functionally graded materials.
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BibTeX
@misc{landry2026quasicrystals,
title = {{Quasicrystals are Functionally Graded Materials}},
author = {Michael J. Landry and Dominic Bollettieri and Akhil Sadam and Denisse Córdova Carrizales and Mingda Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05478},
eprint = {2611.05478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05478},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasicrystals are Functionally Graded Materials
AU - Michael J. Landry
AU - Dominic Bollettieri
AU - Akhil Sadam
AU - Denisse Córdova Carrizales
AU - Mingda Li
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05478
UR - https://arxiv.org/abs/2611.05478
AB - Quasicrystals exhibit long-range order without translational periodicity, posing challenges to compute their electronic properties. Here we show that a quasicrystal can be represented exactly as a periodic approximant with a spatially graded phason, establishing a connection to functionally graded materials. Building on this connection, we develop a controlled quantum theory of quasicrystals. We derive a state-dependent control parameter governed by the quantum metric of local Bloch states, determining when finite approximations are reliable. We further construct a Hamiltonian that correctly predicts Bragg gap positions, quasimomentum equivalence, and quasiperiodic eigenstates to all orders in phason strain within a finite Fourier window. We verify the theory numerically and propose a diffraction-based experimental test of the gap shift induced by phason strain. Our framework opens a route to predicting the electronic structure and functional properties of quasicrystals using methods developed for functionally graded materials.
ER -