One-Dimensional Quasicrystals from Incommensurate Charge Order

Area of Science:

• Condensed Matter Physics
• Materials Science
• Crystallography

Background:

• Quasicrystals are ordered structures that lack translational periodicity.
• Only two natural quasicrystals are known, while artificial ones are routinely manufactured.
• Understanding the formation of quasicrystals in natural systems remains a challenge.

Purpose of the Study:

• To present a theoretical framework for a new class of one-dimensional quasicrystals.
• To explore systems with potential for both artificial and natural realization.
• To identify material properties conducive to the formation of one-dimensional quasicrystalline ground states.

Main Methods:

• Theoretical modeling of incommensurately charge-ordered materials.
• Analysis of free-energy contributions in reciprocal space.
• Construction of a theoretical phase diagram.

Main Results:

• Identification of a system where the lowest energy state is a one-dimensional quasicrystal.
• Demonstration that nonlocal correlations drive the quasicrystalline state.
• Prediction of material properties enabling the formation of these quasicrystals.

Conclusions:

• A potentially wide class of one-dimensional quasicrystals can be realized in real materials.
• These findings bridge the gap between artificial and naturally occurring quasicrystals.
• The proposed mechanism offers new avenues for quasicrystal research and discovery.