Emergent Geometry of Inhomogeneous Planar Crystals

Uniform triangular crystals are the ground state for particles that interact isotropically in two dimensions. However, when immersed in an external potential, for example, one arising from an electric field, a flow field, or gravity, the resulting phases are significantly distorted in a way reminisc...

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Bibliographic Details
Published inPhysical review. X Vol. 8; no. 1; p. 011039
Main Authors Soni, Vishal, Gómez, Leopoldo R., Irvine, William T. M.
Format Journal Article
LanguageEnglish
Published College Park American Physical Society 08.03.2018
Subjects
Charged particles
Conformal mapping
Coordinates
Crystal defects
Crystal lattices
Dusty plasmas
Electric fields
Forecasting
Geometry
Ground state
Material properties
Molecular dynamics
Plasmas (physics)
Quantum dots
Self-assembly
Simulation
Tiles
Topology
Unit cell
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Summary:Uniform triangular crystals are the ground state for particles that interact isotropically in two dimensions. However, when immersed in an external potential, for example, one arising from an electric field, a flow field, or gravity, the resulting phases are significantly distorted in a way reminiscent of conformal transformations of planar lattices. We study these “conformal crystals” using colloidal experiments and molecular dynamics simulations. By establishing a projection from these self-assembled inhomogeneous crystals to homogeneous crystals on curved surfaces, we are able to both predict the distribution of defects and establish that defects are an almost inevitable part of the ground state. We determine how the inherent geometry emerges from an interplay between the confining potential and the interparticle interactions. Using molecular dynamics simulations, we demonstrate the generic behavior of this emergent geometry and the resulting defect structures throughout a variety of physical systems.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.8.011039